Saying, Seeing and Acting: The Psychological Semantics of Spatial Prepositions (Essays in Cognitive Psychology)

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Author: Kenny R. Coventry | Simon C. Garrod

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Saying, Seeing, and Acting : The Psychological Semantics of Spatial Prepositions Essays in Cognitive Psychology Coventry, Kenny R.; Garrod, S. C. Taylor & Francis Routledge 9780203689851 9780203641521 English Grammar, Comparative and general--Prepositions, Semantics-Psychological aspects, Space and time in language, Psycholinguistics. 2004 P285.C68 2004eb 415 Grammar, Comparative and general--Prepositions, Semantics-Psychological aspects, Space and time in language, Psycholinguistics.

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Page i SAYING, SEEING, AND ACTING

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Page ii Essays in Cognitive Psychology UK Editors: Alan Baddeley, University of Bristol, UK Vicki Bruce, University of Stirling, UK North American Editors: Henry L. Roediger, III, Washington University in St. Louis, USA James R. Pomerantz, Rice University Essays in Cognitive Psychology is designed to meet the need for rapid publication of brief volumes in cognitive psychology. Primary topics will include perception, movement and action, attention, memory, mental representation, language, and problem solving. Furthermore, the series seeks to defne cognitive psychology in its broadest sense, encompassing all topics either informed by, or informing, the study of mental processes. As such, it covers a wide range of subjects including computational approaches to cognition, cognitive neuroscience, social cognition, and cognitive development, as well as areas more traditionally defned as cognitive psychology. Each volume in the series will make a conceptual contribution to the topic by reviewing and synthesizing the existing research literature, by advancing theory in the area, or by some combination of these missions. The principal aim is that authors will provide an overview of their own highly successful research program in an area. It is also expected that volumes will, to some extent, include an assessment of current knowledge and identifcation of possible future trends in research. Each book will be a self-contained unit supplying the advanced reader with a well-structured review of the work described and evaluated. Also available in this series: Mental Models and the Interpretation of Anaphora Alan Garnham Memory for Actions Johannes Engelkamp Anxiety and Cognition Michael W. Eysenck Rationality and Reasoning Jonathan St. B. T. Evans & David E. Over Visuo-spatial Working Memory Robert Logie Implicit and Explicit Learning in Human Performance Diane Berry & Zoltann Dienes Communicating Quantities Linda Moxey & Tony Sanford The Cognitive Neuropsychology of Schizophrenia Christopher Frith Working Memory and Severe Learning Diffculties Charles Hulme & Susie Mackenzie Deduction Phil Johnson-Laird Hypothesis-testing Behaviour Fenna Poletiek Superior Memory John Wilding & Elizabeth Valentine Superportraits Gillian Rhodes Flashbulb Memories Martin Conway Connectionist Modelling in Cognitive Neuropsychology David C. Plaut & Tim Shallice Working Memory and Language Processing Sue Gathercole & Alan Baddeley Affect, Cognition and Change John Teasdale & Philip Banyard Anxiety: The Cognitive Perspective Michael W. Eysenck Reading and the Mental Lexicon Marcus Taft Bias in Human Reasoning Jonathan St. B. T. Evans Visuo-spatial Working Memory and Individual Differences Cesare Cornoldi & Tomaso Vecchi

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Page iii Saying, Seeing, and Acting: The Psychological Semantics of Spatial Prepositions Kenny R. Coventry Centre for Thinking and Language, School of Psychology, University of Plymouth, UK Simon C. Garrod Human Communication Research Centre, Department of Psychology, University of Glasgow, UK HOVE AND NEW YORK

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Page iv First published 2004 by Psychology Press 27 Church Road, Hove, East Sussex, BN3 2FA Simultaneously published in the USA and Canada by Taylor & Francis Inc 29 West 35th Street, New York, NY 10001 Psychology Press is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2004. Copyright © 2004 Psychology Press All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Coventry, Kenny R. Saying, seeing, and acting: the psychological semantics of spatial prepositions / Kenny R. Coventry and Simon C. Garrod. p. cm.—(Essays in cognitive psychology) Includes bibliographical references and indexes. ISBN 1-84169-116-X 1. Grammar, Comparative and general—Prepositions. 2. Semantics—Psychological aspects. 3. Space and time in language. 4. Psycholinguistics. I. Garrod, S. C. (Simon C.) II. Title. III. Series. P285.C68 2003 415–dc21 2003013938 ISBN 0-203-64152-3 Master e-book ISBN ISBN 0-203-68985-2 (OEB Format) ISBN 1-84169-116-X (hbk) ISSN 0959-4779

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Page v For Kathryn and Oliver.

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Page vii Contents Preface Acknowledgements Figure acknowledgements PART I: SAYING, SEEING, AND ACTING: BACKGROUND TO THE DOMAIN 1. Introduction to the domain Spatial prepositions: classifications and boundaries Saying, seeing, and acting: précis of the argument 2. Saying: spatial prepositions and lexical semantics Spatial language, spatial relations, and minimal specification Herskovits: ideal meanings, use types, and pragmatic principles Lakoff, Brugman, and … dangerous things Embodiment, action, and spatial language Summary 3. Grounding language in perception: from “saying” to “seeing and acting” The geometry of spatial relations Perceptual approaches to spatial relations The importance of action: extra-geometric relations considered The functional geometric framework Perceptual origins of the functional geometric framework Summary and conclusions

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Page viii PART II: SAYING, SEEING, AND ACTING: EVIDENCE FOR THE FUNCTIONAL GEOMETRIC FRAMEWORK 4. Experimental evidence for the functional geometric framework 1: the so-called topological prepositions In On Summary 5. Experimental evidence for the functional geometric framework 2: which way up is up? The projective prepositions Reference frames and projective terms Geometric and dynamic-kinematic routines Conceptual knowledge and context effects Summary and conclusions 6. Experimental evidence for the functional geometric framework 3: other prepositions—proximity, coincidence, and being between Proximity terms: how near is near ? Near and far At Between Summary PART III: PUTTING, SEEING, AND ACTING TOGETHER: THE FUNCTIONAL GEOMETRIC FRAMEWORK IN ACTION 7. Putting it all together The need for situation models: the general argument The functional geometric framework in action: multiple constraints and spatial language comprehension Towards weighting constraints by preposition: delineating routines and functions by terms Summary 8. Cross-linguistic and developmental implications The prelinguistic origins of the functional geometric framework The acquisition of spatial prepositions in English Functional geometry in languages other than English Linguistic relativity and the underlying structure of spatial representations for language Summary 9. Extensions, links, and conclusions The functional geometric framework, embodiment, and situated action

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71 73 73 84 88 91 92 100 109 112 113 113 115 118 120 123 125 127 127 134 144 146 147 147 153 157 161 163 165 165

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Page ix Computational modelling and the neural correlates of spatial language comprehension and production Metaphorical uses of spatial prepositions and underlying models The functional geometric framework and other syntactic categories Conclusions References Author index Subject index

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167 172 174 176 177 191 197

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Page x Preface This book arose out of a project we started some fifteen years ago to try and make sense of the lexical semantics of spatial prepositions such as in, on or over. At the outset it seemed a simple task, just a matter of characterising the geometry of the spatial arrangements of objects that could be described as in, on or over each other. But like many others we soon discovered that this is by no means a simple task. For every intuitively appealing geometric characterisation it turned out to be easy to discover fresh counter-examples. Over the course of the project we came to the conclusion that it is only possible to make sense of the semantics of spatial prepositions in terms of the relationship between the three activities in the title of the book: Saying, seeing and acting. The functional geometric framework we outline provides just such an account.

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Page xi Acknowledgements Many people contributed to this project. These include (in alphabetical order); Siobhan Campbell, Angelo Cangelosi, Richard Carmichael, Mark Crowther, Gillian Ferrier, Pedro Guijarro-Fuentes, Dan Joyce, Gayna Mather, Mercè PratSala, Lynn Richards and Tony Sanford. Without their contribution the book would not have been possible and we gratefully acknowledge their various contributions to the work. We also would like to thank colleagues who have taken time to read and comment on earlier drafts of the manuscript. Special thanks go to Laura Carlson, Lynn Richards, Emile van der Zee and Tony Sanford and a further two reviewers who provided detailed comments on the whole manuscript. Thanks go also to Monika Harvey, Dan Joyce and Mike Tucker for comments on the early chapters (particularly Chapter 3), and to Paul Quinn for his comments and advice on Chapter 8. We would also like to thank Tony Sanford in Glasgow, and members of the Spatial Language Group in Plymouth, for many discussions about spatial language that have contributed innumerably to the ideas developed in this book. Gratitude is also owed to the bodies that provided the financial support for much of the research presented in this volume in the form of research grants awarded to the first author. Specifically we are indebted to the Economic and Social Research Council (Grant Number R000222211) and the Engineering and Physical Sciences Research Council (Grant Number GR/N38145). Thanks go also to Ben Huxtable-Smith and Mark Cooper in Plymouth for their technical assistance in the production of some of the figures in the book and to Kathryn Russel and the rest of the team at Psychology Press for making the process of delivery as painless as possible.

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Page xii Figure acknowledgements Finally, we would like to thank the following publishers for copyright permission to reproduce the following figures: Figures 4.3 and 4.7. Reprinted from Garrod, S., Ferrier, G., & Campbell, G. (1999). In and on: Investigating the functional geometry of spatial prepositions. Cognition, 72, 167–189. Copyright © 1999, with permission from Elsevier. Figures 4.5 and 4.9. Originally published as Figure 1, page 511 and Figure 4, page 519 in Coventry, K. R. & PratSala, M. (2001). Object specific function, geometry and the comprehension of ‘in’ and ‘on’. European Journal of Cognitive Psychology, 13(4), 509–528. Copyright © 2001 Psychology Press. Reprinted with permission. Figure 4.6. Originally published as Figure 2, page 148 in Coventry, K. R. (1999). Function, geometry and spatial prepositions: Three Experiments. Spatial Cognition and Computation, 2, 145–154. Copyright © 1999 Kluwer Academic Publishers. Reprinted with permission from Kluwer Academic Publishers. Figure 5.1 and Figure 5.4. Originally published as Figure 3.8, page 90 and Figure 4.10, page 149 in In P. Bloom, M. A. Peterson, L. Nadel, & M. F. Garrett (Eds.), Language and space (p. 597). Copyright © 1996 The MIT Press. Reprinted with permission from The MIT Press. Figure 5.6. Originally published as Figure 9.3, page 173 from Coventry, K. R., & Mather, G. (2002). The real story of ‘over’. In K. R. Coventry, & P. Olivier (Eds.), Spatial Language. Cognitive and Computational Aspects (pp. 165– 184). Copyright © 2002 Kluwer Academic Publishers. Reprinted with permission from Kluwer Academic Publishers. Figures 5.7, 5.8, 5.9 and 5.10. Reprinted from Coventry, K. R., Prat-Sala, M. & Richards (2001). The interplay between geometry and function in the comprehension of ‘over’, ‘under’, ‘above’ and ‘below’. Journal of Memory and Language, 44, 376–398. (Figure 2, page 381, Figure 6, page 386, Figure 10, page 390, Figure 11, page 392 and Figure 12, page 393.) Copyright © 2001, with permission from Elsevier. Figure 8.2. Originally published as Figure 16.2, page 485 from Bowerman, M., & Choi, S. (2001). Shaping meanings for language: universal and language-specific in the acquisition of spatial semantic categories. In M. Bowerman, & S. C. Levinson (Eds.), Language acquisition and conceptual development (pp. 475–511). Copyright © 2001 Cambridge University Press. Reprinted with permission from Cambridge University Press.

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Page 1 PART I Saying, Seeing, and Acting: Background to the Domain

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Page 3 CHAPTER ONE Introduction to the domain There can be no Whitewash at the Whitehouse. (Richard Milhous Nixon, On Watergate , television speech, 30 April 1973, in New York Times, 1 May 1973) Let’s get out of these wet clothes and into a dry Martini. (Mae West) Hey diddle diddle, The cat and the fiddle, The cow jumped over the moon. ( Mother Goose’s Melody , c. 1765) The human heart likes a little disorder in its geometry. (Louis de Bernières, Captain Corelli’s Mandolin , 1994, chapter 26) Being able to find objects in the world is one of the most basic survival skills required by any living organism. Similarly, being able to describe where objects are, and being able to find objects based on simple locative descriptions, can be regarded as basic skills for any competent speaker of a language. Spatial descriptions pervade our lives and occur in a wide range of contexts, from locating objects, to reasoning about the world, to understanding the concept of place. For instance, terms like to the left of and to the right of not only allow us to locate the positions of objects in space, but also allow us to reason about entities as diverse as symbols in mathematical equations and the relative positions of countries on a map. Terms like up and

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Page 4 down work as well when referring to our moods as they do when referring to the orientation of objects in space. However, understanding how such locative expressions are used and understood turns out to be an extremely difficult problem. Take the cases in the quotations above. The words that are usually assumed to be expressing the location of objects are spatial prepositions (in italics), which are the words we are interested in giving an account of in this book. These cover a range of types of positions and actions. For example, while at in the Nixon quotation may indicate a particular point of coincidence, in the famous Mae West quote out and into almost certainly denote the end point of actions, or the actions themselves. Spatial prepositions are not only interesting in their own right, but for a number of other reasons as well. For example, they are among the hardest expressions to acquire when learning a second language. This is because languages differ in the way in which they map linguistic terms onto spatial relations. For instance, in Spanish there is a single word, en, which maps onto the meanings of both in and on in English. Conversely, other languages subdivide containment and support relations more than does English. For example, in Dutch there are two words corresponding to on in English: aan is used for cases such as The handle is on the cupboard door, and op is used for cases such as The cup is on the table (Bowerman, 1996a). Furthermore, as Bowerman (1996a) again notes, languages that have two terms to cover in and on, as in English, sometimes do not do so in the same way as in English. For example, in Finnish the equivalent of The handle is on the cupboard door and The apple is in the bowl are grouped together using the inessive case (ending -ssa), whereas a different case ending (the adessive -lla) is used for The cup is on the table . Despite the cross-linguistic variability in how locative terms map onto spatial relations and hence the wide range of relations covered across languages, each language only contains relatively few prepositions (or equivalents). As Landau and Jackendoff (1993) have argued, natural languages only encode a limited number of spatial relations between objects and these have to cover the whole range of possibilities. This leads us directly to the issue of polysemy, which is one of the most difficult problems to deal with in lexical semantics. Polysemy refers to the range of distinct but related interpretations that any word may have. Whereas a few words like bank (a homonym) have two unrelated meanings (the place where you put your money and the land on the edge of a river), which both have to be lexicalised, most words illustrate polysemy. To borrow an example from Lakoff (1987), window (a polyseme ) can refer to an opening in a wall or to the glass-filled frame in that opening. In this case, the two senses are distinct but related because the glass-filled frame often co-occurs with the hole in the wall. Spatial prepositions are good examples of polysemous terms. For example,

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Page 5 over in The hand is over the table does not entail contact between the hand and the table, but The tablecloth is over the table does assume contact between the tablecloth and the table. Consider also the case of The plane flew over the Pacific: Here a change of position of the plane is involved following a path, which is often assumed to be a straight line. These are just three of the 100 or so different polysemes for over (dissected by Brugman, 1981, 1988). Exactly how one deals with such extensive polysemy is an issue we will wrestle with throughout the book. Prepositions also form part of a set of expressions, which, together, act as an organising structure for other conceptual material (Talmy, 1983; but see Gentner & Boroditsky, 2001). In particular, within the framework of ‘‘cognitive linguistics”, spatial concepts have been regarded as the primary structuring tool for other conceptualised domains, hence the extensive use of spatial metaphor (Lakoff & Johnson, 1980). For example, spatial terms crop up in expressions of time (e.g., I’ll see you in five minutes ), expressions of emotion ( I’m feeling really up today), and dead metaphors ( I’m on the wagon). Furthermore, from a semantic point of view, spatial prepositions have the virtue of relating in some way to visual scenes being described and, therefore, measurable characteristics of the world (Regier, 1996). Hence it should be possible to offer more precise semantic definitions of these as opposed to many other expressions because the definitions can be grounded in how we perceive the world itself. In lexical semantics, many approaches have tried to capture the meaning of lexical items only in terms of other lexical items (see, for example, Burgess & Lund, 1997; Landauer & Dumais, 1997). However, as Glenberg and Robertson (2000) have noted, approaches that only define words in terms of other words do not deal with the issue of how meaning maps onto the world—that is, the issue of how meaning is grounded. No matter how many words are looked up, the meaning of a word can never be figured out without grounding the symbol in something else (Harnad, 1990). As we shall see with spatial language, too, many approaches to the lexical semantics for spatial terms have tried to capture their meaning without adequate consideration of how language and the perceptual system map onto one another. The approach we will adopt in this book places perceptual representation at the heart of the situation-specific meaning of spatial terms. As the title of the book suggests, spatial language relates to the visual system, but also to the idea of acting in the world. The account we will offer maintains that descriptions of the spatial world not only refer to the positions of objects in space, but also reflect the knowledge of objects in the world acquired through interacting with that world. In the spirit of Michotte (1963), we will argue that what objects are and how they interact (or may interact) with each other are central to the comprehension and production of spatial terms. Furthermore, we will examine the issue of whether conceptual relations between objects are driven by outputs of the visual system (e.g., in

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Page 6 relation to the so-called “what” and “where” systems; Ungerleider & Mishkin, 1982) or whether these conceptual relations are driven by language. Our aim by the end of the book is to present what we term a functional geometric framework for spatial language comprehension and production. The framework puts geometry and knowledge of objects and how they interact with each other together in context to account for the situation-specific meaning of spatial prepositions. However, before we provide a précis of the argument, for the remainder of the chapter we set ourselves the more humble task of specifying in more detail how spatial prepositions are classified semantically and syntactically. This will serve as an important structuring tool when we review the evidence for the functional geometric framework later in the book. SPATIAL PREPOSITIONS: CLASSIFICATIONS AND BOUNDARIES Classifications Preposition: an enormously versatile part of grammar, as in ‘‘What made you pick this book I didn’t want to be read to out of up for ?” (Winston Churchill) Despite the myriad ways in which the spatial world can potentially be carved up, there are only between 80 and 100 prepositions in the English language, excluding the use of situation-specific technical prepositions (e.g., nautical terms like astern ). These are displayed in Table 1.1. As Landau and Jackendoff (1993) point out, the small number of prepositions is in sharp contrast to the large number of words in other syntactic categories (e.g., there are around 10,000 count nouns in the standard lexicon). However, despite this small number of prepositions, each can be used in a diversity of different ways both semantically and syntactically. The quote above from Churchill (a keen commentator on the ludicrousness of the English language) contains no less than eight prepositions, which illustrate several types of uses. As is illustrated in Figure 1.1, in classifying the functions of prepositions the distinction is often made between grammatical uses and local uses (Bennett, 1975; Lyons, 1968). A preposition used grammatically does not carry much meaning; it functions mainly as a syntactic marker (for example, the of and for in the Churchill quote). In contrast, under the banner of local uses come temporal and spatial uses of prepositions. Temporal uses indicate a point in time (e.g., See you on Thursday, in five minutes ) and are interesting in their own right [see, for example, Bennett (1975), Lakoff & Johnson (1980) or Boroditsky (2000) for a discussion of temporal prepositions]. However, our focus is going to be on spatial prepositions that specify

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Page 7 Table 1.1 The prepositions in English (adapted from Landau & Jackendoff, 1993) about above across after against along amid(st) around at atop behind below beneath beside between betwixt beyond by down from in inside into near nearby off on onto opposite out outside outwith (SE) over past through throughout to toward under underneath up upon via with within without Compound prepositions far from in back of (AE) in between in front of in line with on top of to the left of to the right of to the side of Intransitive prepositions afterwards apart away back downstairs downward east forward here inward left N-ward (e.g., homeward) north onward outward right sideways south there together upstairs upward west Nonspatial prepositions ago as because of before despite during for like of since until Note : AE = occurs in American English only, SE = occurs in Scottish English only.

Figure 1.1 Prepositions classified.

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Page 8 a location or change in position of an object in space. Spatial prepositions are commonly divided further into locative or relational prepositions (H. Clark, 1973) and directional prepositions (Bennett, 1975). Locative or relational prepositions describe the location of one object in relation to another (e.g., Keith is in his office), whereas directional prepositions describe a change of position (e.g., Simon went to the eye-tracker room — a few minutes ago) or direction in which an object is located (e.g., The wind vane pointed to the north). To give a more complex example (from Bennett, 1975, p. 18), We went from Waterloo Bridge along the Embankment to Westminster describes a starting point, a change of location, and the path taken during the change of location. Locative/relational terms are often further broken down into topological terms on the one hand and projective terms on the other (sometimes also called dimensional terms; see Retz-Schmidt, 1988). Topological terms include prepositions such as in, on, and near , which usually refer to (static) topological relations between objects. For our purposes, we can further distinguish between the simple topological terms in and on and proximity terms such as near and far, which give information about the distance between objects. Projective terms, such as in front of , to the left of , and above convey information about the direction in which one object is located with reference to another object. However, they are special in that they depend for their interpretation upon a particular spatial frame of reference. In turn, this means that each term can be used in several different ways. As Levinson (1996a) has noted, the classification of frames of reference in familiar European languages remains confused, and we therefore follow Levinson’s (“suitably catholic”) distinction between three basic reference frames (which can be further subdivided; see, for example, Jackendoff, 1996). These reference frames are as follows: (1) Intrinsic (object-centred) frame of reference : The coordinate system used to specify the position of the located object is generated with respect to salient features of the reference object. In the case of Figure 1.2, The bus is in front of the man and The signpost is behind the man locate the bus and signpost with reference to the intrinsic front of the man. Similarly, The man is to the right of the bus locates the man on the right side of the bus with reference to the bus’s intrinsic front. (2) Relative (viewer-centred/deictic) frame of reference : The coordinate system used presupposes an (egocentric) viewpoint distinct from the objects being described. In the case of Figure 1.2, The man is to the left of the bus and The man is to the right of the signpost locate the man from the perspective of the person looking at the picture (i.e., from your point of view in this case). (3) Absolute (environment-centred) frame of reference : The coordinate system used is defined with respect to salient features of the environment,

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Figure 1.2 Frames of reference (the letters in parentheses after each sentence indicate the appropriate reference frames, where R = relative frame, I = intrinsic frame, and A = absolute frame): (a) The bus is in front of the man (I). (b) The signpost is behind the man (I). (c) The man is to the right of the bus (I). (d) The man is to the left of the bus (R). (e) The man is to the right of the signpost (R). (f) The wing mirrors are above the man (I, R, A). (g) The man is below the signpost (I, R, A). (h) The signpost is north of the man (A). (i) The bus is south of the man (A). such as the fixed directions provided by gravity (or the usual horizon under canonical conditions), or the use of “cardinal directions” (north/south/east/ west, etc.), which are arbitrary fixed bearings. In the case of Figure 1.2, The wing mirrors are above the man and The man is below the signpost locate the wing mirrors and man with reference to the gravitational plane, while The signpost is north of the man and The bus is south of the man locate the signpost and bus with reference to points on a compass. Projective prepositions are the only prepositions (in English) that allow intrinsic, relative, and absolute use. Furthermore, sometimes more than one reference frame maps onto the same expression, whereas at other times reference frames conflict. For example, in Figure 1.2, The wing mirrors are above the man is appropriate both from the perspective of absolute and intrinsic reference frames. However, the use of to the right of depends on adopting a single reference frame for this picture. The man is to the right of the bus is only true with reference to the intrinsic reference frame. However, not all languages admit the use of all three reference frames. For example, although Tzeltal (a Mayan language of Mexico) uses an intrinsic reference system for spatial description (albeit with restricted usage), the predominant reference frame adopted is the absolute reference frame, where downhill and uphill have come to mean north and south (Brown, 1994, 2001; Levinson, 1996a). With reference to Figure 1.2, Tzeltal would describe the position of the signpost as downhill (north) of the boy and the bus as

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Page 10 uphill (south) of the boy. Tzeltal does not have terms in the language for left of , in front of , and so on. Finally, in relation to the broader classification of prepositions we have presented, it is important to note that the same preposition can be used in a variety of different ways. For example, over can be used as a temporal ( We talked over lunch), directional ( The cow jumped over the moon ), or locative/relational term ( The portrait is over the fireplace). We will argue later in the book that part of the reason for this relates to the extent to which individual prepositions are influenced by what we will term extra-geometric constraints. Boundaries Spatial prepositions occur within locative expressions, of which there are many types. The simplest form is composed of four main constituents: the preposition, the verb, and two noun-phrases as in The cat is in the basket. For the remainder of the book we will refer to the cat as the located object and the basket as the reference object . However, in the literature there are many alternatives names for located and reference objects, including figure and ground (e.g., Langacker, 1986), primary object and secondary object (e.g., Talmy, 1983), trajector and landmark (e.g., Lakoff, 1986), and theme and reference object (e.g., Jackendoff, 1983), not to mention labels in languages other than English (see Retz-Schmidt, 1988). Our choice of located object and reference object avoids the visual connotations associated with figure and ground, and the movement connotations associated with trajector and landmark. Locative expressions can be structured around a copulative verb or an existential quantifier, such as in The cow is in the field or There is a cow in the field . There are also locative expressions in which the subject of the preposition is a clause, as in The cow is chewing grass in the field . The clause The cow is chewing grass is the subject because it describes the event that is taking place in the field . A spatial prepositional phrase may also fill a case frame of a verb (Fillmore, 1968). For example, in The dog put the bone in the kennel, what is being located in the kennel is not any object, state, or event, but the ‘‘destination” of the action “to put”—that is, in the kennel is the end place of the trajectory of the bone. So it fills the goal thematic role for the verb. For this reason, we will mainly stick to examples containing the verb to be when considering the meaning of spatial prepositions here. Although verbs clearly play an important role in the co-composition of locative expressions (see, for example, Pustejovsky, 1991, 1995, for theoretical analyses; see Chambers, Tanenhaus, Eberhard, Filip, & Carlson, 2002, for online evidence), we wish to separate out the information the preposition brings to the sentence from effects of constraint satisfaction, or contextual modulation associated with the verb of the sentence.

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Page 11 As Talmy (1985) has shown, paths of motion across languages can be lexicalised in the verb or in the preposition. English is what Talmy (1985) has termed a “satellite-framed” language, which expresses path notions (movement into, out of, etc.) in a constituent that is a satellite to the main verb (e.g., prepositions/particles in English). In contrast, Spanish is an example of a “verb-framed” language, as path is expressed in the verb itself. For example, in English one can say Kathryn put the coat on or Kathryn put on the coat , where the preposition expresses a path from located to reference object. However, in Spanish there are no such directional prepositions; instead, one must say Kathryn se pone el abrigo, where se pone is the reflexive verb to put on ( oneself). However, in English, although the preposition can express information about a path, the type of path is affected by the verb. Consider the following sentences: Kathryn walks over the hill Kathryn lives over the hill In the first case, there is a path with the located object in contact with the reference object. In the second case, Kathryn lives on the other side of the hill from the viewpoint of the speaker. Thus the sentences, involving different verbs, depict quite different spatial relations. It could be that the word over brings different information to each sentence—as Lakoff (1987) argues, over has two distinct, though related, senses—or it could be the verb adds to the information given by over, thus reaching a different spatial depiction through principles of semantic composition. Focusing on a neutral verb, namely to be, we are able to avoid this problem. That is, we can get at the information a spatial preposition brings to a sentence without modification. It is also worth pointing out that words like in can be used in a variety of different ways. For example, in is a preposition in In the harbour, but this prepositional phrase can occur either as the complement of a verb, as in It sank in the harbour, in which case it plays an adverbial role, or as the complement of a noun, as in The channel in the harbour, in which case it plays an adjectival role. In can also be used intransitively as in the sentence Harry walked in. Miller and Johnson-Laird (1976, p. 379) comment that, ‘‘to assign in (for example) always to its correct syntactic category suggests diversity where there is considerable semantic uniformity” (see also Miller, 1985). And others have argued that the distinction between prepositions, particles, and locative adverbs is not worth drawing (Jackendoff, 1973). Finally, it is important to account for other uses of prepositions in nonspatial contexts such as metaphor. Indeed, one may argue that an understanding of nonliteral uses may give great insight into the use of prepositions in more literal contexts. We will have more to say about metaphorical uses towards the end of the book.

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Page 12 SAYING, SEEING, AND ACTING: PRÉCIS OF THE ARGUMENT Now that we have narrowed down the domain, we can consider what spatial prepositions actually mean. More precisely, our goal is to understand how language and the spatial world covary. Given a locative expression used in a particular situation, we need to be able to predict the meaning it conveys and how it will be interpreted. If it has not been used appropriately, we need to be able to explain why this is the case. Similarly, given a spatial scene, we need to be able to predict the locative expression that can be used appropriately to describe the spatial relation depicted. These problems, known in artificial intelligence as the decoding and encoding problems, have pre-occupied many linguists, psycholinguists, and logicians before us. However, most theories have started in the same place. Their starting point has been that spatial expressions are associated with the positions of objects in Euclidean space. Furthermore, the lexical entries advocated for spatial prepositions have been essentially the spatial relations that the expression refers to. As we shall see in the first part of Chapter 2, this quickly leads to problems because any given spatial term maps onto a wide range of geometric relations. For example, the geometric relations associated with The flowers in the vase, The crack in the jar , The bird in the tree (etc.) are all different. This has led to a debate about minimal versus full specification for lexical entries. On the one hand, there are minimally specified accounts that have variously invoked “core sense”, “classical”, “truth conditional’’, or “dictionary” theories of meaning. On the other hand, there are fully specified accounts of the cognitive linguists, such as that proposed by Lakoff (1987), which is based on experientialism and embodies polysemy and prototype effects. We will argue that the debate between minimal versus full specification has distracted researchers from a more important issue, neglected in much of the spatial language literature, that spatial language must be grounded in perception and action. In Chapter 3, we first consider recent approaches to spatial language that ground spatial language in visual processes. For example, we consider the relative merits of spatial template theory (Logan & Sadler, 1996) and the constrained connectionist approach of Regier (1996) as ways of characterising how language and visual processing of scenes match up. We then question the assumption that spatial prepositions simply refer to the positions of objects in Euclidean space. Rather, we argue that a range of extra-geometric variables, including functional relations between objects and object knowledge, are crucial factors in determining the appropriate use of spatial terms. Building on the earlier accounts of Talmy (1988), Vandeloise (1994), and Garrod and Sanford (1989), we lay out a functional geometric framework for spatial language comprehension and production and outline the main ingredients of the account: geometric routines, dynamic-kinematic

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Page 13 (extra-geometric) routines, and stored object knowledge that guides how these routines are applied and put together online. We will argue that the fact that spatial prepositions can refer to the location of an object/objects does not necessitate that the meanings of these terms are simply the relations they refer to. We then consider the perceptual origins of the functional geometric framework and argue that the types of representations delivered by the visual system are consonant with the components in the framework. So the first part of the book introduces the background for our main thesis that the language of space is inextricably bound up with the process of seeing our world and acting on it. In the second part of the book, we review the evidence to date for the three key elements we have proposed, dealing with the topological prepositions (Chapter 4), the projectives (Chapter 5) and proximity terms (Chapter 6). We will show that the use of these prepositions is affected by a range of extra-geometric factors, including location control, the functions represented as part of our knowledge of the objects referred to in the locative expression, and the extent to which those objects usually occur together. In the final part of the book (Chapters 7–9), we bring together the ingredients we have assembled into a framework for spatial language understanding. Chapter 7 outlines the need for situation models as a means of integrating multiple constraints online. We consider how models are constructed and the extent to which different sources of knowledge (e.g., as reflected in geometric versus dynamic-kinematic routines) contribute to the interpretation of the particular preposition being used. Chapter 8 considers the implications of the functional geometric framework in relation to understanding languages other than English, how spatial language is acquired, and the mapping between spatial language and spatial conceptualisation. We show that the prelinguistic infant demonstrates knowledge of the types of physical relations, such as those arising from gravity, we have argued are central to the functional geometric framework and we review evidence that children are sensitive to both geometric and extra-geometric constraints in learning spatial language. We then consider how the framework may facilitate understanding of differences between languages in how they refer to space, and the nature of the underlying structure of spatial representation for language. In the final chapter, we broaden out the functional geometric framework to consider a range of issues only briefly touched upon earlier in the book. We consider how the framework may be applied to deal with prepositions used in metaphorical contexts (e.g., I’m under the weather), and links between the framework and recent approaches to embodiment, such as those of Barsalou and Glenberg (e.g., Barsalou, 1999; Glenberg, 1997; Glenberg & Robertson, 2000), are discussed. We also consider the implications the approach has for the study of other syntactic categories, and how the framework may be realised in relation to neuropsychological machinery.

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Page 15 CHAPTER TWO Saying: spatial prepositions and lexical semantics In this chapter, we consider early approaches to spatial prepositions that have focused on mapping language onto spatial relations in the (real or imaginary) world being described. We will begin with the assumption that spatial language refers in some way to the geometric relations between the objects under consideration, and will show how this assumption has played its part in fuelling debates in the literature about how many senses of a word need to be recognised in the mental lexicon. By the end of the chapter, we hope to convince you that comprehension and production of spatial language is underdetermined by geometric relations, and we will lay the foundations for a somewhat different type of account that we develop in the rest of the book. SPATIAL LANGUAGE, SPATIAL RELATIONS, AND MINIMAL SPECIFICATION Historically, a common way to begin spatial language investigations has been to do some armchair theorising. We might assume at the outset that spatial prepositions refer to spatial relations in the world, and that what they specify in a sentence is some geometric description of the relative positions of objects in space. From a methodological point of view, this endeavour involves thinking of sentences and mapping those sentences onto associated spatial scenes. For example, The apple is in the bowl might refer to a bowl (real or imaginary) with an apple spatially enclosed by the bowl. Furthermore, we might allow the specification of clear geometric boundaries, which

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Page 16 separate out the regions appropriate for the use of in as opposed to other spatial prepositions. Importantly, each word in the sentence brings a fixed content (or core sense) to it that combines with other word contents. In the case of spatial prepositions, this has often been represented in terms of a simple relation, such as: In(X, Y) iff Located (X, Interior(Y)) This first-order logic formula represents the necessary and sufficient conditions for an expression of that form to be true. For example, if we consider the sentence The fish is in the tank , fish would be substituted for X, tank would be substituted for Y, and the sentence would only be true if the fish is located interior to the tank. Cooper (1968) provides an ideal meaning of in that is almost identical with this: IN: X in Y: X is located internal to Y, with the constraint that X is smaller than Y—where X is the located object, and Y is the reference object Leech (1969) provides a similar definition, but drops the explicit requirement that the located object be smaller than the reference object: IN: X in Y: X is “enclosed” or “contained” either in a 2D or 3D place Y However, by virtue of the fact that an object must be physically smaller than a container to fit in a container, this is implicit in Leech’s definition. Such an approach is attractive because it provides a one-to-one mapping between language and the spatial world that is easy to implement from the perspective of artificial intelligence and computational linguistics. However, instantly one can see problems with these “definitions” of in, as there are many cases where the conditions for use do not hold, but the use of in is still acceptable. For example, in Figure 2.1(b), The pear is in the bowl is felicitous, but the condition that the located object is interior to the reference object has been flouted. This is also true of (d), where the light bulb is not interior to the socket but in is still appropriate. However, note that in Figure 2(c) the position of the pear is identical to that in 2(b) but in is no longer appropriate. Figure 2.1(e) represents a case which flouts both the requirement that the located object be smaller than the reference object (flowers are normally larger than the vase, certainly in terms of height) and the requirement that the located object be located internal to the reference object (flowers normally stick out the top of a vase). There are also cases where the definition of in given does hold but the use of in is not appropriate. One such example is Figure 2.1(a), where under is the most appropriate preposition to use, although the pear is located internal to the bowl. This situation is complicated by the fact that in is the most appropriate preposition to use in the case of Figure 2.1(d).

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Figure 2.1 Acceptable and unacceptable uses of in: (a) *The pear is in the bowl.1 (b) The pear is in the bowl. (c) *The pear is in the bowl. (d) The light bulb is in the socket. (e) The flowers are in the vase. (f) The crack is in the cup. (g) The racket is in the hand. (h) The racket is in the hand. (i) *The flowers are in the vase. 1 The footnote on page 18 explains the use of the asterisk.

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Page 18 Miller and Johnson-Laird (1976) recognise the problem that the located object does not necessarily have to be smaller than or completely contained by the reference object. Thus they propose the following definition for in: IN(X, Y): A referent X is “in’’ a relatum Y if: (i) [PART (X, Z) & INCL (Z, Y)] where INCL represents “included spatially in”. This definition accounts for some of the cases that the definitions of Cooper (1968) and Leech (1969) seem to have difficulty with, such as Figure 2.1(d) and 2.1(e). However, this definition cannot account for the cases of Figure 2.1(b), where the definition does not hold but the use of in is appropriate, and 2.1(a) where the definition does hold but the use of in is infelicitous. Additionally, the definition would allow cases such as *The jar is in the lid 1 to be appropriate when clearly it isn’t. Furthermore, while The racket is in the hand is appropriate for either the situation in Figure 2.1(g) or 2.1(h), similarly reversing the orientation of the vase and flowers as in Figure 2.1(i) results in a questionable use of in. Finally, The crack in the cup in Figure 2.1(f) is not in the part of the cup normally associated with containment. This state of affairs—that is, the ease with which one can come up with counterexamples to the simple definitions given—is not limited to the case of in. Cooper (1968) provides the following definition of on: ON: X on Y: A surface X is contiguous with a surface of Y, with the constraint that Y supports X Leech (1969) focuses more on contiguity than Cooper (1968) and offers the following definition of on: ON: X on Y: X is contiguous with the place of Y, where Y is conceived of either as one-dimensional (a line) or twodimensional (a surface) For counterexamples to these definitions of on, consider Figure 2.2 (adapted from Herskovits, 1986). The (thin) book is on the table in (a) but the lid is not on the table in (b), although it is as near the table surface as the book is in (a). However, the lid can be said to be on the table in (c). The definition of on given by Leech (1969) does not cover (a) and (c) because the book and the lid, respectively, are not contiguous with the table. The definition given by Cooper (1968) fares better because it has support as a factor in the use of on (thus potentially accounting for (a) and (c) on the grounds that the table is supporting the book and lid even though the support is indirect), but still cannot account for the felicitous use of on in (c), though not in (b). 1 We use an asterisk before a sentence here and throughout the book to denote a sentence that is either semantically/pragmatically ill-informed on its own, or is not appropriate to describe an accompanying visual scene.

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Figure 2.2 Acceptable and unacceptable uses of on: (a) The (thin) book is on the table. (b) *The lid is on the table. (c) The lid is on the table.

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Figure 2.3 The light is on the ceiling. Another problematic case is that in Figure 2.3, which flouts the contiguity condition required in the definitions given by Cooper (1968) and Leech (1969). Miller and Johnson-Laird (1976) improve slightly on these definitions of on using the following: ON: ON(X, Y): A referent X is “on” a relatum Y if: (i) (INCL(X,REGION(SURF(Y))) & SUPRT(Y, X)); otherwise go to (ii) (ii) PATH(Y) & BY(X, Y) where INCL represents “included spatially in”, SUPRT represents “supports’’ and SURF represents “has the (total) surface”. This definition recognises cases such as The house on the river where the house is beside the river, but not on top of the river. They explain the examples in Figure 2.2 by treating on as a “transitive relation with peculiar limitations” (Miller & Johnson-Laird, 1976, p. 387). The limitations on transitivity come from the subdomain of search for “on”, which they claim is associated with the region of interaction of the surface of the relatum, rather than merely the surface. For example, if we consider the scene depicted in Figure 2.4, one can say the following on relations are admissible: The lamp is on the table , The table is on the rug, The rug is on the floor, The table is on the floor. However, The lamp is on the floor is

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Figure 2.4 Acceptable and unacceptable uses of on: (a) The lamp is on the table. (b) The table is on the rug. (c) *The lamp is on the rug. problematic. Miller and Johnson-Laird’s explanation of this is that we can say that the table is on the floor even though it is not touching it because when we search in the region of the floor we will encounter table legs. We cannot say the lamp is on the floor because when we search in the region of the floor we will not encounter the lamp. Hence, the limited transitivity of on as used to describe a pile of objects. Thus Miller and Johnson-Laird rely on the idea that the purpose of locative expressions is to narrow down the domain of search for a referent, and take this “function” to be represented directly at the perceptual level. This explanation still fails to account for the examples in Figure 2.2, however. As indicated before, the lid in Figure 2.2(b) is as near the table as the book in Figure 2.2(a). Therefore, there must be more to an explanation of this phenomenon than simply a limited notion of transitivity based on region of interaction. Additionally, one can say The crack in the glass but not * The crack on the glass. In contrast, The crack in the ceiling is fine, as is The crack on the ceiling. Also, whereas The man on the plane and The child on the bicycle are both acceptable, * The man on the car is not (at least if it is to have the same sense). To deal with one final example here, we consider the well-documented case of over. As Brugman (1981, 1988; see also Brugman & Lakoff, 1988;

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Page 22 Lakoff, 1987) and Taylor (1988) have noted, it is difficult to find an all-encompassing single definition or core sense for over. For example, if we assume that the definition is “at a location higher than, but not in contact with”, then a large number of uses must be treated as exceptions. For example, The tablecloth is over the table requires contact between located and reference objects, whereas The man lives over the hill involves no contact but does not require a “higher than” relation between located and reference objects. Of course, one possibility here is to try to loosen the definition, so that these (and numerous other) problematic cases can be dealt with. For example, Bennett (1975) loosens the no contact requirement, specifying simply ‘‘locative superior” (as compared with “locative higher” for above ). This then licenses contact examples like The tablecloth is over the table , but now problems occur with cases of other located objects such as a suitcase. Clearly, if the suitcase were superior to the table but also in contact with it, then the description The suitcase is over the table would be quite inappropriate. We return to the case of over shortly when we consider Brugman and Lakoff’s analysis of this term in more detail. For the moment, let us summarise the problems encountered so far. We have seen, using examples of in, on, and over, that there are many individual instances of the appropriate or inappropriate use of these terms that present major problems for simple core sense definition accounts. These are not isolated counterexamples, but serve to illustrate some of the problems that are apparent even from the limited vantage point of our metaphorical armchair. Our purpose has not been to be exhaustive. One could easily generate hundreds of further counterexamples for in and on or for any other spatial preposition. Indeed, the spatial language literature contains catalogues of such cases (see, for example, Brugman, 1988; Herskovits, 1986), and interested readers are referred to these excellent treatments. What we can do here though is to classify the counterexamples into two main categories. The first is where the definition overgenerates cases that should fit but do not; these are decoding overgenerations. The second is where the definition does not fit a situation in which the preposition is quite appropriate; these are encoding inadequacies. Furthermore, the two kinds of problem case can often be further subdivided. For example, Herskovits (1986) and Landau and Jackendoff (1993) draw attention to the unacceptability of certain converses. For instance, one can say that The bicycle is near the house but not that * The house is near the bicycle (Talmy, 1983). Furthermore, in some cases the definitions fail to account for context dependencies (H. Clark, 1973; Fillmore, 1971), such as in the use of projectives like behind. As we noted in the last chapter, terms like behind can be used within a number of different reference frames. More generally, Searle (1979) notes that there are important “background conditions” necessary for locative expressions to be used properly. For example, The cat is on the mat only has meaning relative to

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Figure 2.5 Is the cat on the mat? the background condition that there is a gravitational field. Consider the following scenario (with the cat and mat as depicted in Figure 2.5): “Suppose the cat’s owner is in the next room, while I unbeknownst to him have drugged his cat and stiffened his mat with my special stiffening solution. ‘Where is the cat?’ asks the owner from his position next door. ‘The cat is on the mat’, I answer. Have I told the truth?” (Searle, 1979, p. 124) Searle answers his own thought experiment with the argument that the answer is misleading at best and probably should be described as an ingenious lie. However, if one considers the situation where the mat is in its stiffened position and is part of a row of objects similarly sticking up at odd angles, and both speaker and hearer know these facts, then if the cat is jumping from one object to another, and the question, “Where is the cat?” is asked, the answer, “The cat is on the mat” is now appropriate. Searle takes this as an argument that the notion of the meaning of a sentence only has application relative to a set of background conditions (see also Clark, 1996; Sperber & Wilson, 1986). The truth conditions of the sentence The cat is on the mat will vary with variations in these background assumptions and, given the absence or presence of some background assumptions, the sentence does not have determinate truth conditions. This point indicates how flexible meaning can be, and also leads us to consider how background conditions of the type Searle discusses are determined. This is an issue that haunts many of the accounts we shall consider in the early

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Page 24 part of the book, but one which is at the heart of the functional geometric framework we set out later in the book. For now, it is clear that the counterexamples to the minimally specified lexical entries of the type outlined above pose a problem for these accounts and, indeed, it is necessary to treat such cases as exceptions that have to be listed separately in the lexicon. The number of these exceptions soon becomes so large that one loses sight of the main motivation behind the core sense idea: that it should be possible to give a single clear definition for any spatial preposition. As Bennett (1975, p. 5) claims, it is ‘‘both unnecessary and undesirable to postulate as many senses of each preposition as are listed by Lindkvist (1950), Sandhagen (1956), Wood (1967), and in the larger dictionaries”. We now turn to approaches that try to get around this problem by favouring full specification. HERSKOVITS: IDEAL MEANINGS, USE TYPES, AND PRAGMATIC PRINCIPLES Herskovits (1985, 1986, 1988) provides a treatment of spatial prepositions that involves three levels of representation. First, there is the lexicalised ideal meaning for a spatial preposition, which is a lexicalised (abstract) geometric ideal akin to the “definitions” we have considered above. However, in addition to ideal meanings, Herskovits introduced a second lexicalised level of analysis, that of use types, which are derived from the ideal meaning and can be viewed as classes of normal situation types where a normal situation type is a statement of the normal conditions under which speakers use a certain locative expression. The normal interpretation of a use type is different from its geometric meaning in that it includes contextual (pragmatic) constraints and also depends for its interpretation on the associated expressions. However, lexicalised ideal meanings and use types are not enough. Herskovits also proposed a series of pragmatic “near” principles that allow the use types to bend and stretch to fit a wide range of real-world uses. These principles include salience, relevance, typicality, and tolerance. Table 2.1 lists the use types and ideal meanings proposed by Herskovits for in, on, and at. Take, for example, Herskovits’s analysis of in. All the use types proposed from the more abstract geometric ideal gravitate round the ideal meaning, and relate to the ideal meaning in systematic ways. Take, for example, the following sentences involving in: (1) The water is in the vase (2) The crack is in the vase (3) The crack is in the surface (4) The bird is in the tree (5) The nail is in the box (6) The muscles are in his leg

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Page 25 Table 2.1 Herskovitsian ideal meanings and use types for in, on, and at Ideal meaning: In: inclusion of a geometric construct in a one-, two-, or three-dimensional geometric construct Use types: In: Spatial entity in container Gap/object “embedded” in physical object Physical object “in the air” Physical object in outline of another or a group of objects Spatial entity in part of space or environment Accident/object part of physical or geometric object Person in clothing Spatial entity in area Physical object in a roadway Person in institution Participant in institution Ideal meaning: On: for a geometrical construct X to be contiguous with a line or surface Y; if Y is the surface of an object Oy, and X is the space occupied by another object Ox, for Oy to support Ox Use types: On: Spatial entity supported by physical object Accident/object as part of physical object Physical object attached to another Physical object transported by a large vehicle Physical object contiguous with another Physical object contiguous with a wall Physical object on part of itself Physical object over another Spatial entity located on geographical location Physical or geometrical object contiguous with a line Physical object contiguous with edge of geographical area Ideal meaning: At: for a point to coincide with another Use types: At: Spatial entity at location Spatial entity “at sea’’ Spatial entity at generic place Person at institution Person using artefact Spatial entity at landmark in highlighted medium Physical object on line and indexically defined crosspath Physical object at a distance from point, line, or plane

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Page 26 According to Herskovits, in conveys an idea of inclusion or surrounding in all these examples. However, in each case this idea applies to geometric objects in different ways—in some cases, strictly speaking, it may not apply at all. The first five examples illustrate what Herskovits terms “the use of geometric imagination”. In each case the located object is mapped onto the same geometric description (the place of the object), but in each case the mapping is different. The water in (1) is within the volume of containment defined by the concavity of the vase—a volume limited by the inner side of the vase and by a plane running through its rim. The crack in (2), by contrast, is within what Herskovits calls the “normal” volume of the vase—that is, within part of the space of the vase that the vase would occupy if there were no crack. In (4) the bird is in a volume bounded by the outline of the tree’s branches. The fifth example illustrates how a phrase can be ambiguous when two different geometric descriptions of the reference object are equally plausible (lacking further specification by context). The nail could be embedded in the side of the box (either “normally”, that is, sticking out of the side of the box, or completely embedded in the wall of the box) or contained within the box. Example (6) illustrates what Herskovits calls a sense shift. The actual relation between muscles and leg, Herskovits claims, is not one of containment, but is instead the relation ‘‘part of”. Now, allied to ideal meanings is a set of pragmatic “near” principles that provide constraints on the interpretation of a locative expression. These include salience, relevance, tolerance , and typicality. For example, salience allows a noun which basically denotes a whole object to refer to the region occupied by a part of it that is typically salient. For example, in The cat under the table , the cat is under the surface of the table (the table top) and not under the legs. Table thus stands for the top of the table in this expression. Salience can be viewed as referring to the types of foregrounding of objects or object parts that arise in our interactions with and perception of our environment. Relevance has to do with communicative goals, with what the speaker wishes to express or imply in the present context. This pragmatic principle comes into play in cases such as that depicted in Figure 2.6. One can use either in or on with (a) or (b), but the use is dependent on the context; according to whether containment or contact is most relevant. The pragmatic factor of tolerance is Herskovits’s solution to the case we discussed in Figure 2.1(b) above. If an object is part of a group of objects supported by the bowl, some of which are strictly in the bowl , then it can be said to be in the bowl. Finally, typicality introduces a range of the types of background conditions that are not part of the meaning of the spatial expression. For example, in The car is behind the house, it is assumed that the car is near or next to the house, although this is not a part of the meaning of behind according to Herskovits.

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Figure 2.6 Overlap in the use of in and on: (a) The dust is in/on the bowl. (b) The oil is in/on the pan.

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Page 28 Herskovits’s treatment of spatial prepositions includes a welcome consideration of pragmatics, so that simple geometric definitions can be modified to fit a wider range of situations of the kind considered earlier in the chapter. However, although pragmatic “near” principles provide constraints on the interpretation of locative expressions, Herskovits resigns herself to the assertion that some facts of use will remain a matter of convention: All conventional facts of use—facts that are neither determined by the ideal meaning of the preposition and the meanings of the subject and object of the expression, nor pragmatically inferable—will have to be somehow specified in the lexicon, as characteristics of additional senses of the preposition or of idiomatic forms. The kind of lexical representations I suggest, the use type, preserves the relation of the various senses of the preposition to the ideal meaning(s). (Herskovits, 1986, p. 87) Therefore, Herskovits ends up listing the exceptions in the lexicon in much the same way as is required in the minimally specified accounts we have discussed above. The difference is that she maintains that the use types are legitimised on the grounds that they relate in motivated ways to the ideal meaning. However, it is unclear what form use type representations are supposed to take and, additionally, what the role of object knowledge is in her account. Moreover, the use types are lexicalised for prepositions, and this requires that the correct use type be selected from the lexicon in each context, although how this is done is not considered. There are other more general problems with Herskovits’s type of analyses that we reserve discussion of until later. Next, we consider the general approach to spatial terms in cognitive linguistics, focusing on the work of Brugman and Lakoff. LAKOFF, BRUGMAN, AND … DANGEROUS THINGS Whereas Herskovits focuses on the importance of pragmatic principles to bend and stretch lexical entries to fit a myriad of different situations, Lakoff (1987; see also Lakoff & Johnson, 1999) offers a more extreme departure from the simple definitional approach we started out with. In Women, Fire and Dangerous Things, Lakoff (1987), reviews a body of evidence that suggests that categories and concepts do not have fixed boundaries, and exhibit graded structure in most cases. Furthermore, he argues that embodiment is a key element missing in the referential definitional theories thus far considered. According to Lakoff (and other “cognitive linguists”; see also Langacker, 1987, 1988), the structures used to put together our conceptual systems grow out of bodily experience, and the core of our conceptual systems is directly grounded in perception, body movement, and experience of a physical or

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Page 29 social character. Moreover, those concepts that are not directly grounded in experience are imaginative in that they employ metaphor, metonymy, and mental imagery ultimately based on these experiences. We briefly consider each of these issues in turn before examining how they play out in the analysis of over provided by Brugman and Lakoff. First, let us consider the issue of the bounds on categories. Wittgenstein is often credited with the observation that categories do not fit the classical picture. In the Philosophical Investigations, he remarks, for instance, that there are no common properties shared by all members of the category game. Some involve competition, some involve group participation, some involve luck, some involve skill, but they all do not share all of those properties. The result of “look[ing] and see[ing] if there is something common to all’’ is “a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail” (Wittgenstein, 1953, remark 66). Wittgenstein used the term “family resemblances” to cover the relationships between members of a category, such as game, which resemble each other in various ways but do not share common properties with all the other members. It was Eleanor Rosch who took the notion of family resemblance and allied it to what she termed “prototype theory”, showing across a range of experimental methodologies that some examples of a category are somehow more prototypical of that category than other exemplars (see Lakoff, 1987, pp. 41–42 for a brief overview). And this notion of prototype is used in Brugman and Lakoff’s analysis of over. However, the existence of prototype effects does not necessarily mean that they reflect mental representation directly. For example, prototype effects are found for new categories made up on the spot that cannot be stored in advance (so-called ad hoc categories; see Barsalou, 1983), such as things to take from one’s home during fire , things to do at a convention , and so on. Prototypes also change as a function of context, both linguistic (e.g., Roth & Shoben, 1983) and cultural (Barsalou & Sewell, 1984, reported in Barsalou, 1985), and are also present for concepts that are clearly definitional such as odd number (Armstrong, Gleitman, & Gleitman, 1983). Therefore, while gradedness and problems of reference are a fact of life, exactly how one deals with such effects remains an open question (for more discussion of these points, see Coventry, 1998; Margolis, 1994). Now let us turn to the question of “embodiment”. Lakoff contrasts the embodiment view he advocates with the classical view that thought is the abstract manipulation of symbols, and that these symbols are internal representations of external reality. The so-called symbolic tradition in cognitive science is clearly illustrated in the case of language with the views of Fodor (1975; Fodor & Pylyshyn, 1988). For example, Fodor (1975) argues for a language of thought in which conceptual expressions, like language, are built from atomistic (lexical) components combined according to syntactic

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Page 30 principles that allow the generation of an infinite number of expressions in a language. In contrast, Lakoff claims the fact that we have bodies that have a particular structure, and the fact that we have physical and social needs in our environments, fundamentally influence the structure of the concepts we possess and the language we produce and understand. Indeed, the issue of embodiment relates directly to what Harnad (1990) has termed the “symbol grounding problem”. As Glenberg and Robertson (2000, p. 382) put it, “To know the meaning of an abstract symbol … the symbol has to be grounded in something other than abstract symbols”. They propose that the meaning of a sentence is constructed by indexing words or phrases to real objects or perceptual analogue symbols, deriving affordances from those objects and symbols and then meshing the affordances under the guidance of syntax (see also Glenberg, 1997). Therefore, Glenberg and colleagues place action-based representation at the heart of a theory of meaning. However, for Lakoff (1987) space (rather than action) plays the pivotal role in the organisation of conceptual structure. Indeed, Lakoff and Johnson (1980) have argued that spatial relations provide the key organisational structure for nonspatial domains. The fact that spatial terms can be used in temporal contexts (e.g., see you in five minutes ), emotional contexts ( I’m feeling under the weather), and generally structure other domains of experience (e.g., life as a journey ) is cited as one line of evidence for this (but see Keysar, Shen, Glucksberg, & Horton, 2000). As a concrete example of Lakoff and his colleagues’ approach to spatial language, we consider their treatment of the preposition over (Brugman, 1981, 1988; Brugman & Lakoff, 1988; Lakoff, 1987). These authors place spatial senses at the heart of polysemous representations for over, and indeed claim that nonspatial senses are linked to and derived from the central prototypical spatial senses for the term. As such, the analysis of over can itself be regarded as a prototype of cognitive linguistic analyses of spatial language (see also, for example, Casad, 1982; Hawkins, 1984; Janda, 1984; Lindner, 1981, 1982). Brugman (1981) catalogues nearly 100 different kinds of uses of over, and of these polysemes there are “primary” senses from which are extended non-primary ones, although both primary and nonprimary senses exist as categories in the mind of the user. Three central or prototypical senses of over are recognised in the form of the “image schemata” represented in Figure 2.7. These are: (1) The above-across schema (Figure 2.7a): The located object is an object moving on a path above, and extending beyond, the boundaries of the reference object, as in The plane flies over the bridge. Alternatively, the located object could be a stationary, one-dimensional object, as in The line stretches over the wall. In this schema, contact between the located object and the reference object is allowed.

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Figure 2.7 The three prototypical ‘‘image schemata” for over (Brugman & Lakoff; adapted from Lakoff, 1987). TR = located object, LM = reference object. (2) The above schema (Figure 2.7b): The located object is vertically above, but not touching, the reference object, as in The helicopter hovers over the city. (3) The cover schema (Figure 2.7c): The located object is an object whose two-dimensional extent covers the reference object (extends to the edges of or beyond the landmark). In most cases, the located object is construed as being vertically above, and in contact with, the reference object, as in The cloth is over the table .

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Page 32 It is from these prototypical spatial relations/central schemas that all the other senses of over are derived (albeit indirectly in many cases) using three linking principles. Instance links link prototypical senses of over to more specific schema instances of itself. For example, the by-way-of-above schema is connected to schemas that involve contact between the located object and reference object (e.g., Sam drove over the bridge) and to those that do not (e.g., The bird flew over the yard). These more specific schemas are arrived at by further specifying the nature of the reference object and by specifying whether or not there is contact. Transformation links and similarity links are two other ways in which schemas are tied. The first works in terms of a relationship between a specific schema and one or more others; the second operates in terms of feature overlap. The various senses of the word can therefore be thought to be analogous to the spokes of a wheel radiating out from the hub (the prototypical senses). The end point of these “meaning chain” processes is that senses at the periphery might well have little in common, either with each other or with the central sense; they are merely related by virtue of the intervening members in the “meaning chain”. Now, Lakoff (1987) presents the case that one can make a choice as to whether or not these more specific schemas should be lexicalised (i.e., full specification of the lexical entry) or, alternatively, whether one should adopt a minimally specified entry where the more specific schemas arise as a result of the addition of information from the other words in the expression. Lakoff (1987) favours full specification, and the overall structure of over is therefore represented as a densely interconnected network of image schemata (see Lakoff, 1987, p. 436). Only through full specification, Lakoff (1987, pp. 422–423) claims, can the links between senses be emphasised. While Brugman and Lakoff’s analysis of over represents an impressive catalogue of the range of senses of an individual term, it is not clear whether the analysis takes us further than description of the extensive polysemy of the term (but see Harris, 1990, 1994). Coventry and Mather (2002) provide a critique of their analysis (see also Bennett, 1990; Kreitzer, 1997; Sandra & Rice, 1994), so here we confine ourselves to problems that apply generally to fully specified cognitive linguistic accounts of this type. As we mentioned earlier, the existence of prototype effects does not mean that the structure of representation in the lexicon is in terms of one (or more) prototype(s). Lakoff (1987) himself argues against such interpretations of prototype effects early on in Women, Fire and Dangerous Things, but surprisingly with the analysis of over every sense is directly lexically represented. Whereas minimally specified lexical entries are associated with the problem of failing to map onto the extensive polysemy apparent with spatial prepositions, fully specified accounts have the mirror image problem of requiring the addition of a set of principles to indicate which sense is being referred to in any context. Furthermore, although cognitive linguistic accounts

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Page 33 in the main are intended to offer a psychologically plausible alternative to the definitional accounts considered earlier, in practice full specification can be viewed as an extensive list of exceptions with the caveat that the exceptions are related to one another. However, as various authors have noted (e.g., Bennett, 1975; H. Clark, 1983; Johnson-Laird, 1987), it is always possible to subdivide the meanings of a word further and, in principle, a word can therefore have an infinite number of senses. The crucial psychological question is whether or not it is necessary to postulate more than one semantic representation for a word to account for the interpretation of the sentences in which it occurs (Johnson-Laird, 1987). More generally, we can challenge whether Lakoff in his analysis of over actually delivers on the important embodiment arguments he presents in theory. In particular, we can question Lakoff’s focus on geometric space as the fundamental structuring tool for both spatial and non-spatial domains. What Brugman and Lakoff have done is to classify geometric relationships between objects in the world and map these directly onto individual image schemata. For example, Lakoff treats contact versus noncontact, and whether the reference object is extended or not, as two features of the world that characterise different senses of over. They are thus claiming that there is a one-to-one mapping between geometric relations in the world and spatial language. The components that are viewed as discriminant geometric variables then constitute the different senses of over. In essence, this approach is no different to the simple definitional views considered earlier. We agree that embodiment should form part of any account of spatial language understanding, but we will take a rather different view of how it should influence that account in the second part of this book. EMBODIMENT, ACTION, AND SPATIAL LANGUAGE We have now reviewed several approaches to spatial language. We have brought into focus more general arguments about the need to ground meaning in perception, and about the issue of whether concepts and categories are definitional or inherently vague. However, whereas the approaches of Brugman, Lakoff, and Herskovits offer rich and valuable descriptions of the diversity of situations in which individual lexical items can be used appropriately, we are not convinced that they really explain the basic problem of how spatial language is used in realistic contexts. To begin with, it is not clear that lexicalising as many different senses as possible helps to explain the production and comprehension of spatial expressions. We will argue that minimal specification may still be a workable alternative to full specification so long as there are systematic principles to explain how the lexical entry can be flexibly bent and stretched in a context (see, for example, Pustejovsky’s, 1991, 1995, generative lexicon). The

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Page 34 alternative presented in its extreme form by Brugman and Lakoff is to try to avoid case accountability problems by having fully specified lexical entries and in effect putting every sense in the lexicon. As we have argued, this approach suffers from the problem that one needs to then specify how the appropriate sense is selected from the lexicon in each context where the word is used. Although the world is unlikely to be represented in terms of rigid, definitional constructs, the view that prototypes are themselves represented in some kind of radial structure in the head is itself open to challenge (cf. Armstrong et al., 1983; Barsalou, 1999; Margolis, 1994; Murphy & Medin, 1985; Roth & Shoben, 1983; ironically also by Lakoff, 1987). What is clear from Herskovits’s account is that spatial language usage depends on varied conceptualisations of the objects entering into spatial descriptions, but the account says little about how this conceptual knowledge actually comes into play. A second and more interesting issue concerns the nature of geometric representations of the spatial relations between objects. Although these accounts all invoke geometric relations, they do not consider what these representations look like, and how the visual system actually computes them. To ground meaning in perception requires an understanding of what the perceptual system delivers. While simple geometric constructs, such as enclosure or being higher than, have intuitive appeal as primitives in the semantics of spatial expressions, the notion that the visual system produces such limited representations will itself be questioned in the next chapter. Furthermore, we will examine recent approaches that attempt to link spatial language and perceptual processing more directly (e.g., Logan & Sadler, 1996; Regier, 1996; Regier & Carlson, 2001). As Jackendoff (1996) has argued, understanding the interface between different specialised modular systems provides the key to an understanding of a domain such as that of spatial language. For the third problem we return to the armchair occupied at the start of this chapter. What all the approaches considered thus far have in common is the assumption that spatial language refers to geometric positions of objects in space. Spatial prepositions are taken to provide information about the type of geometric relation or relations involved, and any other characteristics of the located and reference objects are largely ignored (Herskovits, 1986; Landau & Jackendoff, 1993; Talmy, 1985). Now, we do not deny that there is a relationship between spatial language and geometric relations in the scene being described, but we do question the completeness of any account that focuses on geometric relations exclusively. As we shall see in the second part of the book, there is abundant evidence that how objects interact with each other, the forces they exert on each other, and the conceptual relations between these objects are important influences on the comprehension and production of spatial expressions. One of our main aims is to provide a

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Page 35 functional geometric framework that puts geometric and other (extra-geometric) factors together to account for the situation-specific meaning of spatial prepositions. In the next chapter, we relate this argument to the so-called ‘‘what” and “where” systems in perception, and show that the approach presented is in line with recent work in perception demonstrating the flexibility and variety of the types of representation of the world perception delivers. SUMMARY We began this chapter with the assumption that spatial prepositions refer to the geometric positions of objects in space. We have considered the inadequacies of definitional accounts, both in terms of accounting for the range of uses of individual lexical items and also in relation to the assumptions such accounts make. We then considered fully specified accounts, in particular the approaches of Herskovits and Brugman and Lakoff. While we endorse many of the arguments Lakoff (1987) makes regarding the importance of embodiment, we showed that in practice the full specification of cognitive linguistic accounts offer no real advantages over the classical accounts Lakoff spends so much time demolishing. So we have now considered some of what has been said about saying in relation to the spatial prepositions of English. In the next chapter, we turn our attention to the role that seeing and acting play in determining the meaning and usage of the spatial prepositions.

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Page 37 CHAPTER THREE Grounding language in perception: from “saying” to “seeing and acting” We have to understand that the world can only be grasped by action, not by contemplation. The hand is more important than the eye … The hand is the cutting edge of the mind. (Jacob Bronowski, The Ascent of Man , p. 3) Defining the spatial relations that underlie the meanings of the prepositions covered in this book seems simple enough (from the point of view of one’s metaphorical armchair). However, it turns out to be surprisingly difficult to pin down what notions like “interior” and “higher than’’ actually mean. There are two sources to the problem. First, from a purely geometric standpoint the concepts are very broadly defined. As we have seen in the last chapter, there is a wide range of configurations in which we can describe something as in something else or on it or over it. This is because natural languages only encode a limited number of different spatial relations between objects and these have to cover the whole range of possibilities (Landau & Jackendoff, 1993). Consider again, for example, the range of configurations where in applies and those where it does not apply shown in Figure 3.1. What is geometrically in common between The tree in the pot and The flowers in the amber in (b) and (d)? Why can the racket be in the hand but not the head in the hat in (a) and (e)? Similarly, why can the man be in the car when he is only partly enclosed in (c) (where his arm is outside the car) but not in (f) (where his arm is inside the car)? 37

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Figure 3.1 Various configurations for which one can and cannot use in: (a) The racket is in the hand. (b) The tree is in the pot. (c) The man is in the car. (d) The flowers are in the amber. (e) *The head is in the hat. (f) *The man is in the car. One approach to the problem is to use coarse-grained geometries that represent only limited information about connections between regions of space, such as the region connection calculus (RCC) developed by Cohn and colleagues (Cohn, 1996; Cohn, Bennett, Gooday, & Gotts, 1997). We describe

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Figure 3.2 Different configurations of a pear and a bowl. In (a) one can describe the pear as in the bowl ; in (b) and (c) this is less appropriate. In (d) one can describe the light-bulb as in the down-turned socket. this approach in this chapter and compare it to other approaches derived from research on perception. We consider Ullman’s theory of visual routines (Ullman, 1984, 1996), the constrained connectionist modelling of Regier (1996), the spatial template approach of Logan (see Logan & Sadler, 1996), and the attention vector sum model proposed by Regier and Carlson (2001). The second and more fundamental problem concerns the scope of locatives. For example, in is described as a spatial relation, but does that fully capture what it denotes? Even in the most appropriate geometry it is difficult to explain why the pear in Figure 3.2(a) can be described as in the bowl , whereas the pear in 3.2(b) or 3.2(c) would not normally be described this way. There seems to be a geometric contradiction here: enclosure without containment in 3.2(b) and 3.2(c), and containment without enclosure in 3.2(a). We shall argue that the contrast arises because of differences in the functional or physical relations between pear and bowl in the two cases. And this contrast motivates the functional geometric framework we outline in the remainder of the book. We shall argue that the comprehension and production of spatial prepositions involves both geometric constraints of the type we have already touched upon and extra-geometric constraints, including

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Page 40 knowledge of the forces objects exert on each other over time. We introduce the notion of the functional geometric framework in this chapter and consider how hybrid relations involving both geometric and extra-geometric relations might help capture the meanings of a range of spatial prepositions. We shall also consider the literature on cognitive representations of spatial and physical information of the kind used to support action. This literature is relevant because it concerns how people perceive complex scenes in terms of their dynamics and kinematics. Crucially, much of the research suggests that our perception of scenes and events lead to representations that encode more than just geometric information; the representations also reflect information about the forces that apply between objects in the scenes. And it is just such information that needs to be incorporated into the functional geometric framework needed for spatial prepositions. We begin with the general question of the geometric representation of locatives such as in. We choose in because containment presents a challenge in terms of geometric specification. It also illustrates the general point that specifying the geometry of locatives is much more complicated for three-dimensional arrangements than for the twodimensional arrangements commonly referred to in work in this area. Then, we consider how this geometric specification relates to perception of visual scenes and discuss various attempts to model the geometry of simple two-dimensional scenes to account for people’s judgements of the interpretation of locative expressions. Finally, we turn to the vexed question of how to introduce function into such representations and examine what is known about the perceptual and cognitive representations supporting action. THE GEOMETRY OF SPATIAL RELATIONS Crangle and Suppes (1989; see also Suppes, 1991) point out that relations like enclosure and contiguity presume geometric invariants that prove difficult to define within a standard point and line geometry. In turn, this makes it difficult to say precisely what is meant by enclosure or contiguity in the definitions of the prepositions. To overcome the problem, Cohn and colleagues (e.g., Cohn et al., 1997) have developed a qualitative geometry of space called the region connection calculus, which treats “regions of space” as fundamental (Cohn, 1996). This qualitative geometry, like Allen’s qualitative calculus of temporal relations (Allen, 1983), is well designed for capturing semantic distinctions (Aurnague, 1995). And as we shall see, it goes some way towards explicating the differences between the scenes in Figure 3.2. We will concentrate mainly on how the geometry handles enclosure and containment. Cohn et al. (1997) define spatial relations such as enclosure in terms of just two primitives: connection and convexity. Connection is a

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Page 41 broadly defined relation that covers everything from simple contact or overlap between regions to their identity. Convexity, on the other hand, relates to the presence in a region of interior spaces, defined in relation to what Cohn calls the convex hull of the region: the smallest convex region to also include the region in question. If one overlays a region’s convex hull on the region itself, then the difference between the two (i.e., their complement) corresponds to the concavities in the region, the places that could contain other regions. An important aspect of the geometry is how it can differentiate between different kinds of concavities, and hence insides, of objects. According to the calculus of Cohn et al. (1997), there are a number of ways that one object can be represented as in another object or in other objects, which reflect different degrees and kinds of enclosure. The strongest form of enclosure is when one region is topologically inside another—that is, when the region is completely surrounded by the other, as in The jam in the closed jar or The flowers in the amber (see Figure 3.3d). However, topological enclosure is not often found in the real world. For example, as soon as one takes the lid off a jar of jam, the jam is no longer topologically enclosed. Consequently, there are various weaker kinds of enclosure defined by the calculus that depend on different ways that an object can have an inside. For instance, one region may be in another when it is a subpart of or overlaps with the other’s convex hull, as defined in the manner described above. Thus the black circle is in the grey region in Figure 3.3. In (b) it is geometrically enclosed by the convex hull as with water in a pool or tea in a cup. In (a) it is only partially enclosed, as with The tree in the pot shown in Figure 3.1(b). The notion of a convex hull can also be applied to groups of objects. For example, when an island is in an archipelago, its region is enclosed by the convex hull of the whole group of islands in the archipelago, as part of their scattered inside (see Figure 3.3c). This kind of enclosure is weaker than enclosure within the region defined by the convex hull of a single object. For example, a scattered inside cannot contain a liquid. Hence, whereas a tree can contain a bird (e.g., The starling is in the tree ), it could not contain liquid in the same sense. Thus when one says that There is water in a tree , the water has to be topologically enclosed by the substance of the tree itself. These basic forms of enclosure apply to both two- and three-dimensional regions. However, we need to define additional constraints for three-dimensional regions if the geometry is to explain the use of in. For example, if anything enclosed by the complement of the object’s region and its convex hull is necessarily in the object, then the fly in Figure 3.3(e) would have to be in the cup. Clearly, it would not be described this way. To get around such problems, Cohn, Randell, and Cui (1995) define additional, more refined forms of enclosure for three-dimensional regions. For instance, they draw a contrast between tunnel and containable insides, which underlies the

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Figure 3.3 Different forms of enclosure according to Cohn et al. (1997). distinction between putting a finger into the handle of a teacup as opposed to pouring the tea into the cup (Figure 3.3e). If for a three-dimensional object something is not enclosed topologically or by one of these specialized insides, such as the containable or tunnel inside of the cup shown in Figure 3.3(e), then it only qualifies for the weakest kind of enclosure, which is insufficient to support the appropriateness of in as a description for threedimensional objects. Armed with this array of basic geometric relations, one can define different degrees of enclosure to reflect different degrees of spatial constraint in

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Page 43 the real world. The system can even deal with some of the difficult cases shown in Figure 3.2 in which a pear can be described as in a bowl even though it is not within the convex hull of the bowl. For example, for Figure 3.2(a), we can put together two enclosure relations. First, the located object (i.e., the pear) displaces a region that is in a scattered inside defined by the convex hull of the other fruit. Second, this latter region partially overlaps the containable inside of the bowl. So, by application of transitivity, the located object (i.e., the pear) becomes weakly enclosed by the reference object (i.e., the bowl). Note that this provides a realisation of the pragmatic tolerance principle Herskovits (1986; see p. 26 above) proposed to account for similar cases. Thus, Cohn and co-workers’ qualitative geometry captures a number of different situations where one can say object A is in object B . However, is there any psychological evidence to support this account? In other words, do regions and their convex hulls constitute basic perceptual categories? A second question is whether this intuitively satisfactory geometry can by itself account for the full range of uses of prepositions such as in. In other words, is the in relation purely geometric or are there other features of the situation that determine our use of the preposition? Let us start by considering perceptual approaches to spatial relations. PERCEPTUAL APPROACHES TO SPATIAL RELATIONS Visual routines Explaining how we perceive complex spatial relations like containment or support has proved much more difficult than one might imagine. Despite the great advances in understanding low-level perceptual systems, including their neural basis, higher-level perception of complex relations between objects is still not very well understood. One of the most influential early attempts to look at the perception of spatial relations such as enclosure is that of Ullman (1984, 1996). He was especially interested in trying to understand how the visual system can compute at a glance whether one object is inside or outside another. He argued that perceptual processing of this sort requires specialised visual routines different from the basic processes of low-level vision. In fact, he argued that these routines operate on the output of the low-level processes, what he termed the base representation , to yield a more flexible incremental representation of the visual scene. Ullman’s visual routines are constructed out of a limited set of operations strung together in time. As an illustration, consider how the visual system might work out at a glance that one figure (e.g., the x in Figure 3.4) is either inside or outside another (e.g., the regions defined by the contours y and z in Figure 3.4). Despite the intuitive simplicity of this task, it turns out to be

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Figure 3.4 Schematic representation of the inside/outside problem described by Ullman (1984, 1996). beyond the capacity of the low-level parallel perceptual processes assumed to yield the base representation (Minsky & Papert, 1969). Instead, Ullman proposed a routine based on the idea of starting at the x and then progressively colouring in the region around the x until a boundary contour is encountered. If in the end any point beyond the scene remains uncoloured, then the x must be inside the contour (as in the case of contour y in Figure 3.4), otherwise it must be outside the contour (as in the case of contour z in Figure 3.4). Interestingly, like Cohn and colleagues’ RCC system, this routine works on regions of space and is constrained to capture only coarse-grained topological relations between objects. Ullman’s work is important because it raised a number of questions about what it means to talk of a perceptual representation of a scene (see also Lee, Mumford, Romero, & Lamme, 1998). As he argued, the base representation that is automatically delivered by the visual system probably does not contain information about spatial relations such as inside/outside . Rather, these have to be derived through visual routines. Furthermore, even though some routines may almost always be applied to a scene, they are in principle optional and subject to attention control. As a consequence, we may often

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Page 45 arrive at different perceptual representations for the same scene depending on the task in hand. As we shall see later, there is even some question as to whether the perceptual representation we end up with might not also contain other kinds of information about the physical relations between objects. Ullman’s basic arguments about the nature of these high-level perceptual routines have had considerable impact on psychologists’ views about what the perceptual system actually delivers and how this might relate to representing complex spatial relations. For example, his filling-in routine has been implemented in a model by Regier (1996), which was designed specifically to address the nature of the spatial representations underlying such prepositions as in, on, and over. Regier’s model used a constrained connectionist network to learn to discriminate between dynamic scenes portraying the different spatial relations. The scenes were presented as short “movies” in which a located object moved about a two-dimensional array relative to a fixed reference object. The system then had to learn to map positive instances of scenes involving different spatial relations between located and reference objects onto the appropriate spatial prepositions. An important feature of the model was how constraints were imposed on the input array before the information was passed to the connectionist network proper. These constraints gave the network information about such things as whether, at various points in the movie, the located object overlapped with the reference object. This is crucial for learning prepositions like in. Other constraints yielded information about the relative orientation of the centre of mass of the located and reference objects. This is crucial for learning prepositions like above (see discussion of his later attention vector sum model below). In implementing the constraints, Regier used some of the principles proposed by Ullman, and also dealt primarily with regions of space rather than points and lines. Regier’s (1996) model was an impressive attempt to define the representation of spatial relations in a perceptually well-motivated fashion because the model respects known characteristics of the visual system. However, the model is limited in terms of the “visual” inputs that it can actually deal with. For example, with in it could only learn from scenes containing objects associated with convex two-dimensional regions. As we have seen when discussing Cohn and co-workers’ region connection calculus, most of the interesting examples of containment involve nonconvex regions and adding the third dimension greatly increases the geometric complexity of enclosure and containment. Regier did recognise that he would have to take into account the convex hulls of his regions if he were to extend the system to deal with a wider range of visual scenes. However, there is no attempt to deal with the serious problems raised by moving into three dimensions. We shall consider some of the more detailed aspects of Regier’s model and its more recent extensions later. For the moment, we describe a somewhat different

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Page 46 perceptually motivated account of the representation of spatial relations by Logan and colleagues, which is based on what they call spatial templates. Spatial template construction The idea that there may be a common spatial representation system underlying the apprehension of both spatial language and spatial relations has been gaining popularity recently (see, for example, Bryant, 1997). The basis for this claim largely resides in a series of empirical demonstrations that show that judgements of spatial relations and judgements of the appropriateness of spatial prepositions to describe spatial relations are highly correlated. We can begin with an examination of the framework nicely summarised by Logan and Sadler (1996; see also CarlsonRadvansky & Logan, 1997) and developed more recently by Regier and Carlson (2001). Logan and Sadler claim that spatial templates underlie the apprehension of spatial relations and spatial prepositions. To work out whether a spatial relation applies in a given situation, it is proposed that a spatial template (or templates) representing regions of acceptability for the relevant relation are mapped onto a visual scene. The template is a representation that is centred on the reference object and aligned with the reference frame imposed on or extracted from the reference object. A useful way of thinking about spatial templates is to imagine a camera lens that can be imposed on the visual scene in a number of ways. On the viewfinder imagine that there is a grid, which, for the sake of argument, consists of 7 columns and 7 rows, each spaced equally apart (see Figure 3.5). Therefore, there are 49 different points on the grid, and each point can be represented by a two-point value ( x , y), where x is a coordinate point on the horizontal axis and y is a point on the vertical axis. Imagine

Figure 3.5 Example of a spatial template for above , adapted from Carlson-Radvansky and Logan (1997). G = good region, B = bad region, A = acceptable region.

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Page 47 further that the lens has been zoomed in on the visual scene such that the reference object is centred on the grid at the midpoint (point (4, 4)). So, if one places an object in any of the squares around the reference object, one can get an acceptability judgement for each spatial relation (e.g., in, on, over), and the set of acceptability judgements can be used to define a template for each of these relations. Hence for Logan and Sadler (1996), different spatial relations are associated with different spatial templates, each containing graded ratings across their coordinates. Computing goodness of fit is a relatively complicated matter and need not concern us for the moment. What is more important is the notion of how a spatial template is established, and how spatial templates map onto the myriad of types of relation associated with individual lexical items considered in the previous chapter. To map a spatial template onto a visual scene, it is necessary in some way to bind the arguments of the relation in the stored spatial template to the objects in the perceptual representation. In other words, what Logan and Sadler call spatial indexing is required to establish the correspondence between a symbol and a percept. Once spatial indexing has taken place, reference frame adjustment is required to extract the relevant reference frame from the reference object, to choose a scale and a direction as appropriate. Going back to our camera lens analogy, the camera needs to be moved around so that the picture is the right way up, and the camera needs to be zoomed in as appropriate to achieve the right scale. We can see how this kind of approach operates by considering consistent findings across a range of experimental paradigms. For example, Logan and Sadler (1996; see also Hayward & Tarr, 1995) report the results of four experiments that they argue support the spatial template framework. In a production task, participants were presented with a visual scene with the reference object (in this case a box) centred at the midpoint on the scene, and participants were asked to draw an x [above/below/to the left of/to the right of] the box . The results produced consistent patterns across participants that were replicated in a rating paradigm in which participants had to rate the appropriateness of each of the 49 coordinate points on a grid imposed over the visual scene to map onto the x is [above/below/to the left of/to the right of] the 0 (a zero was used as reference object in this case). The results of these studies show that the most appropriate region for above , for example, is directly higher than the reference object. When the located object was positioned at the same point on the y axis, but moved left or right of the centre point of the reference objects on the x axis, then the ratings went down. Similarly, moving the located object downwards on the y axis was found to reduce appropriateness ratings. Therefore, the points marked in the production study map onto the highest ratings given in the rating study. A further experiment involved participants rating the similarity in meaning of word

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Page 48 pairs using a multidimensional scaling approach. The results of this study again correlated with the results from the rating study just described. The similarity relations mapped onto the overlap in ratings for different terms and coordinates; therefore, Logan and Sadler argue that this provides evidence that people are indeed using spatial templates to compute relations. Another interpretation of the results in Logan and Sadler’s (1996) first three experiments is that visual routines are employed to check the different types of relations. For example, one can imagine a visual search for an above relation that involves moving from the reference object to the located object. As Ullman (1984, 1996) argued, visual routines take time to apply in contrast to basic perceptual processes. Therefore, if a visual routine was applied, it should be predicted that the time taken to make the judgements should correlate with the distance between x and y. On the other hand, if multiple spatial templates are imposed on a scene in parallel, it is argued that the distance between located object and reference object would not affect the time to make the judgement. In a reaction time study designed to test directly between these options, Logan and Sadler indeed found no distance effects, providing some support for the existence of spatial templates. Now, you may be thinking that the spatial template approach sounds like a more precise geometric specification of the cognitive linguistic approach to spatial language considered in the last chapter. Indeed, spatial template theory directly represents prototype effects for each spatial relation, and Logan and Sadler (1996, p. 499) claim that ‘‘in cases of polysemy where there is more than one conceptual representation associated with a given word (e.g., over; Lakoff, 1987), there is a different spatial template for each conceptual representation”. Therefore, while spatial template theory grounds words like above more directly in perception, the issue of how one selects the appropriate spatial template for a preposition in context from the large number of different templates that would be presumably required for prepositions like over remains unresolved. So spatial template theory finds itself sharing some of the same rocky ground as the fully specified cognitive linguistic accounts, such as Brugman and Lakoff’s analyses of over. The attention vector sum model A slightly different approach within the perceptual tradition has been proposed in a recent model described by Regier and Carlson (2001). Their attention vector sum model (hereafter AVS) can be regarded as a natural development of spatial template theory, and has been designed initially to deal with the prepositions above , below , left, and right. However, whereas spatial template theory provides a description of the regions on a template, Regier and Carlson have developed a computational model to compute the relations for the same set of data that Logan and Sadler (1996) used, as well

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Page 49 as data from a further range of experiments conducted by Regier and Carlson. As the name suggests, AVS takes into account the role of attention in determining a spatial relation and has much the same character as one of Ullman’s visual routines. In the AVS model, the direction indicated by a spatial relation is defined as a sum over a population of vectors that are weighted by attention. Using this method, spatial templates are conceptualised as a vector representation rather than an axial representation (à la Logan and Sadler) and, as a result, the model successfully accommodates a series of factors that Regier and Carlson show empirically to impact upon the appropriateness ratings given by participants across scenes varying the shape of reference object and the position of located object. The AVS model produces acceptability judgements indicating how well a given term describes the relationship between a located object, always schematised to a single point, and a reference object with two-dimensional extent. The model works by focusing an attentional beam on the reference object (labelled LM in Figure 3.6) at the point that is vertically aligned with the closest part of the located object (labelled TR; see Figure 3.6a). As a result, parts of the reference object nearest to the located object are maximally attended and more distant parts are attended less. This produces a distribution of attention across the reference object. In addition, vectors are defined that are rooted at positions across the reference object and that point to the located object (see Figure 3.6b). This results in a population of vectors, which are weighted by the amount of attention being paid at the location of their roots (see Figure 3.6c). The model then computes the sum over this population of weighted vectors, yielding an orientation (see Figure 3.6d) that can be compared with the upright vertical (see Figure 3.6e). The relatively simple computational architecture maps onto an impressive array of empirical data, and is also supported by evidence of population vector encoding in several neural subsystems (e.g., Georgopolous, Schwartz, & Kettner, 1986). Specifically, in a series of seven experiments, Regier and Carlson show how the AVS model returns acceptability ratings that closely fit the data produced regarding the relative influence of three main factors: proximal and centre-of-mass orientation, the grazing line, and distance. These factors are discussed more fully in Chapter 5. Furthermore, the model out-performs a series of other models that Regier and Carlson also test against the data, including a modification of the model produced by Gapp (1995). The AVS is an impressive model, but as Regier and Carlson recognise, it suffers from several limitations. Notably they acknowledge that the AVS does not take into account extra-geometric variables, and they are currently developing their model to try to do this. We will pick up on this issue in Chapter 7. Furthermore, the AVS model currently only deals with a few prepositions, only operates with two-dimensional abstract shapes, and does

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Figure 3.6 The attention vector sum model (adapted from Regier & Carlson, 2001). not deal with different shapes of located object. However, despite these limitations, the model produces methods of computing relations between objects that do map onto real data and, as such, the model provides a valuable means of computing acceptability judgements which has the potential to extend to (at least) some other terms. Earlier, we showed how Cohn and colleagues’ work offered a promising geometric formalisation for spatial relations. The AVS model specifies a kind of perceptual routine for dealing with the above relation, for example. And, to the extent that AVS takes into account attention, it goes beyond a purely geometric account of the relation. However, such accounts still fail to deal with the geometric contradictions discussed at the beginning of this chapter and in the last chapter. Recall, there was a scene we presented in Figure 3.2 above in which a pear is not geometrically enclosed by a bowl (Figure 3.2a), yet we can

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Page 51 naturally say The pear is in the bowl . This was contrasted with other scenes in which the pear is geometrically enclosed (Figure 3.2b and 3.2c), yet we would not normally describe it as in the bowl. You might argue that part of the problem relates to the container in 3.2(a) being upright, while the container in 3.2(c) is inverted. However, Figure 3.2(d) depicts much the same geometry for a light-bulb and a down-turned socket, yet here there is no problem in describing the light-bulb as in the socket. So what is the crucial difference between these situations? Whereas the location of the pear in Figure 3.2(a) and of the bulb in Figure 3.2(d) is controlled by the bowl and the socket, this is not the case for the pear in Figure 3.2(b) and 3.2(c). In other words, if one were to move the bowl in 3.2(a) or the socket in 3.2(d), the pear and bulb would be expected to move with them; but, if one were to move the bowl in 3.2(b) or in 3.2(c), under most circumstances the pear would not move with it. We will argue that spatial relations such as containment underlying spatial prepositions such as in involve both geometric relations (e.g., enclosure) and extra-geometric relations (e.g., location control), which come together in what we shall call a functional geometric framework. Furthermore, we will argue that such a framework underlies a range of spatial prepositions and that it accounts for part of the problem in producing a simple geometric or visual perceptual account of their meaning. THE IMPORTANCE OF ACTION: EXTRA-GEOMETRIC RELATIONS CONSIDERED The function of spatial language As should be clear by now, when theorising in one’s metaphorical armchair it is tempting to assume that spatial prepositions refer to the positions of objects in space. The corollary of this is that the “content” a spatial preposition contributes to the meaning of an expression (whether couched in linguistic or perceptual terms) is the set of geometric positions the preposition refers to. However, as Marr (1982) articulated most clearly in the case of vision, the most important level of explanation required of a process (such as vision) is to ask what that process is for (what Marr termed the computational theory level of explanation). Thinking about what spatial language is for takes us back to the embodiment issues we discussed in the last chapter. Of course, spatial language allows one to locate objects in the environment. It is well recognised that spatial language also provides us with information about changes in the positions of objects over time (e.g., directional prepositions). However, less obviously, spatial language tells us that objects will remain in the same relative positions over time, and that objects may or may not be in a position to interact with each other. Describing where an object is

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Page 52 located goes beyond the description of a geometric position of objects as a snapshot in time. Understanding spatial language is also about the purpose that location serves for the users of that language. For an organism to act in the world, knowing that objects are likely to remain in the same relative positions over time is crucial. Furthermore, knowing that particular objects afford particular functions has essential survival value. We might, therefore, expect spatial language to be as much about how objects interact with each other as it is about the abstract positions of objects in Euclidean space. There is a long tradition in vision of approaches that place action as a central driver of the visual process. For example, Gibson (1950, 1966, 1979) placed movement and action as the central pillars underlying his “ecological” approach to vision. Indeed, in his later work (Gibson, 1966, 1979) he went as far as to claim that animals detect “affordances” in their environment—for example, a flat tree stump affords sitting on—and that these affordances are directly perceived. In relation to the perception of causality, Michotte (1963, p. 3) observed that “the phenomenal world does not consist of a simple juxtaposition of ‘detached pieces’, but a group of things which act upon each other and in relation to each other”. While the influence of so-called “functional relations’’ (to use Michotte’s term) has been recognised for quite some time in the spatial language literature [see, for example, the discussion of at in Miller and Johnson-Laird (1976) or in Herskovits (1986); see also Ullmer-Ehrich, 1982], it was not until the late 1980s that the importance of functional relations between objects began to receive more attention and to take on a more prominent role. In particular, Garrod and Sanford (1989), Talmy (1988), and Vandeloise (1991, 1994) made similar arguments that the forces objects exert on each other are important for the meaning of locatives (in the case of Garrod & Sanford, 1989; Vandeloise, 1991) and a range of other syntactic categories (Talmy, 1988). We can refer to the set of factors other than geometric routines as extra-geometric factors, as they go beyond the types of geometric relations we have thus far considered. The functional geometric framework we will develop in the remainder of the book combines both geometric and extra-geometric constraints to establish the situation-specific meaning of spatial expressions. Functional relations and force dynamics Consider again the case of in and on. Location control has been proposed as a component of the meaning of both of these terms (e.g., Coventry, 1998; Coventry, Carmichael, & Garrod, 1994; Garrod, Ferrier, & Campbell, 1999; Garrod & Sanford, 1989; Vandeloise, 1991, 1994). For an object to be in or on another object, the reference object needs to be able to constrain the location of the located object. One of the consequences of enclosure (in most cases) is that enclosure affords location control. For example, Garrod et al.

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Page 53 (1999) define a relation of functional containment for in and functional support for on, both of which involve the constraint of location of the located object over time by the reference object. Similarly, Vandeloise (1991, 1994) argues that the relationship between container and contained in his account implies that the contained object moves toward the container, and that the container controls the position of the contained object. According to these accounts, “inness” is a hybrid relation that involves both a geometric containment relation and a certain kind of control relation whereby a container constrains the location of its contents. For a person to be in a queue means that the queue and its movement predict that person’s location; for a pear to be in a bowl means that when the bowl is moved the pear should move with it. At the end of the subsection on “The attention vector sum model” (see p. 51), we showed how the location control relation can explain the difference in perceived ‘‘inness” for the pear in Figure 3.2(a) as compared to Figures 3.2(b) and (c). It can also explain the difference between the situation in Figure 3.2(d), with the light-bulb, and in Figure 3.2(c), with the pear, since the socket controls the location of the bulb (i.e., when the socket is moved the bulb should move with it) but the bowl does not control the location of the pear. Similar problematic examples can be explained in the case of on. Thus, if a picture is on a wall or a light on a ceiling, then the wall and ceiling indirectly stop the picture and light from falling; if a kite is on a string , the string functionally supports the kite against the force of the wind. So the cases of in and on illustrate how the two components, the functional and the geometric, combine to define a functional geometric relation. In these cases, the geometric constraints of enclosure and contact with a surface are directly associated with varying degrees of location control; geometry and function are inextricably linked for in and on. Note also that the geometric component for in and on admit to different degrees of enclosure or contact, which has implications for location control. When objects exhibit only weak enclosure, in Cohn and colleagues’ sense, then firm evidence of location control is required to support an in relation. For example, whereas the pear in the bowl is only very weakly enclosed in Figure 3.2(a), it is firmly held by the other fruit and this means that the bowl can be seen to be controlling the location of the pear. However, when the evidence for location control is weak, there needs to be a strong geometric enclosure to support the in relation. The same is true for the on relation. A light can be on the ceiling even though it may only be indirectly in contact with the ceiling through a cord, just so long as it is clear that the ceiling supports the light. Force dynamics refer to how entities interact with respect to force, and includes such concepts as exertion of force, resistance to such force, the overcoming of such resistance, blockage of the expression of force, and the

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Page 54 removal of such blockage. For Talmy (1988, p. 50), force dynamics “emerges as a fundamental notional system that structures conceptual material pertaining to force interaction in a common way across a linguistic range: the physical, psychological, social, inferential, discourse, and mental-model domains of reference and conception”. Underlying all force dynamic-patterns is the steady-state opposition of two forces. These involve different types of interaction between what Talmy (1988, p. 53) terms the agonist (the focal force entity) and the antagonist (the force element that opposes it). The salient issue in this interaction is whether the agonist is able to manifest its force tendency or, on the contrary, is overcome. The antagonist is considered for the effect that it has on the agonist, effectively overcoming it or not. Although Talmy originally applied force dynamics for verbs of motion, one can easily envisage how force dynamics may come into play in spatial contexts. With the assumption of a gravitational field, one can view an object in a container as an agonist with a tendency towards motion, and the container as the antagonist with a stronger force strength required to hold the agonist stationary and in place. Thus our previous work (e.g., Coventry et al., 1994; Garrod & Sanford, 1989; Garrod et al., 1999), and that of Vandeloise (1991, 1994) and, by extension, Talmy (1988), agrees on the importance of location control/force dynamics as an important constraint on the comprehension and production of in and on. Building on this earlier work, we next turn to overview the functional geometric framework. THE FUNCTIONAL GEOMETRIC FRAMEWORK The functional geometric framework aims to capture the representation of spatial relations not just in terms of how viewers see such relations, but also in terms of how they act on the world they see, and in terms of how objects meaningfully interact in that world. Here we spell out the components of the framework before considering its perceptual origins. The functional geometric framework involves two types of component, which, in combination, provide the material that enables the establishment of the situation-specific meaning of a range of spatial prepositions. These components are displayed in Figure 3.7. First, as in any other account, there is the geometry of the scene being described. Where objects are located in space is clearly central to the process of how one describes location using language. Indeed, earlier in the chapter we explored examples of ways of computing geometric relations using what we have termed geometric routines (such as the AVS model of Regier & Carlson, 2001), similar to those proposed by Ullman for complex geometric relations. Second, there are various extra-geometric factors that enter into the meaning of spatial terms, which can come from two sources. One source of

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Figure 3.7 Component parts of the functional geometric framework. extra-geometric information is what we shall call dynamic-kinematic aspects of scenes, such as those involving location control. We will suggest that these extra-geometric properties can be captured by reference to dynamickinematic routines. Another source of extra-geometric information central to the comprehension and production of spatial prepositions is general knowledge of the functions of objects and how they usually interact with each other in particular situations. Contrary to the view that spatial prepositions rely on only coarse-grained “schematised” (Talmy, 1983) properties of the objects involved in the spatial expression (H. Clark, 1973; Landau & Jackendoff, 1993; Talmy, 1983), we will argue that what objects are fundamentally influences how one talks about where they are located. In the next chapters, we review evidence for the importance and existence of each of these components. We set the stage by considering these components individually; in particular, we address the issue of what the approach buys a language user vis-à-vis acting and communicating in the spatial world. Geometric and dynamic-kinematic routines We have already argued that comprehension and production of spatial language involves both geometric routines and dynamic-kinematic routines. Where objects are located (computed using geometric routines), and how objects are interacting or may interact with each other (computed using dynamic-kinematic routines), in combination influence how one selects and interprets spatial expressions. First, let us consider what might motivate encoding such complex relations in language. Then, we can consider how they might come about in the first place. Recognising spatial relations between objects enables us to build mental models of situations and allows us to draw spatial inferences about them (Johnson-Laird, 1983). Geometry alone does not support many spatial inferences. If one knows that X is in Y and that Y is in Z, then one can sometimes draw the geometric (topological) transitive inference that X is in Z.

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Page 56 However, there is only a limited number of geometric inferences associated with spatial relations, such as in or on, and they are often both not secure and of no particular consequence. For example, a golfer may have a golf club in his hand and his hand in a glove, but we would not necessarily want to conclude that the club was in the glove. Similarly, if we know that X is on Y and that Y is on Z, then we can sometimes infer that X is on Z. However, whereas this may be true if X and Y are two books on a table Z, it would not hold if X were a book, Y a table and Z the floor. By contrast, functional geometric relations such as containment or support lead to a much wider range of spatial inferences. For example, if Y contains X, then we know that Y controls the location of X. So, we know that when Y moves X will move with it or, if we want to move X independently of Y, then we will have to remove X from Y beforehand. Similar spatial inferences can be made on the basis of the support relation. For instance, if we know that X is on a support Y, then we can infer that if Y is removed, then X will fall to the ground. Hence, functional geometric relations license a range of spatial inferences that go beyond what can be inferred from the geometry of the situation alone (see also Talmy, 1988). That these inferences depend upon the physical properties of our world as opposed to the geometry of that world becomes apparent when we consider extraterrestrial situations, such as being on a satellite without gravity. In the case of projective terms like left and below , Friederici and Levelt (1990) tested two science astronauts who were part of the crew on the D1 Spacelab mission in 1985. The main finding was that, although gravity was absent, the participants were still able to assign reference frames in space using head– retinal coordinates as the primary references (see Chapter 5). So, with regard to the use of reference frames, and the assignment of geometric axes in the spatial world, the lack of a main gravitational axis does not prove problematic. However, for dynamic-kinematic routines the prediction is rather different (Figure 3.8). It might be expected that location control inferences for containment on the satellite would not be the same as on earth. Without gravity, location control is only guaranteed when there is full topological enclosure. For something to be in something on a satellite is therefore rather different than for it to be in something on earth. And it is not clear what it means for something to be on something in a satellite unless it is attached to another surface, because support inferences are no longer valid on the basis of contact alone. Hence, the geometry of the situation in itself does not determine the spatial inferences that arise from a functional geometric relation. Long-term satellite dwellers would soon come to adopt a somewhat different geometric definition for prepositions like in and on. So one of the main benefits of a functional geometric representation is that it supports a range of real-world inferences that go beyond the simple geometry of the situation being represented. But where do such relations

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Figure 3.8 Is the pear in the bowl? come from? An attractive possibility is that they arise from learning about interactions with the physical world. As Michotte (1963, p. 3) originally argued, “the regulation of conduct requires a knowledge of what things do or can do and what living creatures (and ourselves in particular) can do with them”. For instance, imagine how a child learns to control the location of the liquids that she drinks, paddles in, or washes with. First, the child will learn to identify objects that can be used to contain liquids, such as cups or pails or any object that has a containable inside. Then the child will learn how to transfer the liquid into the region associated with the containable inside of those objects (e.g., by pouring the liquid into them). Now, imagine the child learning to control the location of her toys. Again, she will find she can insert objects into other larger objects that also possess containable insides. Eventually she will come to learn an association between the goal of controlling the location of objects in the world and the geometry of enclosure. Objects that are geometrically enclosed according to the kind of scheme discussed by Cohn and colleagues are subject to location control by the objects that geometrically enclose them. As a result, certain kinds of geometric configurations will become especially significant for the child because they play an important role in determining how objects interact with each other. What are the implications of the link between an extra-geometric spatial relation and the geometry of the situations that it comes to be associated with? First, the function (e.g., location control) can be said to define the range of geometric configurations that support that function. Those configurations that best support location control of this kind can then be regarded in some sense as prototypical configurations or prototypes for the geometry of “inness” (although it does not necessarily follow that they are lexicalised as such). Hence, for prepositions such as in, location control and geometric

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Page 58 enclosure are highly correlated. The result of this is that the configurations associated with the function (in this case location control by virtue of enclosure) may be geometrically diverse. For instance, in the case of containment, they can range from the reference object minimally surrounding the located object (e.g., soup in a shallow bowl) to complete enclosure of it (e.g., beans in a sealed can). Later in Chapter 8 we shall argue that different limits on this diversity might help to explain some of the differences between the ranges of meaning of locatives in different languages. Projective prepositions also appear to be subject to similar constraints. For one object to be over or above another object involves a more elaborate version of the geometric notion ‘‘higher than”, which, as we have seen, can be computed rather nicely using the AVS model (Regier & Carlson, 2001). As many researchers have shown, the optimal “higher than” relation is where the located object is positioned directly higher than the reference object within the bounding box of the reference object (among other constraints; see Hayward & Tarr, 1995; Logan & Sadler, 1996; Regier & Carlson, 2001). Just as enclosure and location control are associated with the prototypical in relation, a prototypical over or above relation is constrained not only by the geometry of being “higher than”, but also by potential dynamic interactions associated with gravity. That objects fall to the ground is a fundamental property of the world we live in. So it is not surprising that it enters into how we talk about spatial relations such as over and above . And, as in the case of in or on, the choice of geometric routines is going to be constrained by knowledge of the world. As we pointed out at the beginning of this chapter, there are potentially an infinite number of geometric relations that could be used to carve up the world (Crangle & Suppes, 1989). However, we suggest that the ones languages encode—and there are only a limited number across all languages—are drawn from just those relations that provide the most constraints in terms of interacting with the world. Although we have suggested that the geometric routines associated with superior and inferior relations are themselves influenced by extra-geometric constraints, there are also separate extra-geometric factors associated with the use of these prepositions. For an umbrella to be over someone is saying much more than the umbrella is higher than that person; it is saying that the umbrella is in a position to protect that person from getting wet. Yet again, the child interacting with the world must be able to understand that objects have specific functions, and that these functions may generalise across a range of types of objects and situations. An umbrella can protect someone from getting wet and, when it is not in the correct position to protect that person, it is not fulfilling its function. Therefore, while the geometric routine of the type proposed by Regier and Carlson is one type of routine useful for these terms, an additional set of extra-geometric routines is required to calculate the degree to which objects are fulfilling their protecting functions,

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Page 59 for example. Furthermore, while the geometric and extra-geometric routines for in and on may be highly correlated, as we shall see in the next chapters, for superior and inferior relations it would appear that these routines may well be independent. Other projectives, like in front of and behind, involve knowledge about the likelihood with which located objects and reference objects are able to interact with one another. John is behind the wheel indicates that John is in control of the vehicle. Similarly, The soccer player is in front of goal indicates that he is in a position to potentially score a goal. This means that knowledge of the likely path of the ball should the soccer player strike the ball is important in establishing whether he is in fact in front of goal. Proximity terms like at are also subject to the same constraints. The archer is at the target can mean that, should the archer launch the arrow, the archer is in a position to hit the target. As a final example of the importance of dynamic-kinematic routines, consider the preposition between. According to the Oxford English Dictionary, for one object to be between two others means that it is at a point in the area bounded by two or more points in space. However, just like the other examples we have given, between also has a dynamic-kinematic component to its meaning, which involves separating or keeping apart either physically or mentally (Coventry & Garrod, in press). For example, The referee moved between the boxers indicates that the referee is trying to keep the boxers apart so that they do not make contact with each other. Thus this dynamickinematic routine for between is likely to involve judgements about the ability of the located object to keep the reference objects at bay, which requires the estimation of forces applying between objects. So we have argued that two different types of routine are implicated when trying to comprehend a range of spatial prepositions. We now turn to consider one further set of constraints that are central to the functional geometric framework. These constraints have to do with knowledge of objects: what they are and how they interact with each other. As is nicely encapsulated in the title of a paper by Carlson-Radvansky, Covey, and Lattanzi (1999), we now examine “what effects on where”. Object knowledge: stored representations and contextual factors guide routines Routines, both geometric and extra-geometric, are constrained by what objects are or, more precisely, what they are seen to be. There are two ways in which what we identify objects as being may influence the relationships we judge to hold between those objects. First, it may affect the kind of visual routines that we apply to objects in a configuration. Clearly, location control only happens to be important if an object is identified as a container or as a

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Page 60 supporting surface. So routines associated with identifying location control may only be applied in certain cases. The issue is whether objects are defined solely in terms of the features we can see, or whether we also bring prior knowledge to bear in characterising what those objects are. To give a concrete example, one could perhaps argue that the identification of an object with container-like dimensions will always initiate a convex hull routine and an associated location control routine irrespective of what the object is. If both routines are satisfied, the object should then be identified as a potential container. However, consider the scene in Figure 3.9. Although the ball is positioned in the same location relative to the table in 3.9(a) as the ball is to the bowl in 3.9(b), it is infelicitous to describe the ball as in the table .

Figure 3.9 (a) *The ball is in the table. (b) The ball is in the cup.

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Page 61 Objects are often associated with particular functions, and retrieval of this functional information from memory may promote the application of different routines. Another example of this is the case (as we shall see in the next chapter) where the same object can be labelled either as a plate or a dish. For the same configuration of located object and reference object, when the reference object is labelled a plate, on is judged appropriate, but when the reference object is labelled a dish, in becomes appropriate. So how the same object is conceptualised can influence the types of computations that are performed on the visual scene (see also Herskovits’s, 1998, discussion of “schematisation”). Similarly, the appropriateness of a particular spatial relation may be affected by the specific functions of the objects involved. For example, just as children learn that particular shapes of objects afford particular functions, they may learn further that objects with the same general properties may be more suited for specific purposes. For example, a fruit bowl has dimensions that afford containment of solids, but are not particularly suited to the containment of liquids from the point of view of location control. Conversely, we learn that jugs have dimensions that do afford location control for liquids. Therefore, certain types of objects become associated with each other by virtue of the functions they afford. A second way the identification of objects may affect the relationships seen to hold between them comes from knowledge about how they are interacting in that particular situation. For example, in the case of spatial relations to do with proximity, denoted by prepositions such as near , at , by, and so forth, what is usually of interest is the proximity of the objects relative to some activity or situation . A clear example is in the use of the preposition at . For someone to be at a piano, at a desk, or at the office, usually assumes that they are in the appropriate position to play the piano, work at the desk, or work in the office. In such cases, the geometry is dependent on how we interact with the reference objects in those particular situations. Although in some cases being in a position to interact implicates the use of a dynamic-kinematic routine to establish indeed whether interaction is possible (for example, the pianist needs to be able to reach the piano keys, so a viewer might have to estimate rotation of the pianist’s arm), many associations between objects may be learned and stored, thus reducing the number of detailed routines that need to be applied in a given context. For instance, for a postman to be near a postbox, the distance between postman and box may be quite different from that of an ordinary passer by who is not carrying a letter. We shall examine just such cases in the next chapters. Consider also the case of a person in a car versus flowers in a vase. For the person’s location to be controlled by the car, the person needs to be completely enclosed by the car (save perhaps for a waving arm outside a window). However, the flowers in the vase need only be partially enclosed

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Page 62 by the vase for their location to be controlled. In these cases, knowledge of objects and the functional relations between objects constrain the application of geometric and extra-geometric routines. Again, an apple can be piled high above a bowl on top of other objects that are in the bowl, but a liquid must be inside the space a container displaces for location control to hold. The final point we wish to note here is that there is a degree of arbitrariness as to how objects are conceptualised. In English, we can say The man is in/on the bus/plane/train when the man is inside each of the vehicles. However, The man is on the car can only be used to describe a man standing on the top surface of the car (i.e., on the bonnet or roof). Therefore, in English, vehicles with certain dimensions are considered supporting surfaces when describing travel, whereas others are considered containers. As Bowerman (1996a) has argued, children acquiring a language are not only constrained by the pre-linguistic spatial conceptual system they possess, but they are also constrained by the distinctions made in the language they are exposed to. These sometimes rather arbitrary associations and conceptualisations must be learned and represented in memory. For example, as Feist (2000) notes, in Polish one cannot say the equivalent of The man is on the bus. In Polish people have to be in (the preposition w ) vehicles irrespective of the dimensions of the vehicle. We will have more to say about cross-linguistic work later in the book. Now we return to perception and consider the perceptual origins of the functional geometric framework. PERCEPTUAL ORIGINS OF THE FUNCTIONAL GEOMETRIC FRAMEWORK Over the last two decades, there has been increasing evidence that visual processes extract a variety of different kinds of information via different neural pathways. Neurophysiological studies of monkeys by Mishkin, Ungerleider, and Macko (1983; see also Ungerleider & Mishkin, 1982) indicated two distinct neural systems, the ventral and dorsal pathways, which extract two quite different kinds of information. They argued that one system, the “what” system, is associated with the ventral pathway and extracts information sufficient to establish the identity of objects in terms of their colour and form. The other system, the “where” system (or ‘‘where” and “how” systems; see Creem & Proffitt, 2001; Goodale, 1997), is associated with the dorsal pathway and is now assumed to extract visuo-motor information that specifies the size, location, and orientation of objects to inform grasping movements. The animal research has been substantiated by studies on patients following damage to the associated areas of the human brain (see Goodale, 1997; Goodale & Humphrey, 1998). Certain brain lesions in the ventral pathway can lead to patients being unable to recognise objects or purposefully indicate the size or orientation of objects, yet be able to

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Page 63 efficiently grasp those objects and carry out the appropriate preshaping of the hand before picking them up (Goodale, Milner, Jakobson, & Carey, 1991). Other lesions, in the dorsal pathway, produce the opposite effect. Patients have unimpaired object recognition, but are unable to correctly preshape their hand in picking up an object or to put the hand into the correct orientation when trying to pass an object through a slit at different orientations (Perenin & Vighetto, 1988). So there is now considerable evidence for at least two visual processing systems, which could support distinct models of the visual world. One model would represent information needed to differentiate between objects, and the other would represent information needed to locate and manipulate those objects. There has been some speculation that spatial prepositions might relate more to the output of the second “where” system than to the output of the first “what” system. Landau and Jackendoff (1993) suggested that this might explain why languages only differentiate between a relatively small set of possible spatial relations. As they point out, it is odd that we encode a myriad different configurations of eyes, nose, and mouth to represent different faces, yet languages only seem to encode eleven or so basic spatial configurations in their locative expressions. They suggest that this implicates the ‘‘where” system in the recognition of the basic spatial configurations underlying spatial prepositions (because it is thought to provide only limited information about the detailed geometry of any visual scene). There is even some neurophysiological evidence in favour of this speculation. Damasio, Grabowski, Tranel, Ponto, Hichwa, and Damasio (2001) report a positron emission tomography (PET) study that investigated areas of brain activity associated with naming actions, such as running or walking, and spatial relations between concrete objects, such as one object being in or on another object, as depicted in photographs. They found that naming of both actions and spatial relations produced activity in areas associated with the dorsal “where” system (e.g., the supramarginal gyri). However, functional components of spatial relations, such as location control, also relate to dynamic aspects of relations between objects (e.g., if one object is moved, the other should move with it). What kinds of mental representations might be associated with dynamic information and how might they relate to functional geometric notions such as location control? A good place to start is with models of motor planning that are at the interface between vision and action. This is because spatial prepositions, such as in or on, are encountered as often as not in situations where objects are being manipulated: pouring coffee into a cup, putting clothes in a drawer, placing an ornament on a mantelpiece, putting a hat on one’s head. These activities require action plans that depend as much on the physical properties of the situation as they do on its geometry. In other words, in pouring a cup of coffee one needs to estimate the trajectory of the coffee and how fast it

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Page 64 will flow to determine where to put the pot relative to the cup (i.e., in putting the pot over the cup). Similarly, when pouring one has to establish the size and orientation of the cup and how much space is left in it to take the fluid. We believe that functional relations are likely to be (partly) represented at this level and so will form part of the visuomotor representations that inform such actions. Jeannerod (1994) offers an interesting discussion of the kind of models that might support motor actions and motor imagery. He draws a distinction between “semantic” visual representations, usually associated with visual imagery, and “pragmatic” representations associated with motor imagery. He assumes that motor images underlie such things as preparing for an action, rehearsing an action, or even dreaming about an action. And he argues that the two representations, the semantic and the pragmatic, have a neural correspondence with the ‘‘what” and the “where” systems described above (see Jeannerod, 2001). Whereas “semantic” representations encode relatively detailed information about objects in a scene, pragmatic representations encode visual properties in relation to affordances— that is, those visual characteristics that are important in organising motor programmes for manipulating the objects. These include information about the size, weight, and shape of objects, as well as special features of those objects that are relevant for their manipulation, such as the location of handles for grasping. Tucker and Ellis (1998) have shown that viewing an object offers a direct potentiation of the actions it affords. Participants were shown photographs of common, graspable objects (such as a pan) depicted upside down and in normal positions with the graspable part of the object (the handle of the pan) oriented to be maximally graspable by the participant (in line with the hand making a judgement) or minimally graspable (facing away from the hand making a judgement). The participants had to decide whether the object presented was upright or inverted by pressing a key with the left or right hand as quickly as possible. Tucker and Ellis found an object–action compatibility effect. Making a judgement was faster if the response (pressing using the left or right hand) was compatible with the orientation of the handle of the object, even though the judgement to be made had nothing to do with actions that potentially could be performed on those objects. Furthermore, similar effects have been found using real objects (Ellis & Tucker, 2000) and using wrist rotation as a means of responding. In the following chapters, we see that some of the special features of objects outlined by Jeannerod (1994) can influence judgements about prototypical spatial relations. For example, where the head of a toothbrush is located influences the position where people judge a toothpaste tube should be when it is above the toothbrush (CarlsonRadvansky et al., 1999). It is likely that both “pragmatic” visuo-motor representations and “semantic” visual

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Page 65 representations play some role in the interpretation of spatial prepositions (see also Coventry, 2003). A second place where one might expect to find encoding of functional control information is in our interpretation and representation of viewed actions. There is now a considerable literature on the perception of action and biological motion. Much of the interest stems from the pioneering work of Michotte (1963) on how we see causality in simplified dynamic visual arrays, and of Johansson (1973, 1976) on perception of human motion from patch-light displays. In both cases, the problem was to explain how viewers infer complex relationships between objects or their parts on the basis of an impoverished but moving visual input. More recently, the focus of attention has been on the extent to which such recognition depends on the dynamical properties of the underlying events. A distinction is drawn between dynamics, the forces that cause the changes of motion, and kinematics, the changing pattern of the motion itself. The question is whether we learn to discriminate between and represent these complex scenes purely on the basis of the kinematics or whether our representation incorporates the dynamics of the situations. This contrast was suggested by some of Michotte’s original observations about what happened when simple inanimate events, such as one billiard ball colliding with another, were perturbed. For instance, in one case he introduced a slight delay between the first contact of the balls and the subsequent movement of the ball that had been contacted. Viewers recognised that the scene was unnatural in some way and described the unnaturalness as involving the injection of energy. In fact, as Bingham, Schmidt, and Rosenblum (1995) point out, this kind of perturbation is similar to that involved in animate as opposed to inanimate motion. This is because in animate motion the muscles introduce energy into the dynamics of the situation. Bingham et al. demonstrated that viewers can clearly distinguish between animate events, such as the swinging of an arm, as compared to matched inanimate events, such as the swinging of a pendulum, on the basis of impoverished moving patch-light displays. They argued that this suggests that we incorporate dynamical information in our models of the different kinds of events. Interestingly, they also demonstrated that viewers can recognise events involving fluid motion from impoverished patch-light displays. For example, we can identify something falling into water and disturbing its surface, or leaves being blown in the wind, on the basis of patterns of moving light-patches. Again, this suggests that the perceptual system is well attuned to representing different kinds of nonrigid motion. This is an important point because, in many earlier accounts of how we derive dynamics from kinematics, it was assumed that the visual system relied on assumptions of rigidity in the underlying moving forms. There has been a related discussion about the nature of physical imagery and the role of dynamics in the models we use to reason about the physical

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Page 66 world. Schwartz (1999) demonstrated that in solving simple physical problems, such as how far one needs to tip different sized containers before fluid pours out of the top, people use dynamic models rather than geometric models to simulate the events. He required participants to imagine pouring fluid from containers of different sizes while they were in different orientations. He found that imagined tilt was affected by gravitational factors independent of the perceived vertical and they were affected by additional factors such as the viscosity of the imagined fluid (i.e., whether it is water or molasses in the container). Furthermore, the results fitted predictions from a dynamic model of the situation better than from a related geometric model. The research contrasting kinematic and dynamic representations is clearly directed at representing configurations involving movement. In Bingham’s work, it was the motion of rigid and nonrigid objects; in Schwartz’s work, it was the motion of fluid in a tilting container. However, there is also evidence from work on what has been termed representational momentum that we view static scenes in terms of the forces inferred to act between the objects in the scene (e.g., see whole issue of Visual Cognition, 2002, Vol. 9(1–2) for a review of work in this area; see in particular Bertamini, 2002). For example, Freyd, Pantzer, and Cheng (1988; see also Freyd, 1988) carried out experiments in which they observed systematic memory errors for scenes involving the same objects in the same geometric configurations, but with different forces acting on them. Thus, when a plant pot is first seen supported by a chain, then just hanging in the air, observers tend to misjudge the position of the plant as being lower in a subsequent memory test. They argued that this reflects a kind of unfreezing of a perceived force holding the plant up in the first scene. Hence, in static scenes forces are represented as being in equilibrium with each other. In fact, this observation led Regier (1996) and Regier and Carlson (2001; see above) to incorporate the notion of direction of potential motion into the model described earlier in the chapter. This was to deal with the preposition above . The idea is that in determining whether one object is above another or not, the viewer has to take into account the direction the object would move if the perceived force applying to it was removed. In general, for a static object the force must be that opposing gravity. So the direction of potential motion corresponds to downward. Regier then combined this direction of potential motion vector with other vectors relating to what he called the proximal orientation and the centre of mass orientation of the located object and the reference object to yield a formula for determining the applicability of above to his simple two-dimensional scenes. Freyd and co-workers’ results are consistent with those we shall describe for on in Chapter 4. We observed systematic differences in confidence of on descriptions as a function of perceived alternative control. This would be consistent with the idea that viewers perceive the notional forces applying to

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Page 67 67 the objects in the scene and incorporate the information into any judgement as to the appropriateness of the on description. Likewise, Regier’s use of vectors to represent the potential motion of the located object for the above relation is consistent with the incorporation of location control information described earlier. Both are quasigeometric characterisations that incorporate information about the notional forces applying to objects in a scene. Thus, the research on perception of action, mental simulation of action, and perception of static scenes implicates dynamic mental models. All of this is consistent with the idea that we construct and use mental representations that incorporate physical features of the perceived world of the kind assumed to underlie the functional geometric framework. In our discussion of the representation of in and on in the previous section, we proposed the physical property of location control as a functional component in the meaning of these terms. Location control reflects actual or potential forces that operate between objects in the world. Other examples of functional properties and the prepositions associated with them include: threatening contact (directly: towards; indirectly: over), holding together or keeping apart ( between), and being in a position to interact with ( at ). In the next chapters, we consider in more detail these and other prepositions and the evidence for the functional components of their meaning. SUMMARY AND CONCLUSIONS This chapter began by considering the problems faced in providing a clear geometric specification of the spatial relations underlying our use of prepositions such as in. It ended by arguing for a quasi-geometric account based on a functional geometric framework, which involves both geometric and extra-geometric aspects of spatial relations. Much of the discussion in between was concerned with the perceptual and cognitive basis for the representation of spatial relations. Part of the attraction of the geometric approach to the meaning of the spatial prepositions comes from the idea that vision must provide a simple and coherent geometric representation of what we view. Hence, it should be possible in principle to define a direct mapping between the basic visual representation and the meaning of the prepositions. However, on closer examination it is clear that the kind of geometric information required for interpreting prepositions like in may not be provided automatically in a basic visual representation. Determining relations such as inside/outside is a real challenge to the visual system, in that it requires visual routines that go beyond the basic automatic processes assumed to underlie visual perception (Ullman, 1984, 1996). Even computing simple relations like above depend on quite complicated processes according to Regier and Carlson’s (2001) attention vector sum account. Furthermore, research on how to derive such relations is still in its

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Page 68 early stages, with most models being limited in their application. For example, both Ullman’s (1984, 1996) and Regier’s (1996) accounts of in are restricted to simplified two-dimensional images and Regier’s system can only deal with convex regions. Yet, Cohn and co-workers’ RCC analysis shows that adding the third dimension greatly increases the complexity of the geometry and notions such as containment are critically dependent on being able to represent regions containing concavities. Current perceptual models also fail to deal with the basic geometric contradictions in our use of certain spatial prepositions. For instance, how we can describe a pear as in a bowl when it lies outside any region that the bowl encloses, yet not be able to describe it as in it when it lies under an upturned bowl. We argued that such geometric inconsistencies could be explained in terms of functional geometric representations that incorporate extra-geometric aspects of the relation between the pear and the bowl, such as how the container controls the location of its contents. At this point we considered what information spatial relations convey and discussed the importance of what we called extra-geometric information. One important source of extra-geometric information comes from how we act in space. In other words, it concerns not only geometric relations between objects, but also what has been called force dynamics—the forces that relate objects to each other and relate us to objects that we are acting upon. The discussion led to the introduction of the functional geometric framework that is at the centre of our account of spatial language. The first two elements of the framework are geometric routines, which recover geometric information about spatial relations, and extra-geometric dynamic-kinematic routines, which recover information about the forces assumed to act between objects in space together with other kinds of nongeometric spatial information. The final extra-geometric element of the framework relates to knowledge of objects themselves and their stereotypic functions. The contrast between a purely geometric and the functional geometric approach to the meaning of the prepositions has a parallel in arguments about the nature of perceptual representation. Do they only reflect geometric information or do they also reflect extra-geometric information about the notional forces in a scene? We began by considering research on the neuropsychological basis of vision. This work challenges the idea that the visual system produces a single coherent representation of a scene. Rather, it suggests that there are at least two distinct visual pathways that yield two different kinds of information. The “what” system yields information sufficient to discriminate and identify the objects that we view, whereas the “where” system yields information sufficient to tell us how to interact with those objects, how to locate and grasp them, how to put things into them, and so on and so forth. It has been suggested that this latter system may play the most important role in how we represent spatial relations of the kind

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Page 69 underlying the spatial prepositions. This is for two reasons. First, those same prepositions are used to denote interactions with objects, such as putting something on or in or over something else. Second, the range of spatial distinctions being made by the linguistic system seems to be more in line with the coarse-grained output of the “where” system (see Landau & Jackendoff, 1993). Furthermore, there is some recent evidence to suggest that naming spatial relations is associated with activity in parts of the brain associated with the “where’’ system. This led to the question of what kind of representation might incorporate functional geometric information proposed for prepositions like in and on. Two areas of research appeared relevant: one was associated with motor images and motor plans (Jeannerod, 1994), the other with the perception and representation of action (Bingham et al., 1995). In the context of motor imagery it is suggested that the visual system, in particular the “where” component of the system, is designed to recognise affordances (i.e., visual characteristics related to features of an object that are important when we interact with it). In relation to the functional geometric framework, these might include functionally containing regions of the object or functionally supporting regions. Hence, a visuo-motor representation of a scene could be cast in a functional geometry of the kind we have been considering for in and on. Representations that reflect affordances of objects may also contain functional information that is crucial for understanding other prepositions, such as over, at , and in front of . As we shall see in Chapter 5, where a viewer judges one object to be over another object depends on how they intend to interact with it, and how those objects interact with each other; likewise with the prepositions in front of and at (Chapter 6). In this respect, the functional geometric representation of any scene may contain more than information about location control relations. In the context of perception of actions and events, there is also evidence for the involvement of something like a functional geometry. This is because we discriminate between different actions on the basis of the forces that apply. Hence, we are able to make a clear distinction between animate and inanimate events and between situations that correspond to real physical events, such as one billiard ball colliding with another and so propelling it across the table, as opposed to those that do not (Michotte, 1963). Incorporating force information into the perceptual representation is similar to incorporating location control information into the definitions of containment and support. Furthermore, the experiments of Freyd et al. suggest that such information is perceived in static as well as kinematic images. So the research on perception of complex scenes indicates that the perceptual representation contains more than just geometric information. It also incorporates information about the notional forces applying between objects in the scene and information that is relevant to how we might interact with

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Page 70 those objects. It is just such information that needs to be incorporated into a functional geometric representation to support the use and interpretation of prepositions like in, on, and over. In the next part of the book, we consider the evidence for the components of the functional geometric framework across a range of types of spatial prepositions.

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Page 71 PART II Saying, Seeing, and Acting: Evidence for the Functional Geometric Framework

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Page 73 CHAPTER FOUR Experimental evidence for the functional geometric framework 1: the so-called topological prepositions I’m giving him a useful Pot to Keep Things In. (A.A. Milne, Winnie-the-Pooh, chapter 6) In this chapter, we consider the case of the two so-called “topological” prepositions, in and on. These prepositions are our first empirical port of call for a number of reasons. First, previous chapters have been peppered with examples using in and on, so we feel obliged up front to show empirical support for the armchair examples provided thus far. Second, as we shall see in Chapter 8, it just so happens that in and on are the first locative terms to be acquired in English (and in most languages). In this sense, they can be regarded as basic terms any general account of spatial language understanding needs to be able to deal with. Additionally, they provide the opportunity to discuss a wide range of factors that influence their comprehension and production that carry over to the projective and proximity terms to be considered later. IN Evidence for the dynamic-kinematic routine of location control Three-dimensional containers are a natural place to start when considering the comprehension and production of in. As Winnie-the-Pooh quite rightly 73

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Page 74 intimates, containers have the useful function of constraining the location of the objects they contain. As we have argued in the previous chapter, putting an object in a container means that the object will stay in the same position over time unless someone else intentionally removes it. As such, containers exemplify the notion of functional geometry that we outlined in the previous chapter. For a located object to be in a container, this entails more than just spatial enclosure/inclusion; containment also entails the notion of location control, whereby the reference object constrains the location of the located object over time. Location control is a concept that can readily be tested; indeed, there is much empirical evidence for the influence of location control on the comprehension and production of in. Imagine an apple perched high on top of a pile of other fruit in a bowl. Imagine further that the bowl is moved and the apple moves with the bowl such that the movement of the bowl continues to determine the location of the apple. In contrast, imagine the case where the apple is wobbling on top of the pile of fruit (although remaining in constant contact with the fruit), but the rest of the fruit and bowl remain stationary. In the first case, location control is seen to hold because the bowl is clearly controlling the location of the apple over time. However, in the second case, the bowl is not seen to control the location of the apple because the apple is moving of its own accord. Coventry (1992, 1998) presented participants with videotaped images of real objects (various types of fruit, balls, and containers) that directly manipulated these factors (see Figure 4.1 for examples). In one study, participants had to complete a sentence of the form the located object is the reference object to describe the position of the located object relative to a container. In the scenes presented, the located object was positioned at four different heights on top of other objects in the bowl. The heights ranged from the located object positioned inside the bowl just below the rim (height 1 in Figure 4.1a), to just above the level of the rim (height 2), to well above the rim (height 3), to very high above the rim (height 4). The effects of the movement manipulations were striking. In was produced most (compared with the production of other prepositions) in cases where location control was strongest (where the located and reference objects were moving together at the same rate) and least when the located object was moving of its own accord while the bowl remained stationary (mean ratio use of in is displayed in Table 4.1). Furthermore, these effects were robust across a range of objects and scenes, from natural-looking piles of ping-pong balls and fruit to more “unnatural”-looking scenes where the located object was more precariously supported by other objects and was located outside the convex hull of the container (see Figure 4.1b). For the latter unnatural scenes, although in was produced much less frequently overall, effects of location control were nevertheless identical.

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Page 75

Figure 4.1 Examples of the video scenes used by Coventry (1992, 1998). The scenes shown here are static. For the location control condition, the whole scene (bowl plus complete contents) was shown to move smoothly from side to side at the same rate. For the non-location control condition, the located object (the pear in (a) and the red apple in (b)) was shown to wobble from side to side, but to remain in contact with the other fruit.

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Page 76 Table 4.1 Mean ratio use of in for movement by height in video experiment testing location control (Coventry, 1992, 1998) Movement Height Static Located object moving objects moving Located and reference 1 (lowest) 0.97 0.96 0.99 2 0.97 0.91 0.99 3 0.92 0.87 0.97 4 (highest) 0.80 0.74 0.93 Note : The higher the value, the more in was used. Another way in which location control can be compromised is when the located object remains stationary, but the reference object moves together with the other contents. In a series of studies, Ferrier (1996; reported in Garrod, in press) compared movement of this type with static scenes involving videotaped images of ping-pong balls in glass bowls that were presented in various arrangements. She had participants rate their confidence in in descriptions together with that for a range of other spatial descriptions; the mean value for the in judgements is shown in Figure 4.2 as a function of scene dynamics. The figure shows a dramatic effect of scene dynamics on viewers’ confidence. Scenes in which the container (i.e., bowl and other

Figure 4.2 Results of experiment reported by Ferrier (1996). Positions 3, 4, and 5 in her study were all above the rim of the container.

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Page 77

Figure 4.3 Schematic representation of the video scenes used by Garrod et al. (1999). balls) moved but the contents (i.e., target ping-pong ball) remained stationary led to low confidence in in descriptions compared with the static scenes with the same distance between located and reference object. Perhaps the most striking evidence for location control comes from two experiments reported by Garrod et al. (1999). They presented static scenes, but in situations where there were alternative potential sources of location control. Furthermore, they tested directly the relationship between viewers’ judgement of location control and confidence in descriptions involving in. The studies used video-clips of different arrangements of a pile of ping-pong balls and a glass bowl and contained two manipulations (see Figure 4.3). First, the configurations varied in terms of the geometric relationship between a black ping-pong ball and the bowl itself. The range of relative positions is shown as P1–P5 from the left to right of Figure 4.4. Position P1 has the ball in contact with the bottom of the bowl, at position P3 it is level with the rim, and at positions P4 and P5 it is above the rim. The other factor that was manipulated was the degree to which the location of the black ping-pong ball could be seen to be controlled by an external source. In half of the scenes (those labelled alternative control in Figure 4.3), the ball was attached to a thin (but visible) piece of wire suspended from above the bowl. According to the extra-geometric routine of location control, viewers’ confidence in describing the black ping-pong ball as being in the bowl should relate directly to the degree to which they see the container (i.e., the bowl) as controlling the location of the located object (i.e., the black ping-pong ball).

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Page 78 To test this, participants made two judgements about these scenes. One group viewed the scenes and after each scene had been presented was asked to indicate what would happen to the black ping-pong ball if the bowl were moved sideways. To help them in making the decision, they were shown an empty bowl being moved sideways as an illustration. The proportion of viewers who judged the ball as maintaining its relation to the bowl following the hypothetical movement was taken as an indicator of the degree to which the bowl was seen as controlling the location of the ball. The second group of viewers was given the same scenes (intermixed with other scenes from other experiments) and were asked to rate the appropriateness of different descriptions of the configuration of ball and bowl. They were given a range of descriptions of the form “The ball is in/on/over … the bowl” and had to rate each one for its appropriateness. Comparing the two sets of judgements—location control judgements and judgements as to the appropriateness of in descriptions—gives a measure of the degree to which location control correlates with understanding of the in relation. The results are shown in Figure 4.4. Figure 4.4 shows a strong linear relationship between viewers’ confidence in in descriptions (shown on the y axis) and viewers’ judgements as to the degree to which the bowl is seen to control the location of the ball (shown on the x axis). However, the correlation is not perfect because it breaks down when there is strong geometric enclosure (i.e., when the ball is in positions 1 and 2, as shown by the circles at the top of the figure). The results indicate

Figure 4.4 Relationship between perceived control and rating of in (adapted from Garrod et al., 1999).

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Page 79 that location control is an important component of containment when the enclosure of contents by container is not complete (e.g., when the ball is in positions 3–5 in Figure 4.3). Yet another way of manipulating location control is to tilt the container away from its usual orientation. The greater the degree of tilt, the lower the level of location control. This is because located objects are more likely to fall out of tilted containers that are moved than upright containers that are moved. Indeed, Coventry (1992, 1998) and Ferrier (1996) showed that tilting the container does reduce the production and appropriateness rating of in; the greater degree of tilt, the less appropriate in descriptions become, despite the constant geometric relationship between the located and reference objects. Location control can also be manipulated indirectly by varying the animacy of the located object. Feist and Gentner (1998) and Feist (2000) presented participants with scenes showing a coin or a firefly in a hand or in an inanimate container (at various degrees of concavity). As with the alternative control manipulation in Garrod et al. (1999), one object (i.e., the firefly) has the potential to fly away and hence is only subject to weak location control, whereas the other object (i.e., the coin) does not. Similarly, the hand could possibly close further around the located object and so exert further location control, whereas the inanimate container cannot. Indeed, Feist and Gentner found that ratings for in were lower for animate- than for inanimate-located objects when placed ‘‘in” the hand. Animacy of the reference object (e.g., the hand versus the container) also influenced acceptability ratings. The ratings were higher for the hand condition than for the inanimate container condition, just as would be expected. Feist (2000) has replicated these results using a range of different methodologies. So, there is considerable evidence for the application of what we have termed the dynamic-kinematic routine of location control to in. However, although this routine is clearly central to the comprehension and production of in, there are many cases of its use where location control seems less relevant. For example, The island in the archipelago or The marble in the circle suggest geometric enclosure, but do not seem to involve strong elements of location control. Additionally, we noted that the effects of movement and alternative control are only strongly present when the located object is positioned above the rim of the container in the experiments reported above. For these reasons, we also need a geometric routine that allows calculation of degree of containment/enclosure independent of the extra-geometric routine of location control. Indeed, in previous chapters we suggested that Cohn’s region connection calculus (Cohn, 1996; Cohn et al., 1997) provides a useful means of encapsulating degrees of enclosure across a wide range of types of two- and three-dimensional scenes and is, therefore, a good formalism in which to define a geometric routine for establishing enclosure.

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Page 80 Region connection calculus conveniently allows for gradations of forms of enclosure. The strongest form of enclosure is when one region is topologically inside another (i.e., when a region is completely surrounded by another), as in The jam in the closed jar or The flowers in the amber . However, as we pointed out in Chapter 3, topological enclosure is not often found in the real world. Consequently, there are various weaker kinds of enclosure defined in the calculus that depend on different ways that an object can have an inside. For instance, one region may be in another when it is a subpart of, or overlaps with, the other’s convex hull. The notion of a convex hull can also be applied to groups of objects. For example, when an island is in an archipelago its region is enclosed by the convex hull of the whole group of islands in the archipelago, as part of their scattered inside. This kind of enclosure is weaker than enclosure within the region defined by the convex hull of a single object. For example, as we pointed out in Chapter 3, a scattered inside cannot contain a liquid. Armed with this array of basic geometric relations, one can define different degrees of enclosure to reflect different degrees of spatial constraint in the real world. Put together with the dynamic-kinematic routine of location control, these routines jointly cover many of the problematic cases we have considered throughout the book thus far. However, to cover all cases, a third type of information is required—conceptual knowledge to do with objects and what they are for. Conceptual knowledge and context effects Some containers are more appropriately designed for liquids, whereas others are only suited to hold solids. Labels given to different containers map onto the possible functions that they have. Labov (1973) gave pictures of containers of different sizes to a group of participants and found that they labelled them according to their dimensions. For example, when the ratio of width to height was about 1:1 the label cup was used most frequently, but when the height was greater than the width vase was the most common description. This suggests that particular labels are associated with particular dimensions of objects. Furthermore, in a second study, Labov asked participants to imagine the objects they had just labelled in a neutral context now being used in specific ways. For example, they were asked to imagine that they saw someone holding the object, stirring in sugar with a spoon, and drinking coffee from it. Not surprisingly, Labov found that how the container was used in the imaginary context had strong effects on category boundaries. Therefore, an object’s perceived function has measurable effects on what people are likely to call it (see also the discussion of Smith, in press, Chapter 8). How an object is labelled also influences its perceived function in a scene and, in turn, influences how one describes the location of an object with reference to that object. Coventry et al. (1994) found that the specific labels

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Page 81 given to a reference object influenced the use of prepositions to describe the spatial relation between a located object and that reference object. Participants were shown video recordings of real objects and were asked to either rate the appropriateness of sentences to describe the scenes, or were asked to complete a sentence of the form The located object is the reference object . They found that the production of, and acceptability judgements given for, in were affected by the label given to the reference object. When the same reference object was labelled a dish versus a plate , in was rated as more appropriate and was used more frequently in the sentence completion. When the object was labelled plate , on was preferred and rated more highly. Therefore, the label given to a reference object influences the appropriateness of the preposition used. Feist and Gentner (1998) and Feist (2000) report a similar effect of labelling on the comprehension and production of in and on. Feist and Gentner manipulated the level of concavity of a reference object, from plate-like low levels of concavity to vase-like high levels of concavity. Not surprisingly, this manipulation not only influenced the labels given to containers (e.g., plate was the preferred label for a low level of concavity), but in was rated as being more appropriate for reference objects with high concavity levels, while on was more appropriate for the flatter reference objects. These results, taken on their own, might be consistent with a co-occurrence relations account of the kind we argued against in Chapter 2. Perhaps particular nouns have lexical entries that have selection restrictions, or perhaps prepositions have selection restrictions that licence use with a particular set of objects. However, Coventry et al. (1994) found that in was judged to be more appropriate and is used more frequently to describe the relationship between a located and reference object when the two are functionally linked. For instance, in is used more and is rated to be more appropriate for the solid object (marked with an x) in the bowl in Figure 4.5(b) than for the same solid object (marked with an x) in the jug in Figure 4.5(c). Furthermore, adding liquid to the jug further decreased the use (and rating) of in (Figure 4.5d), but made no difference in the case of the bowl (Figure 4.5a). Thus, the addition of water appears to make the object-specific function of the jug more salient, further reducing the appropriateness of this as a container of solids. Coventry and Prat-Sala (2001) have shown that this finding is not limited to jugs and bowls, but generalises to a basic difference between containers that are primarily containers of liquids versus those that are primarily containers of solids. Coventry et al. (1994) interpret this finding as evidence that different types of containers have spheres of functional influence associated with them (see the related notion of REGION in Miller & Johnson-Laird, 1976). In other words, different labels for containers may well be associated with different regions of applicability, which go beyond the use of convex hulls based purely on the dimensions of objects.

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Figure 4.5 Examples of scenes used by Coventry et al. (1994) and Coventry and Prat-Sala (2001). Ferenz (2000) also provides evidence that how an object is construed influences the appropriateness of the prepositions in versus near . Ferenz presented participants with a selection of container-like novel objects that were either labelled according to function or according to the “stuff” the object was made from. For example, participants were shown a “blicket” and were told that it has the function of carrying food to picnics. They were then shown a ball on the end of a stick, which was positioned either close to the interior wall of the object or the same distance from the outside surface of the object (among other positions). Participants had to rate the appropriateness of the sentences the ball is in/near the blicket or the ball is in/near the ceramic. The locations of the ball in the empty space contained by the reference object were more naturally described as being near it than in it when the reference object was labelled in terms of its substance. The fact that an object may be conceptualised in many different ways leads to situations in which the same object may be processed using different routines, and these may vary according to the language itself. For example, in English one can be in or on a bus or plane, but one has to be in a car. Vehicles afford location control, but also can be conceptualised as containers or supporting surfaces. In English, the application of on relates to the size and the length to width ratio of such vehicles. Large long vehicles are more easily regarded as supporting surfaces, but small objects with a low height to width ratio are more usually regarded exclusively as containers. However, in Polish, vehicles are all conceptualised as containers: the equivalent of

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Page 83 in (the Polish preposition w ) is appropriate for vehicles but the equivalent of on ( na) is not (Cienki, 1989; Feist, 2000). There is also evidence that the routines applied may be weighted according to a range of contextual factors. For example, Ferrier (1996) demonstrated that dynamic contexts could affect confidence in in judgements for the stationary scenes that followed. In the study she used a scene with a ball in the equivalent of P4 in Figure 4.3. However, in one condition it was preceded by a dynamic context in which the ball was first seen floating in mid air (it was suspended on an invisible nylon filament), and then the bowl together with the other balls was moved under it until the ball came to rest on the top of the other balls in the bowl. This was compared with the final stationary scene without any prior dynamic context. She argued that the same scene viewed with a dynamic context inconsistent with the bowl controlling the location of the ball should lead to much lower confidence in in descriptions. In fact, the mean ratings for in descriptions following the dynamic context manipulation were substantially (and reliably) lower than those without the context (see Garrod, in press). So the results followed the basic prediction of the functional account; introducing a prior context incompatible with the functional interpretation of the preposition significantly reduced subjects’ confidence in the description. There was also a counter-effect with respect to confidence in on judgements where the prior context produced an increase in confidence for on judgements. Coventry (1999), based on an example from Garrod and Sanford (1989), also provides evidence that context, this time in the form of a text, can influence the appropriateness of in to describe the same static scene. Consider the scene in Figure 4.6. Imagine also that the length of string is halved. Ordinarily one would not say in either case that The pear is in the bowl. However, if one was playing a game that involved manipulating the frame in such a way that one had to place the pear as depicted, one could meaningfully say that The pear is in the bowl . Indeed, Coventry found that in was produced more in a sentence completion task, and was rated as more

Figure 4.6 Example of scene used by Coventry (1999).

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Page 84 Table 4.2 Results from context study (Coventry, 1999): mean ratings for in by condition (standard deviation in parentheses) Condition Low height High height No context 2.50 (1.64) 1.83 (1.60) Game context 3.27 (2.68) 2.56 (2.27) appropriate in an acceptability judgement task, in the game context as compared to no context conditions (see Table 4.2). Given that there is no enclosure in the scene being described, this shows that how routines are deployed can be affected by the context. In this case, given that there is a location control element in the game scenario, a weaker version of containment is licensed (containment by the circumference of the container). In summary, the empirical evidence we have reviewed for in demonstrates the interplay between the three elements of our functional geometric framework: geometric routines, dynamic-kinematic routines, and stored conceptual knowledge. Although in the main we have only considered in applied to stationary scenes, it is likely that dynamic routines are also important when in is used to identify a path from a source to a goal (e.g., when one says The football is in the net to describe a ball that has just left the soccer player’s foot from the penalty spot). We have shown that in used statically relies on judgements of what might happen. This depends on being able to judge how the positions of objects will change over time. Similarly, for the ball to be in the net (in the sense intended above) relies on the judgement that the ball is moving in the right direction at the right speed for it to end up in the net. Therefore, the dynamic-kinematic routine that we have argued is central to the static use of in can apply to dynamic uses of in also. ON Evidence for the dynamic-kinematic routine of location control Like containment, the notion of support can be regarded as more than a geometric construct in which there is contiguity (contact) between a located object and reference object. Support also has a location control component. Just as we have argued that containers constrain the location of their contents over time, one can regard constraint of location over time as a key feature of supporting surfaces. Indeed, both Garrod et al. (1999) and Coventry (1992) have found experimental evidence for location control with scenes involving on.

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Figure 4.7 Examples of on scenes used by Garrod et al. (1999). Garrod et al. (1999) investigated the influence of location control on confidence in on descriptions in a similar way to the testing of the influence of alternative control for in descriptions overviewed above. The video-taped scenes showed a heavy weight resting on a plank of wood. The various conditions are illustrated schematically in Figure 4.7. Degrees of alternative support were varied with the presence of either a string or chain attached to the weight in three different ways: (1) attached only to the weight (i.e., not acting as an alternative controller), (2) loosely attached to both weight and an alternative support (i.e., acting as a weak alternative controller), or (3) attached to both weight and alternative support and taut (i.e., acting as a strong alternative controller). To estimate the degree to which viewers judged the location of the weight to be controlled by the plank it was sitting on, they were asked to indicate what they thought would happen if the plank were removed. Would the weight remain in the same position or would it fall? To establish viewers’ confidence in on descriptions, a different group of participants were asked to rate the appropriateness of different descriptions of the relationship between weight and plank (e.g., “the weight is on/over/ by … the plank”). The relationship between confidence in on descriptions and judgements of the degree to which the plank was seen to control the location of the weight

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Figure 4.8 Relationship between perceived control and rating of on (adapted from Garrod et al., 1999). is shown in Figure 4.8. Again, just as was the case for in, the figure shows a strong linear relationship between confidence in on descriptions (shown on the y axis) and judgements of location control (shown on the x axis). Confidence in on descriptions is determined by the extent to which one sees the location of the weight as being controlled primarily by the plank. Thus, the experiment indicates that viewers judge the appropriateness of descriptions containing on as a function of the degree to which the location of the reference object (e.g., the plank) is seen to be controlling the location of the located object (e.g., the weight). Coventry (1992) also reported evidence for the importance of location control on the rating of on. Using scenes with a ring around a finger, the size of the ring was manipulated such that it was either in contact with the finger or not. In addition, the ring was either shown to be moving up and down along the finger or it remained stationary. The movement was similar to that of a ring being put on and taken off the finger but without ever moving past the tip of the finger. Not only did ring size affect ratings (not surprisingly, the large ring was given a lower rating than the small ring; see Table 4.3), but there was a significant interaction between ring size and movement. Whereas movement did not influence ratings when the ring was not in contact with the finger, movement of the appropriately sized ring was found to reduce the confidence in on descriptions. This finding again shows that independent movement of the located object, which indicates a weakening of

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Page 87 Table 4.3 Results of on judgements for ring study (Coventry, 1992): mean ratings Movement Ring size Static Ring moving Small (normal) 8.54 6.47 Large 3.04 2.46

Figure 4.9 Examples of on scenes used by Coventry and Prat-Sala (2001). location control, does reduce the appropriateness of on despite the fact that the ring is in contact with the finger in both cases. In addition to these studies showing the relationship between location control judgements and the use of on, other indicators of location control have also been found to influence the rating of on. In two experiments, Coventry and Prat-Sala (2001) manipulated the position of the located object and reference object by tilting either the reference object or the located object. In one experiment the located object was either positioned in the centre or on the edge of a supporting surface, and the reference object was either positioned normally or rotated by 45 degrees or 90 degrees (see Figure 4.9). It was found that rotating the reference object reduced the rating of on and, additionally, ratings for on were lower when the located object was positioned on the edge of the reference object. These findings can be interpreted as further evidence for location control. When the reference object is rotated, location control is reduced. Similarly, when the located object is positioned on the edge of the reference object, this also reduces location control as the located object would be more likely to fall off were the reference object to be moved.

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Page 88 Therefore, on is influenced by the extra-geometric dynamic-kinematic routine of location control, as found for in. Also, as in the case of the geometric routine for in, the geometric routine for on can be specified in terms of Cohn’s region connection calculus (RCC). One of the primitive relations in the RCC is connection. Recall from Chapter 3 that connection is a relation between two or more regions that ranges from complete overlap of the regions to mere contact. Although contact, which is the key topological relation assumed to underlie on relations, would appear to be an all-or-nothing type of relationship, support relations do admit to different “degrees” of contact. This is because support is a weakly transitive relation (Miller & Johnson-Laird, 1976). For example, a book that is on the top of a pile of books on a table can be described as on the table , even though it is not in direct contact with the table (see Figure 2.2 in Chapter 2). However, a book in contact with the table, which, in turn, is in contact with the floor, could not be described as on the floor. We suggest that one of the ways that the extra-geometric factor of location control interacts with the geometry of contact for on relations is that clear evidence of location control should license on in situations where there is this kind of indirect contact. In other words, in situations where the salient controller is in indirect contact with a located object, it can serve as a reference object for on relations. Conceptual knowledge and context effects Also like in, conceptual knowledge is required to explain why certain types of routine are associated with particular objects. For example, objects like a table are regarded as supporting surfaces, and resist the application of geometric routines other than contiguity/support even when there is another relation present in the scene that is associated strongly with a different preposition. For instance, a marble positioned in a large hole gauged out of the table is still on the table rather than in the table (see Figure 3.9 in Chapter 3). Recall also that Coventry et al. (1994; see also Coventry & Prat-Sala, 2001) found that on was the preferred preposition to describe the same object labelled as a plate versus a dish, and Feist (2000) has also shown similar effects across a wider set of differently labelled objects. Although the evidence is less extensive for on than for in, it clearly supports the three elements of the functional geometric framework we have argued are necessary for an account of situation-specific meaning. SUMMARY We have considered in and on together in this chapter as they are regarded in the literature as the two most basic prepositions. The evidence we have reviewed shows that the essential purpose of containers and supporting

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Page 89 surfaces, that they constrain the location of other objects (by virtue of the force of gravity), means that their use depends on applying the same dynamic-kinematic extra-geometric routine of location control. Indeed, we have seen across a range of studies that evidence for location control increases confidence in in and on judgements. What differs between in and on is the geometric routine that applies, and also the degree of location control that in versus on affords. In Chapter 7, we will argue that degree of location control provides an important dimension with which to predict when participants shift from one preposition to another as a scene changes. However, before we do that we need to turn our attention to other geometric and dynamic-kinematic routines. In the next chapter, we consider projective prepositions.

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Page 91 CHAPTER FIVE Experimental evidence for the functional geometric framework 2: which way up is up? The projective prepositions …for what is it that makes the front of a man—what indeed but his eyes? (Herman Melville, Moby Dick) Projective prepositions have received considerable attention in the literature, particularly in relation to the problems surrounding reference frame assignment. Recall in Chapter 1 that when we briefly discussed these terms, we noted that projectives require the assignment of a reference frame involving a direction and a starting point with respect to which geometric positions can be defined. For example, imagine you have lost your copy of Saying, Seeing , and Acting, and a colleague tells you that it is ‘‘To the left of the computer monitor”. You may start to search for the book by looking to the left of the monitor from your point of view (i.e., you assume a relative/ viewer-centred reference frame) or, alternatively, you may look on the monitor’s left (i.e., you assume the intrinsic reference frame). To understand how the three components of the functional geometric framework operate in the case of projective terms, we need to consider reference frame assignment in some detail. Once we have done this we will assess evidence for the importance of the individual components in the functional geometric framework with respect to these prepositions.

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Page 92 REFERENCE FRAMES AND PROJECTIVE TERMS Properties of reference frames Spatial reference frames (or spatial “perspectives”; cf. Tversky, 1996) are not only important for projective terms, but permeate spatial description (e.g., Schober, 1993; Taylor & Tversky, 1996); in fact, they play a central role in spatial cognition more generally (see, for example, Couclelis, Golledge, Gale, & Tobler, 1987; Marr, 1982; O’Keefe & Nadel, 1978). Recall that in Chapter 1 we outlined the three basic types of reference frames that occur across languages (following Levinson, 1996a); one can distinguish between the intrinsic, relative , and absolute reference frames (for other related classifications, see Garnham, 1989; Jackendoff, 1996; Levelt, 1984; Retz-Schmidt, 1988). These reference frames can be defined as follows (adapted from Eschenbach, 1999; Levinson, 1996a): (1) Intrinsic : an intrinsic relation Rel ( Loc, Ref ) relates the positions of the located object ( Loc) and the reference object ( Ref) on the basis of a frame of reference that is established by the functional-spatial structure of Ref. This frame of reference assumes an object-centred coordinate system where the coordinates are determined by the properties of the reference object. (2) Absolute: An absolute relation Rel ( Loc, Ref) relates the positions of Loc and Ref on the basis of a frame of reference that is established by the functional-spatial structure of the common surrounding of Loc and Ref. The fixed direction can be provided by gravity or by using arbitrary fixed bearings (e.g., cardinal directions). (3) Relative : a relative relation Rel ( Loc, Ref, V ) relates the positions of Loc and Ref on the basis of a frame of reference that is established by the position and functional-spatial structure of an additional entity V . V may be implicitly given, it is different from Loc and Ref, and it may also be a spatiotemporal process, such as a process of motion. The principal means by which intrinsic, relative, and absolute spatial relations can be differentiated is through patterns of invariance under rotation (Levinson, 1996a). Consider the scenes in Figure 5.1. In Figure 5.1(top row), The ball is in front of the chair describes the position of the ball using the intrinsic reference frame, which relates the ball to the intrinsic front of the chair. Rotating the viewpoint (e.g., by standing behind or to the side of the chair) or rotating the whole array makes no difference to the intrinsic use. By contrast, rotating the chair means that the ball changes from being in front of the chair to being behind the chair. In Figure 5.1(middle row), The ball is to the left of the chair locates the ball with reference to the relative (or viewer-centred) reference frame. In this case, rotating the reference object

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Figure 5.1 Properties of frames of reference under rotation according to Levinson (1996a). makes no difference to the description of the ball. However, rotating the viewer or rotating the whole array does make a difference, and forces a change in spatial description accordingly. Finally, in Figure 5.1(bottom row), The ball is north of the chair locates the ball with reference to the absolute

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Page 94

Figure 5.2 Converseness and reference frames.

Figure 5.3 Transitivity and reference frames. frame. Here, rotating the position of the viewer or the reference object makes no difference, but rotating the whole array would lead to a change of direction (e.g., as the array is rotated clockwise, the relationship would change progressively through east, south, and then west). Levelt (1984, 1996) offers an interesting discussion of the semantic properties of these different reference systems. Consider, for example, the relative versus intrinsic use of left and right. For the relative system converseness holds, but not for the intrinsic system. This is clear when we compare the scenes in Figure 5.2 (adapted from Levelt, 1984). In (a) if one says A is to the left of B , then it holds that B is to the right of A for both relative and intrinsic use. However, this is not true in (b); the converse does hold with relative use, but not with intrinsic use. With the intrinsic use in (b), A is to the right of B and B is to the right of A (hence with intrinsic use one can say A is on B’s right and B is on A’s right). Similarly, the relative system is transitive, but the intrinsic system is not. Consider Figure 5.3. Again, from the perspective of the viewer (relative frame of reference), one can say in picture (a) that A is to the left of B, that B is to the left of C and, therefore, A must necessarily be to the left of C. Transitivity also holds for picture (b) with relative use. However, transitivity for intrinsic use does not hold for picture (b); A is to the left of B, B is to the left of C, but A is not to the left of C. One of the consequences of the local intransitivity associated with the intrinsic system is that it becomes difficult to reason with left and right when used intrinsically (Levelt, 1984, p. 330).

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Page 95 Indeed, such problems led Johnson-Laird (1983) to argue that one needs mental models of the scenes to cope with the difficulties involved (a point we discuss in detail in Chapter 7). Prepositions involving the vertical dimension (such as over and above ) differ from the in front/behind and left/right dimensions with respect to frame of reference instantiation (see Levelt, 1984, pp. 331–347 for extensive discussion). According to Levelt, the point of view of the observer is irrelevant for the relative use of above and below . Thus converseness and transitivity can apply to relative uses of above and below. However, the vertical orientation of the speaker’s perspective is only one factor. Levelt argues that a number of cues operate on the perception of a scene from the viewer’s perspective, including verticality perceived in terms of alignment with the retina’s vertical meridian, its orientation with respect to some visual frame (horizon or whatever), and its alignment with the vestibular vertical. Intrinsic uses of above and below are extremely limited due to what Levelt (1984, p. 345) refers to as the principle of canonical orientation ; for the intrinsic system to refer to a reference object’s intrinsic dimension, that dimension must be in canonical position with respect to the reference frame of orientation of the located object. There can only be genuine intrinsic use of over and above for frames of reference other than the perceived vertical. However, these latter cases are quite limited as well; it is, for instance, still not possible to violate converseness or transitivity. The intrinsic uses of the projectives are particularly fascinating because they highlight the importance of functional geometric models of the objects themselves. Most three-dimensional objects can be thought of as having no more than six sides (cf. Miller & Johnson-Laird, 1976): a top and bottom, a left and right, and a front and back. The definition of sides is based on the human model of a man standing upright with his head pointing to the stars. The top is taken to be where the head is and the bottom where the feet are. Front and back are then usually associated with the orientation of the main perceptual apparatus, that is eyes, nose, and ears in the midline; again these are based on the canonical representation of Homo erectus looking straight ahead. Finally, left and right are associated with what we have learned to call our left and right hands. This intrinsic human scheme can then be generalised to other objects according to two basic principles that derive from what Herskovits (1986) called the coincidence situation and the encounter situation. In the coincidence situation, the reference object takes on an intrinsic orientation by analogy to the human scheme. Thus, for animals the top corresponds to the side normally oriented upwards, the front contains the main perceptual organs, and the left and right correspond to the sides where humans would have a left or right hand when projected onto the top/bottom and front/back orientation of the animal. Thus animals take on an orientation from projecting a

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Page 96 normally oriented human onto the normally oriented animal frame; an orientation scheme that might be loosely derivable according to Gentner and Gentner’s (1983) structure mapping principle. This means that the front/back and top/bottom of the animal do not necessarily correspond to the same sides when the animal is laid out next to the human form. For instance, the front of a snake or a hippopotamus does not correspond to where its belly is, rather it is the side of the head which matches the front side of a human when standing erect. Similarly, the top of the two animals corresponds anatomically to their back rather than the uppermost surface of the head. However, the situation is not so straightforward when it comes to inanimate objects, in which case it depends on how we normally interact with the object. Here the projection can either derive from the coincidence situation, according to which vehicles, for instance, are assigned sides in the same way as animals; or, alternatively, it can come from the encounter situation, which reflects orientation in relation to a viewer encountering the object in question. In the encounter situation, top and bottom are assigned in exactly the same way as with coincidence: the top of an object is simply the uppermost side when the object is in its standard orientation as seen by a human viewer. So the top of a desk is its uppermost surface and the top of a painting is the part nearest the ceiling when the painting is hung on a wall. However, assignments of front/back and left/right are quite different from the coincidence assignments, since we usually encounter objects face on. The intrinsic front of the object corresponds to the side that usually faces us, and the intrinsic left and right correspond to the sides where our left and right hands would be when facing that object. Hence the front of the desk, mirror, or painting is the side that we usually encounter face on, and their left and right are the sides where our left and right hands would be under those circumstances. Finally, there is a third projection scheme, which lies somewhere between the intrinsic and relative paradigms described above. Sometimes described as the accidental intrinsic scheme (or motion intrinsic frame; Jackendoff, 1996), it depends on local features of the situation under discussion. Thus symmetrical objects like billiard balls can take on an accidental orientation when in motion. Their front/back becomes aligned with the direction of motion, and their left/right is then assigned relative to this front/back arrangement. Under other circumstances, objects can take on accidental orientations from the scenes in which they are embedded. For example, a tree facing a street inherits a front and back by analogy with a prototypical viewer encountering the tree as seen from the street. In a similar fashion, the front of a church will depend upon the notional perspective of the narrator: when this is from the inside, the front corresponds to where the altar is; when from the outside, it corresponds to where the entrance is (Fillmore, 1982).

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Page 97 Reference frame activation and assignment So there are several reference frames that can be used to assign direction to spatial relations. But are there any preferences for choice of particular reference frames? And, can multiple reference frames be simultaneously activated during spatial language processing? Sometimes different reference frames coincide in relation to a particular arrangement of objects in space. For example, in John is under the stars , the stars are above John intrinsically (the head is the top of the body), absolutely (in the gravitational plane), and relatively (given that the description normally assumes speaker and hearer are similarly in contact with the Earth’s surface). However, conflicts between reference frames also can occur. For example, in face-to-face communication, an expression like The bin is to the left of the desk could refer to the speaker’s (relative) left, the hearer’s (relative) left, or left with reference to the intrinsic reference frame (in which case the positions of hearer and speaker are irrelevant). Carlson-Radvansky and Irwin (1993) tested whether specific reference frames were preferred for above . Participants were presented with pictures in which reference frames were either aligned (coincided) or misaligned (conflicted) with each other. For example, consider the pictures in Figure 5.4 (adapted from Carlson-Radvansky & Irwin, 1993; Levelt, 1996). In (a), the ball is positioned higher than the chair from the viewer’s point of view, in the gravitational plane, and in relation to the intrinsic properties of the reference object. In (b), the ball is higher in both the relative and absolute frames, but not in the intrinsic frame. In (c), the ball is higher in both the absolute and intrinsic frames, but not in the relative frame. In (d), the ball is only higher in the absolute frame, and so forth. Using scenes of this type, Carlson-Radvansky and Irwin (1993) found that participants are able to use a variety of reference frames to define above . There is a strong preference for absolute above followed by a small, but nonetheless significant, preference for intrinsic above , with little preference for using the relative frame (but see discussion of Friederici and Levelt, 1990, on p. 56). However, the absolute frame does not predominate with projective terms that do not operate in the gravitational axis. There is evidence that in front of and behind are predominantly influenced by the intrinsic or the relative reference frames. For example, it has been shown that by the age of 5 children prefer to place a located object according to the intrinsic reference frame when the reference object has an inherent front and back (e.g., Harris & Strommen, 1972). Also, clearly left of and right of involve competition between the relative and intrinsic frames. For example, Graf (1994; cited in Kessler, 2000) found that the time taken to respond “left” or “right” to a question such as “In which hand is the cup?’’ increased as a function of the degree to which the orientation of the person holding the cup differed from

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Figure 5.4 Aligned and misaligned reference frames (adapted from Carlson-Radvansky & Irwin, 1993; Levelt, 1996). The numbers in parentheses represent the percentage of above responses using similar scenes found by Carlson-Radvansky and Irwin (1993). Note that deictic = positive frame.

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Page 99 that of the viewer in cases where the person holding the cup in the picture was rotated past 90 degrees. More generally, Franklin and Tversky (1990) have shown that objects accessed on the left–right dimension are accessed slower than objects in the front–back and above–below dimensions when learning imaginary environments (see also de Vega, Rodrigo, & Zimmer, 1996). So there is evidence that people are able to use a variety of different reference frames. There is also evidence that multiple reference frames are automatically activated and compete in assignment of a direction to a spatial relation (see Carlson, 1999). For example, Carlson-Radvansky and Irwin (1994) presented participants with pictures of the type illustrated in Figure 5.4, but this time they had to indicate as quickly as possible whether sentences presented with the pictures were acceptable or unacceptable descriptions of the pictures. The response pattern (i.e., acceptable vs. unacceptable judgements) mapped onto the data produced by Carlson-Radvansky and Irwin (1993). However, the reaction time data indicated that multiple reference frames were simultaneously activated during the early stages of processing. For example, yes responses were significantly faster when the absolute, relative, and intrinsic frames coincided (e.g., Figure 5.4a) than when they did not. Furthermore, Carlson-Radvansky and Logan (1997) presented evidence that reference frames are activated automatically. They instructed participants to use only one specific reference frame to define an above relation and found that response times were still quicker when reference frames coincided than when they did not, despite the fact that participants were instructed to consider only the one frame. Carlson-Radvansky and Jiang (1998; see also Carlson & Logan, 2001) used a negative priming paradigm to provide evidence that the selection of a reference frame benefits from inhibition of non-selected reference frames. For example, imagine a hunter pocket-watch rotated 90 degrees clockwise from its canonical orientation, with a pea positioned directly higher than the watch in the gravitational place (Prime A). Imagine instead a pea positioned in the same location as before, but this time a football replaces the pocket-watch (Prime B). Imagine now an apple rotated 90 degrees from its canonical upright such that the stalk is pointing to the right, and the pea is to the right of and in line with the stalk (probe trial). Carlson-Radvansky and Jiang found that responding true to The pea is above the stalk on the probe trial was significantly slower when it followed Prime A than when it followed Prime B. In other words, the response was delayed when there was a conflict between the reference frame associated with the prime, which inhibits the intrinsic frame, and that used in the probe. Furthermore, this inhibition of the intrinsic frame carried over to slower below responses on probe trials also. There is also some preliminary evidence from the measurement of event-related potentials to support multiple activation and selection/inhibition of

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Page 100 reference frames (Carlson, West, Taylor, & Herndon, 2002; Taylor, Faust, Sitnikova, Naylor, & Holcomb, 2001; Taylor, Naylor, Faust, & Holcomb, 1999). Event-related potentials are useful because they indicate the time-course of cognitive processing. For example, Carlson et al. (2002) found that competition in assigning directions to space was associated with modulation of a frontal slow wave and computing and comparing the spatial relation was associated with modulation of a parietal slow wave. Furthermore, these modulations were differentially influenced by the type of reference frame used to define the spatial term (and by the participant’s response). Reference frames are central to the comprehension and production of projective terms. Clearly, one needs to answer the question of which way up is up before one can use a projective term appropriately. However, we have little more to say here about how reference frames are structured and applied. Instead, we refer the reader to the excellent coverage of these issues elsewhere (see, for example, Spatial Cognition and Computation, 1999, Vol. 1(4), which is entirely dedicated to this issue; see also van der Zee & Slack, 2003, for an edited collection of papers on the issue; and the papers by Levelt, Levinson, and Tversky in Bloom et al., 1996). Now we turn our attention to geometric and dynamic-kinematic routines across a range of projective terms. GEOMETRIC AND DYNAMIC-KINEMATIC ROUTINES Geometric routines Once a reference frame has been selected, speakers have to judge the appropriateness of terms in relation to that reference frame. A useful place to start is to consider the simple case of abstract geometric shapes presented in two-dimensional grids. There is much evidence for graded structure in relation to projective terms like above and over. A number of studies (Carlson-Radvansky & Logan, 1997; Hayward & Tarr, 1995; Crawford, Regier, & Huttenlocher, 2000; Logan & Sadler, 1996; Munnich, Landau, & Dosher, 2001) have shown the importance of certain axes in determining the appropriateness of the prepositions in English (and in other languages; Munnich et al. , 2001). For example, Hayward and Tarr (1995; see also the discussion of spatial templates in Chapter 3) presented participants with crosses positioned at various points on a grid relative to a stationary reference object. In one experiment, participants had to rate the appropriateness of each cross to describe the cross as [ preposition] the reference object. They found that the highest ratings for above , for example, were directly higher than the reference object, within the region extending up from the outside edges of the reference object (the bounding box ). More recently, Regier and Carlson’s (2001) attention vector sum (AVS) model provides what we can regard as a geometric routine for the above

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Page 101 relation, which maps onto the data from Logan and Sadler (1996) and Hayward and Tarr (1995), as well as data from their own experiments. In particular, Regier and Carlson show that there are a number of dimensions that together predict the acceptability of above better than any single dimension on its own. They asked participants to rate the acceptability of above to describe the position of a located object (a single point) with reference to a reference object (which changed shape according to the manipulations used). In four experiments, Regier and Carlson tested the influence of proximal orientation and centre-of-mass orientation on participants’ acceptability judgements for above . Proximal orientation (see Figure 3.6 in Chapter 3) is the angular deviation relative to upright vertical of a line connecting the closest two points of the located and reference objects. Centre-of-mass orientation is the angular deviation (again relative to upright vertical) of a line connecting the centres of mass of the located and reference objects. In one experiment they kept proximal orientation constant while varying centre-of-mass orientation. They found that acceptability ratings decreased with increased deviation of centre-of-mass orientation (i.e., ratings were lowest for the greatest deviation in angle from upright vertical). Similarly, in another experiment they manipulated proximal orientation while keeping centre of mass constant, and found independent evidence for the influence of proximal orientation on acceptability judgements. Additionally, they found evidence for the importance of two other factors: the grazing line and distance. The grazing line is the line running through the topmost part of the reference object, and distance is the distance between located and reference objects. The AVS model (see pp. 48–51) was found to fit the empirical data better than other available models, and also includes an attentional component that could account for a wide range of additional empirical effects. The AVS model has the potential to be developed to account for the appropriateness of a range of spatial terms to describe the geometric position of one object with reference to another object, at least with respect to scenes involving abstract two-dimensional objects. For example, in front of used intrinsically relates to the bounding box of the located object set by the intrinsic front of the object. Dynamic-kinematic routines Just as we have seen with the comprehension and production of in and on, there is a range of types of evidence that dynamic-kinematic routines are also important for the comprehension and production of projectives. Carlson-Radvansky and Radvansky (1996) found that the presence of a functional relation between objects to be described influences the choice of reference frame used to describe the locations of those objects. Imagine a picture of a postman holding a letter standing near and to the left of a

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Page 102 postbox. When the postman was standing facing the postbox with hand outstretched as if to be posting the letter, then participants had a preference for using intrinsic descriptions (e.g., The postman is in front of the postbox). In contrast, when the postman was standing with his back to the postbox, then extrinsic-relative descriptions were preferred (e.g., The postman is to the left of the postbox). Therefore, the use of the intrinsic reference frame is preferred when the located object and reference object are in a position to interact with each other. Following on from this, it might be expected that blocking the postman’s access to the postbox would diminish the appropriateness of in front of to describe the postman. Richards (2001) and Richards and Coventry (2003a) tested this by placing a screen between located and reference objects using similar manipulations to those just described. Indeed, as expected, they found that the production of in front of (intrinsic reference frame) decreased when access to the reference object was obstructed by the screen in a free production task. In another study, Carlson-Radvansky et al. (1999) asked participants to rate the appropriateness of The coin is above the piggy bank to describe the location of a coin positioned in relation to a piggy bank that had a coin slot in various positions on its back. According to Logan and Sadler (1996), Regier (1996), and Regier and Carlson (2001), the optimal rating for above should be directly higher than the centre of mass of the piggy bank. However, the piggy bank used by Carlson-Radvansky et al. was of the type displayed in Figure 5.5. The position of the slot varied so that it either coincided with a position directly above the centre of mass of the piggy bank or did not. They found that the acceptability ratings shifted as a function of slot position. The

Figure 5.5 A representation of the piggy bank used in the study by Carlson-Radvansky et al. (1999). (Each participant saw only one slot position.)

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Page 103 highest ratings were in cases in which the coin was aligned with the slot, rather than directly higher than the centre of mass of the piggy bank. These results are consistent with the idea that participants use a dynamic-kinematic routine (similar to location control for in and on) to determine what would happen to the coin should it be dropped towards the piggy bank. If the coin is predicted to fall into a slot, then it is judged to be optimally above the piggy bank. Coventry et al. (1994) present evidence consistent with this interpretation in relation to the preposition over. Participants were presented with video scenes of a tilted jug positioned higher than a glass. When the jug and glass were shown to contain water, over was judged to be significantly more appropriate than when they were empty. In other words, in a situation in which the liquid could be poured from the jug into the glass, over was preferred. Coventry and Mather (2002) tested more directly whether there is a relationship between comprehension and production of the preposition over, and judgements of object interaction over time. In one experiment, participants were shown a diagram (partitioned into three segments) of a building that lies on the flight-path of an aeroplane and were asked to indicate in which segment they considered the plane to be over the building (see Figure 5.6). There were three conditions: a control condition with no additional context (Condition 1) and two experimental conditions in which participants were told that the diagram was of a fighter-bomber on a mission to bomb a building (Condition 2) or target (Condition 3). Coventry and Mather found that in the context conditions (2 and 3), segment one was selected significantly more than in the no context control condition, as is shown in Table 5.1. Knowledge about paths of objects being dropped from a moving plane have been shown to deviate markedly from Newton’s laws (e.g., Green, McCloskey, & Caramazza, 1980; McCloskey, 1983), so Coventry and Mather also asked participants where they thought the bomb should be dropped so as to hit the building/target. The judgements

Figure 5.6 One of the aeroplane scenes used by Coventry and Mather (2002).

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Page 104 Table 5.1 Segment choice in the study of Coventry and Mather (2002) Condition Segment 1 Segment 2 Segment 3 Control ( n = 26) 4 18 4 Bomb context “building” ( n = 26) 9 16 1 Bomb context “target” ( n = 26) 14 11 1 Note : Values represent the number of participants choosing each segment. of where the bomb should be dropped correlated significantly with segment choice. This shows that judgements of location control in terms of naive physical knowledge about how objects fall to the ground influences the rating of over. Although Coventry and Mather found that the acceptability rating and production of over was influenced by the bombing context, in another study they found that above was not so affected by the context. Following this indication that over may be more affected by dynamic-kinematic routines than above , Coventry and Prat-Sala (1998) and Coventry, Prat-Sala, and Richards (2001) set out to examine the effects of functional relations versus geometric routines on the comprehension of over, under, above , and below . In one experiment, they manipulated both geometric and functional relations across two distinct types of material sets. One set were cases where one object had the function of protecting another object (a person) from falling objects (e.g., top nine pictures in Figure 5.7). The other set of objects used showed associated objects interacting with each other with varying degrees of success (e.g., bottom nine pictures in Figure 5.7). Three positions of object were depicted for each scene, and they were shown to be operating functionally, nonfunctionally, or in a situation where function was less relevant. For example, the top nine pictures in Figure 5.7 show the three levels of geometry and functionality for scenes involving an umbrella. The columns illustrate three different positions of the umbrella rotated away from the gravitational plane. The rows represent the three levels of functionality. Rain is depicted as either falling on the umbrella (functional condition, middle row) or on the man (nonfunctional condition, bottom row), or no rain was present (control, top row). Participants had the task of rating how appropriate sentences of the type the located object is over/above the reference object (e.g., The umbrella is over/above the man) or the located object is under/below the reference object (e.g., The man is under/below the umbrella) to describe each picture. First, Coventry et al. (2001) found an effect of geometry as one would expect; rotating the umbrella, for example, away from the gravitational plane reduced the appropriateness of over and above . However, they also found equally strong effects of the

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Page 105

Figure 5.7 Sample scenes used by Coventry et al. (2001).

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Page 106 functional manipulation. The highest ratings were given to the functional scenes and the lowest ratings were given to the non-functional scenes. More importantly, effects of function were found even when the objects were in geometrically prototypical positions for those terms (e.g., directly above the centre of mass of the reference object for over). This indicates that functional factors have an influence even when the geometrical constraints are at their strongest. Additionally, this study found the first systematic evidence that over/under and above/below are differentially influenced by geometry and functionality. Whereas ratings of above and below were better predicted by the geometric manipulation than ratings for over and under, ratings for over and under were more influenced by functionality than those for above and below . This pattern of ratings is shown for the second material set (e.g., bottom nine pictures in Figure 5.7) in Figure 5.8. In another experiment, Coventry et al. (2001) set out to examine differences between over/under and above/below in cases where there is a conflict between frames of reference. Consider the scenes in Figure 5.9. With the scenes on the left, the relative/absolute (gravitational) and intrinsic (object-centred) frames of reference are aligned. With scenes in the middle and on the right, the relative/absolute and intrinsic frames do not coincide, but conflict. In other words, one can say that The shield is above the Viking for scenes on the left according to both frames of reference, but for scenes in the middle and on the right The shield is above the Viking is only appropriate

Figure 5.8 Interaction between preposition set (‘‘over/under” vs. “above/below”), geometry, and function in Coventry et al. (2001).

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Figure 5.9 Sample scenes examining frame of reference alignment/misalignment in Coventry et al. (2001). according to the relative/absolute frame of reference. The experiment examined whether the functional relation in the scene being described would lead to a predominant use of the relative/absolute (gravitational) reference frame. This would be consistent with the protection function highlighting the importance of gravity. Furthermore, in light of the differential influence of geometric and functional factors for the prepositions above/below as opposed to over/under , they suspected that there might be differential preferences for the two kinds of preposition. The effects found were particularly striking. For above and below , conflict of frame of reference effects were found consistent with those reported by Carlson-Radvansky and colleagues; misalignment of reference frames was associated with a lower overall acceptability rating for these terms compared with scenes where reference frames were aligned. However, these terms were not found to be influenced by the functionality manipulation. Conversely, over and under were influenced significantly by functionality, but were not affected by conflict of frame of reference in the same way as

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Figure 5.10 Data from Coventry et al. (2001) comparing effects of geometry (top graph) and function (bottom graph) between preposition sets (“over/under” vs. “above/below”) when reference frames are aligned or misaligned. above and below (see Figure 5.10). Rather, ratings were lowest when the reference object was in the supine position, and no differences were found between the extreme frame of reference conflict scenes and the aligned scenes. The interpretation of this finding is related to functionality. When the located object (e.g., the man) is in the supine position, the surface area of the reference object (e.g., the umbrella) is not large enough to protect the man from getting wet. Therefore, the reference object is not able to fulfil its

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Page 109 function and, as a consequence, the ratings given to the functional and the control scenes become more like the ratings for the non-functional scenes in which the reference object is not fulfilling its function. In a further series of studies, Coventry, Richards, Joyce, and Cangelosi (2003b) manipulated the degree to which an object can fulfil its function (e.g., through changing its size, or by damaging the object). They then determined effects on the appropriateness of over, under, above , and below (using the same types of materials displayed in Figure 5.7). For example, increasing the size of an umbrella increases the protection function that the object affords, while an umbrella full of holes does not afford much protection from the elements. Indeed, Coventry et al. found that increasing the size of the protecting objects magnified the functional effect for all spatial terms, such that the effects of the functional manipulation occur as strongly for above/below as they do for over/under . In contrast, the addition of holes to the (same-sized) umbrella was found to weaken the function effect as expected. Clearly, we have found much evidence for the importance of dynamic-kinematic routines on the comprehension and production of a range of projective terms. Furthermore, the weighting given to dynamic-kinematic routines has been shown to differ across spatial terms and types of objects. We now turn to consider the evidence for the importance of the third component in the functional geometric framework, object knowledge. CONCEPTUAL KNOWLEDGE AND CONTEXT EFFECTS There is much evidence that object knowledge influences both the selection of a reference frame, and the comprehension and production of a range of projective terms once that reference frame has been aligned. As part of the postman experiment described above, Carlson-Radvansky and Radvansky (1996) also manipulated the functional relations between the objects. They compared functionally related pairs of objects (e.g., postman and postbox) to pairs of unrelated objects (e.g., postman and birdhouse) and found that the intrinsic reference frame was produced significantly more for related objects (e.g., The postman is in front of the postbox) than for the unrelated objects. In contrast, the relative/absolute frames were produced significantly more for the unrelated objects (e.g., The postman is to the left of the birdhouse ) than for related objects. This indicates that knowledge of the relations between objects and how they normally interact plays an important role in the selection of reference frames. Carlson-Radvansky and Tang (2000) also found the intrinsic reference frame is preferred over relative/absolute reference frames for above , using a similar task to the one used by Carlson-Radvansky and Radvansky (1996). Located objects positioned in line with the intrinsic frame were rated more acceptable for pictures denoting related objects interacting than in pictures

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Figure 5.11 Sample materials from Carlson-Radvansky and co-workers’ (1999) placement study (adapted from Carlson, 2000). where unrelated objects interacted or where the related objects were not shown to interact. This study shows interplay between object knowledge and dynamic-kinematic routines. Carlson-Radvansky et al. (1999) also report a second study in which they found that, for functionally related objects, there was a deviation in object placements towards the functional part of the object, but this deviation was not so marked for functionally unrelated objects. They presented a range of reference objects in which the functional part (e.g., the bristles on a toothbrush) was either aligned (Figure 5.11a) or misaligned (Figure 5.11b) with the object’s centre of mass. They then presented pictures of different located objects that were either functionally related to the reference object (e.g., a toothpaste tube, Figure 5.11c) or unrelated to the reference object (e.g., a tube of paint, Figure 5.11d). The task for participants was to stick the picture of the located object above the reference object. When the functional part and centre of mass of the reference object were misaligned, they found that participants positioned the related located objects between the centre of mass and the functional part, and that the deviations towards the functional part were greater for the related objects than for the unrelated objects (see also Carlson & Covell, in press). Note that the deviation in this study was not fully aligned with the functional part (as in the piggy bank study in the same paper). This result may be interpreted in a number of ways (see Chapter 7), but clearly the study illustrates the influence of object knowledge on understanding of above .

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Page 111 Coventry et al. (2001) also investigated the influence of object knowledge in the umbrella-type studies reviewed above. They compared objects that do not have a known protecting function with those that do. For example, a suitcase was substituted for the umbrella in the scenes in Figure 5.7. Clearly, a suitcase is not known as something that offers protection against the rain. So the question is whether it will still be judged as over the person to the same degree as something like an umbrella, which is known to have this function. While they found that the ratings for the inappropriate functional objects were lower overall than for the appropriate protecting objects, no interactions were found between this variable and any of the other variables examined. In other words, the effects of functionality and geometry were present for the non-stereotypically functioning objects just as they were for the stereotypically functioning objects. This is clear evidence that how objects are functioning in context is important, irrespective of our stereotypic knowledge about those objects. There is also evidence for a range of contextual factors influencing how projective terms are interpreted. For example, Grabowski and Miller (2000) review a series of studies that manipulated the context in which spatial expressions such as in front of and behind (and their German equivalents) are interpreted. Consider the following scenario (depicted in Figure 5.12). A driver and a (front-seat) passenger are inside a car in the right-hand lane of a (German) road. The passenger says to the driver, “Could you please drop me off/stop in front of/behind the white car/tree”. Now imagine that you are a learner driver on a driving test and the passenger is a driving examiner or, alternatively, that you are the driver and are taking your friend home

Figure 5.12 The scene used by Grabowski and colleagues (adapted from Grabowski & Miller, 2000).

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Page 112 (the passenger). In a series of studies spanning comprehension and production tasks, Grabowski and colleagues (Grabowski, Herrmann, & Weiss, 1993; Grabowski & Weiss, 1996) found that when the reference object was the car (denoted by the crossed circle in Figure 5.12), the intrinsic in front and behind regions were used irrespective of the context. Thus, subspace 3 in Figure 5.12 was preferred for in front of and subspace 1 for behind. However, when the reference object was a tree (i.e., with no inherent front and back), in the driving test scenario in front of was assigned predominantly by alignment with the direction of motion of the car, whereas in the lift home scenario in front of was assigned either with reference to the direction of motion of the car, or with reference to the temporal interpretation of in front of (stopping before the white car). Furthermore, Grabowski and Miller show that the use of a non-oriented reference object (tree) also leads to inconsistencies between comprehension and production and, therefore, to a low level of communicative correspondence. SUMMARY AND CONCLUSIONS In this chapter, we have considered what are in many respects the most complicated and the most widely studied of the spatial prepositions. Projectives are complicated because they require a frame of reference for their interpretation. They are also particularly interesting in relation to the functional geometric framework because both the assignment of the reference frame and the subsequent interpretation of the prepositions clearly depend on extra-geometric factors. Take, for example, Carlson-Radvansky and co-workers’ piggy bank scenario. First, assigning an intrinsic frame of reference to the piggy bank depends on a combination of knowledge of pigs (e.g., to establish where the top is likely to be) and quite probably also of the function of piggy banks (e.g., to appreciate that they have to be in a certain orientation for coins to be placed in them). Then, to understand a relation like over or above when it refers to a coin and a piggy bank depends upon appreciating what someone is likely to want to do with the coin and the piggy bank. Where over or above is depends on more than just which way is up. So it is perhaps not surprising that the semantic problems thrown up by the projectives have led those such as Johnson-Laird to argue for the importance of mental models in spatial reasoning. As we pointed out in Chapter 3, one of the main motivations behind the functional geometric framework is how it might help to explain some of the locative inferences that we draw from descriptions of scenes. In the functional geometric framework, such inferences derive from understanding the functional relations between the objects in the scene and incorporating both geometric and functional information into the model of the scene that we build. Projective prepositions, such as over, serve to illustrate the advantages of this kind of framework.

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Page 113 CHAPTER SIX Experimental evidence for the functional geometric framework 3: other prepositions—proximity, coincidence, and being between Thus far we have considered in and on and projective terms, such as over and in front of . However, other spatial prepositions have received less detailed treatment in the literature. Among these are proximity terms, like near , far, and at , which provide information about the relative distance between objects without specifying a direction, and expressions like between, which don’t easily fall into the categories of topological, projective, or proximity terms. We first consider proximity terms and then consider the specific case of between. PROXIMITY TERMS: HOW NEAR IS NEAR? Many prepositions in English give information about the distance between a located and reference object without necessarily specifying a direction in which the distance is projected. The very fact that these terms, which include near , beside, far from , and at , are labelled proximity terms suggests that distance is the primary information that they communicate. However, they do not specify distance alone. Their use is also determined by the objects involved and the environment in which those objects occur. For example, the size and mobility of the objects being described influence the use of proximity terms. With reference to size, two small objects, such as a paperclip and pencil, may be regarded as far from one another when they are one metre apart, but a car one metre from a lorry would be regarded as being near the lorry (and may be dangerously close if the lorry and car are in motion).

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Page 114 Thus the size of the objects being described influences the distances appropriate for use of proximity terms. Additionally, the scale in which those objects occur also influences proximity terms. Indeed, Langacker (1987, p. 118) notes that some proximity terms (such as close to) appear to permit “apparently unlimited focal adjustments with respect to scale”. Imagine the paperclip and pencil one metre apart on a table versus one metre apart in a desert. The use of small-scale space adjusts relative distance such that small distances become greater, whereas large-scale space adjusts relative distance such that small distances are reduced. The objects themselves can also ‘‘call up” distance norms, which can be used to establish scale (Miller & Johnson-Laird, 1976). Consider The golf ball is near the hole versus The billiard ball is near the hole . In the first case, the large scale of a golf course means that on a par-five hole the golf ball could be near the hole when it is several metres from it, but in the second case the context of the billiard table near the hole would mean centimetres (rather than metres) from the hole. Note that in this case the balls and holes are the same size; it is only the context that is changing. Small objects are also usually located with reference to larger objects. The coin is beside the fence is acceptable but *The fence is beside the coin is not. And mobile objects are usually located with reference to immobile objects, but not vice versa. For example, one can say The bike is near the fence but *The fence is near the bike is unacceptable (Landau & Jackendoff, 1993; Talmy, 1983). This is because the bike can move but the fence cannot. Furthermore, it is perfectly acceptable to say The truck is near the post box , whereas *The post box is near the truck is less acceptable. Although the truck is larger than the post box, it is potentially mobile, whereas the post box is not. This means that the smaller post box becomes an effective reference object. However, the appropriate use of proximity terms is not just determined by distance, size, and mobility. Indeed, the conclusion we will come to for these terms mirrors what Morrow and Clark (1988) have argued in relation to the verb approach. Morrow and Clark (1988) present convincing evidence that when listeners interpret the verb approach, they have to determine the region of interaction in relation to a situation model. More specifically, Morrow and Clark outline five properties of the situation model that influence the region of interaction: size of located object, size of reference object, speed of located object, purpose of located object, and distance from the observer. To test the influence of these factors, they presented in various contexts descriptions of the form Located object X is just approaching reference object Y. For example, to test for purpose they used I am standing by the side of a park looking at a rare lizard on a tree stump. A woman is just approaching it with binoculars/a sketch pad (see Table 6.1 for other examples). Participants had the task of reading each description and estimating the distance between

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Page 115 Table 6.1 Examples of scenarios used by Morrow and Clark (1988) Size of located object manipulation I am standing on the porch of a farmhouse looking across the yard at a picket fence. A tractor / mouse is just approaching it. Size of reference object manipulation I am standing across the street from a post office with a mailbox in front of it. A man crossing the street is just approaching the post office/mailbox. Speed of located object manipulation I am standing by the side of a parking lot, looking at the far side. A woman has just skated /hobbled into the lot, from the far side. Purpose of located object manipulation I am standing at the entrance to an exhibition hall looking at a slab of marble. A man is just approaching it with a camera/chisel . Distance of observer manipulation I am standing one block from/next door to a new house being constructed. A carpenter is just approaching it. located object and reference object. Overall, Morrow and Clark found evidence for all the properties they had outlined except for distance from the observer. Distances from located object to reference object averaged about 40 feet longer for the large than the small located objects, about 9 feet longer for the large than the small reference objects, about 8 feet longer for the fast than the slow located objects, and about 15 feet longer for purposes that could be accomplished at a distance as opposed to those that could not. Morrow and Clark, therefore, provide evidence that multiple factors jointly determine the appropriate distance for the verb approach, and that these factors are put together in a situation model. But how does this apply to the proximity prepositions near and far? NEAR AND FAR Adopting the methodology developed by Morrow and Clark, Carlson, Covey, and Klatt (in preparation, cited in Carlson, 2003) examined the influence of the size of the located and reference objects on the distance inferred between them for a range of prepositions including near and far. They found that distance estimates varied as a function of the size of the objects. Estimates were smaller for smaller objects and larger for larger objects, mirroring Morrow and Clark’s findings for approach. In addition to the restriction that mobile objects are usually located objects, whereas reference objects are more often immobile, there are other cases

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Page 116 where potential movement, and knowledge about such movement, influences the comprehension and production of near and far. As with Newton’s laws, there is a relationship between distance, speed, and time. A bicycle 5 kilometres from a house is far from the house, but a car the same distance away may be near the house. This is because the bicycle would take longer to reach the house, given its limited speed, than the car would. Consider also the case of a car and bicycle the same distance from the house, but this time the vehicles and house are separated by a series of lanes too narrow for the car to negotiate but not for the bicycle. Under such circumstances, although the distance is the same, the car is somehow less near the house than the bicycle. Coventry, Mather, and Crowther (2003a) presented participants with pictures of either a Ferrari or a Robin Reliant at various distances from a reference object. Whereas a Ferrari is known for its speed and elegance, a Robin Reliant is a three-wheeled car often lampooned for its appearance and limited speed. Texts were presented with the pictures which indicated that the cars were travelling at a constant speed of 20, 70, or 120 mph. Additionally, the driver of the car was systematically varied. He was either Richard Baker, an elderly classical music presenter on radio who was regarded as a slow driver in pretests, or Chris Evans, a disc jockey and media mogul famed for his fast lifestyle and regarded as a fast driver in pretests. Not surprisingly, although the speeds were identical for both vehicles and drivers, The Ferrari is near the house was rated consistently more appropriate than The Robin Reliant is near the house at all three speeds. There was also a significant effect of the driver of the car. Overall, near ratings were higher when Chris Evans was driving than when Richard Baker was driving. Therefore, despite being told that the car was travelling at a constant speed, participants’ judgements were affected by both the speediness of the vehicle and expectations about the speed the driver was likely to drive at. In a somewhat different series of studies, Ferenz (2000) tested whether the functional relationship between objects influences judgements of the appropriateness of different proximity terms. In one study, he used pictures of functionally related objects (e.g., a couch and a TV) or unrelated objects (e.g., a bicycle and a cooker). They were presented with their intrinsic fronts either facing each other or facing away from each other (see Carlson-Radvansky & Radvansky, 1996, for the rationale behind this manipulation). Hence, when the related objects (e.g., the couch and TV) were positioned facing away from each other, they were in a non-functional relative position: a person seated on the couch could not view the TV programme. In other words, the TV was not easily accessible (see also Vandeloise, 1991, for an extended discussion of accessibility for the French prepositions près and loin de). Participants had to rate the appropriateness of sentences of the form The located object is near the reference object to describe the scenes. For the non-functional pairs of objects, no effect of orientation was found.

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Page 117 However, functionally related objects were given significantly higher ratings for near when they faced each other than when they were facing away from each other. Ferenz (2000) also examined how qualified relative distances are affected by the functional relationship between the two objects. Sentences like The couch is too near the TV make sense as they stand because of our knowledge of the interaction between couches and TVs (e.g., the TV may be too close for the viewer to see it when seated on the couch at that distance). In contrast, sentences like The book is too near the computer monitor are difficult to interpret without additional information, such as … to put the modem between them. Indeed, Ferenz shows that functional relationships between objects do provide an implicit reason for qualified relative distance, whereas nonfunctional relations require further qualification before they are rated as acceptable. So there is evidence that conceptual knowledge about objects and how they usually interact with one another influences the appropriateness of proximity terms. However, we have not addressed the issue of whether these effects point to the use of separate dynamic-kinematic routines, as we have argued for in, on, over, under, above , and below . The difference between prepositions that provide information about distance and the other prepositions thus far considered is that distance is meaningless without a context. You need scale to establish whether a distance is near or far and contextual factors determine scale. Therefore, the answer to the question “how near is near ?” depends on constructing a distance ratio taking into account all the available information. The findings on the use of proximity terms are similar to those for distance estimation on the basis of memory for locations. Memory for learned distances violates formal principles of Euclidean geometry, such as axioms of symmetry (i.e., that the distance from A to B is the same as the distance from B to A). For example, there is evidence that the estimated distance between a good landmark and a poor landmark is greater when the poor landmark is the referent than when the good landmark is the referent (e.g., Cadwallader, 1979; Rosch, 1975; Sadalla, Burroughs, & Staplin, 1980; see McNamara & Diwadkar, 1997, for a review). McNamara and Diwadkar (1997; see also Goldstone, Medin, & Halberstadt, 1997; Holyoak & Mah, 1982) offer a contextual scaling model that attributes asymmetries in proximity judgements to the cognitive processes involved in magnitude estimation, and not to the representation of the distance between those places in memory itself. According to the contextual scaling model, asymmetries arise because stimuli differ in the contexts they evoke and magnitude estimates are scaled by the context in which they are made. If the contextual scaling model applies to proximity terms, then we can make some predictions. McNamara and Diwadkar (1997) showed that the

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Page 118 direction of the asymmetry effects can be manipulated by the order in which locations are retrieved. In one experiment, they had participants learn the location of places on a map and manipulated how distance estimates were elicited. When participants were asked how far it was from location A to location B, an asymmetry effect was found in which the second location in the expression was used as a context with which to scale the judgement. However, when participants were asked to retrieve the name of A first and then estimate the distance from location A to location B (and, therefore, use A as the location to establish the context for the judgement), McNamara and Diwadkar found a reversal of the direction of the asymmetry effect. Similarly, we might expect asymmetries in the rating of the appropriateness of proximity terms when the located objects and reference objects are reversed, or when it is unclear which object is the reference object. Ferenz (2000) asked participants to rate How near are the X and the Y to each other? using the same materials mentioned above (e.g., a couch and a TV either facing each other or facing away from each other). In the case of this sentence, it is unclear which object is the reference object and which is the located object. Whereas The couch is near the TV clearly specifies the TV as the reference object, The couch and TV are near each other does not. Using this alternative question, Ferenz found no influence of functional relations on ratings. Presumably, when there is no clear distinction between located and reference objects, there is less contextual information available to moderate the distance judgement. AT The importance of both geometric and interactional elements for the preposition at has long been established. For example, Miller and Johnson-Laird (1976) note that it is not necessary to be contiguous (as H. Clark, 1973, suggested) or juxtaposed to something in order to be at it. For a located object x to be at a reference object y requires that the located object x is included in a region of the reference object y where it can “interact with y socially, physically or in whatever way x ’s normally interact with y’s” (Miller & Johnson-Laird, 1976, p. 388). Thus, whereas there are cases such as The man being at the piano, in which the man is both spatially localised at the piano and interacting with it, there are also cases, such as The man being at the window or The woman at the supermarket , where located and reference objects do not have to coincide spatially. However, interaction is not necessary for at to be appropriate. For example, The snail is at the stone does not imply that the snail is interacting with the stone, but rather that the snail is near the stone at a point on a projected path. Therefore, there are both geometric and extra-geometric aspects to the comprehension and production of at . We can then ask the question of whether at , like in and on, involves

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Page 119 two different routines, or whether at , like near and far, is dependent on a range of conceptual and contextual factors that scale the region appropriately. Like other distance relations, point of coincidence requires a scale to work out what that relation is, so at might be regarded as being more like proximity terms in this respect than so-called topological terms. Whether or not at is appropriate requires that potential interactions between located and reference objects need to be considered in the context in which that relation occurs. This obviates the need, as we have also seen for proximity terms, to specify precise distances between located and reference objects. Rather, at is appropriate if a point of coincidence has significance either in terms of clear interaction ( The man is at the supermarket , The woman is at the window, John is at work) or in terms of a change in location ( The snail is at the stone). Herskovits (1986) argues for a range of distinct “use types” for at , which separate interactional uses (e.g., person using artefact , person at institution) from spatial uses (e.g., spatial entity at location ). However, as with Morrow and Clark’s (1988) treatment of approach, the alternative is to assume that a range of factors come together to establish the appropriate region (concrete or abstract) in which the term can apply. Coventry (1992) has tested whether point of coincidence is enough to sanction the use of at for two different located objects presented the same distance from the reference object, but in situations either where there is interaction between the objects or not. Participants were presented with simple pictures (see Figure 6.1, left and middle pictures) for at involving either the “person using artefact’’ use type or the “spatial entity at location” use type, versus complex pictures involving both uses (i.e., with two located objects in the same picture; see Figure 6.1, picture on the right). They were then asked to complete sentences of the form The located object is____the reference object with a single preposition for the single pictures, or with two prepositions, one for each of the sentences of the same form, for the complex pictures. For the simple pictures with only one located object and one sentence to complete, many participants used at for both use type situations. However, the same participants, when presented with both located objects in

Figure 6.1 Examples of scenes used by Coventry (1992).

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Page 120 the same picture, used at for the person using artefact located object but switched preposition for the no interaction located object (switching to proximity prepositions like near and beside). This result illustrates that point of coincidence is not enough to license the use of at in both cases (for the complex pictures). Having a clear region of interaction is important and predisposes viewers to choose at . By contrast, when there is no obvious region of interaction, they tend to avoid at. Of course, this result is consistent with the view that there are two different senses for at (supporting Herskovits’s distinct “use types” analysis). However, a more parsimonious explanation (without the need to lexicalise different senses) would be that the factors that combine to establish region of interaction for each located object are incompatible and lead to the choice of different proximity terms for the two objects. So the use of at , like more standard proximity terms, depends on a range of conceptual and contextual information that establishes the region of interaction appropriate for the use of the term. We now move to consider a rather different preposition again, between, which has received less attention in the literature to date. BETWEEN Between differs from the other prepositions considered thus far in that it requires two reference objects (or sets of reference objects) for its use to be appropriate. For example, The boat is between the sky and the deep blue sea locates the boat with reference to the two reference objects, the sky and the sea. Similarly, The river is between the mountains assumes that there are two mountains or two sets of mountains as reference objects. O’Keefe (1996) suggests that between is appropriate if the sum of the distances from each of the reference objects to the located object is not greater than the distance between the two reference objects. In other words, an object placed in the space separating two objects should be appropriate. Van der Zee and Watson (in press) make a similar point about what they call the naive view of the geometry of between, which is illustrated in Figure 6.2. For located object x to be between reference objects y and z, then there should be a line that intersects y or z first, then the located object x , and then z or y last (see Figure 6.2a). Furthermore, there must be a projection plane p containing the projections x ′, y′, and z′ for x , y, and z, respectively, such that x ′ is included as a part of both y′ and z′ (see Figure 6.2c). Indeed, van der Zee and Watson (in press) carried out dot placement studies in which they found that the region defined as between above does map onto appropriate use of between (although there were some discrepancies; see van der Zee and Watson for a discussion). However, there are other senses of between that need to be considered that involve extra-geometric relations.

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Figure 6.2 Geometry and “between” (van der Zee & Watson, in press). According to the Oxford English Dictionary, between can also indicate that the located object separates the reference objects either physically or mentally. In other words, it either holds them apart or holds them together. Therefore, just as Garrod et al. (1999) found that alternative control of a located object reduces the appropriateness of on, it might be expected that alternative control of reference objects (i.e., alternative separators for those objects) may similarly reduce the appropriateness of between. Coventry and Garrod (in press) report a study (data collected by Jaqueline Dalimore) that tested the influence of alternative control on the comprehension of between. The experiment presented participants with different arrangements of wooden blocks and wooden balls and elicited judgements of the appropriateness of descriptions such as The ball is between the blocks. Sentences containing a range of prepositions were used. There were 37 scenes, some of which included an alternative source of separation/connection for the reference objects. There were three levels of alternative connector: (1) no alternative source; (2) loose alternative—nonrigid like a chain; and (3) rigid and substantial alternative (e.g., a bolt between the two blocks). An example set of materials is shown in Figure 6.3. Just as expected, the confidence in between judgements varied systematically with the degree of alternative connection between the blocks, as is illustrated in Figure 6.4. A similar finding is reported by van der Zee and Watson (in press). They used pictures of blocks, and compared between judgements when the blocks were labelled as blocks or when they were labelled as thumb and index

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Figure 6.3 Between scenes reported by Coventry and Garrod (in press).

Figure 6.4 Mean confidence (on a scale from 1 to 5) in between judgements for scenes containing increasingly strong alternative connectors for the reference objects (reported in Coventry & Garrod, in press).

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Page 123 finger. When the blocks were labelled as thumb and index finger, ratings for between were high in the region directly in line with the fingertips of the index finger and thumb and slightly above the index finger and thumb; when they were labelled as blocks, these regions were judged as less appropriate. Again, the results support the notion that the potential of reference objects (i.e., the fingers) to contact the located object (i.e., the ball) and control its location influences the appropriate region for between. Therefore, there is evidence for both geometric and dynamic-kinematic routines for between. Although not tested, there is also likely to be conceptual information associated with particular objects that influence how routines are applied. For example, between the sheets assumes contact (direct or indirect) of the sheets with the sleeper, but contact would not be expected for the located and reference objects in the case of between the houses. SUMMARY This chapter has looked at a very different set of prepositions from those discussed in Chapters 4 and 5. Unlike topological prepositions and projectives, the meaning of proximity terms does not depend on dynamic-kinematic routines; but, like both topological and projective prepositions, it does depend on extra-geometric factors associated with the construction of a suitable situation model for the scene being described. In the case of near and far, the crucial thing is in the scaling of the space and, as Morrow and Clark show, this is influenced by as many factors as one might care to imagine. It depends on the size of the relevant objects in the scene, the speed at which they may be travelling, the scale of the scene itself, the purpose for which the description is given, and our knowledge about the objects in the scene. Together these factors constrain the nature of the situation model that viewers construct and, in turn, their interpretation of the prepositions. In the case of at , the extra-geometric considerations are different again; they depend on a detailed knowledge of the regions within which objects interact with each other or within which we interact with those objects. To this extent, the semantics of at is particularly dependent on applying specific knowledge about objects and situations as opposed to applying general knowledge, of the kind used in dynamic-kinematic routines associated with the topological prepositions, about how objects interact in a physical world. However, whatever the source of the knowledge, it is still expressed in relation to the construction of a situation model of the scene being described. With respect to that model, at points to a region of interactional significance with the reference object. Finally, we turned our attention to a term that does not fit into the proximity paradigm: the preposition between. Between is different from the other spatial prepositions we have considered in that it is a three-place semantic

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Page 124 predicate; it requires two reference objects as well as the located object (others in this family include among and amidst, which are multi-place predicates). Despite appearing to have a purely geometric definition, its interpretation turns out to also be associated with extra-geometric factors that involve the physical or mental connection between objects. Again, the interpretation of between is going to depend upon the kind of situation model that a viewer will construct. As van der Zee and Watson (in press) show, the region between finger and thumb is not the same as that between two inanimate blocks. So the proximity prepositions plus between all point to the crucial role of the situation model in determining the precise spatial relations that they denote. In the next chapter, we attempt to pull together the various geometric and extra-geometric components of the meaning of the spatial prepositions into a general functional geometric framework for the spatial prepositions.

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Page 125 PART III Putting Saying, Seeing, and Acting Together: The Functional Geometric Framework in Action

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Page 127 CHAPTER SEVEN Putting it all together In the first part of the book, we argued that three types of information are central to an understanding of spatial language: geometric information, extra-geometric information available from the scene, and stored conceptual information. The functional geometric framework, therefore, requires geometric routines, extra-geometric routines that capture dynamic-kinematic relations between objects, and stored representations that reflect stereotypical functional relations between objects. In the second part of the book, we have seen that there is considerable evidence that these factors are important predictors of the comprehension and production of a range of spatial prepositions, including topological, proximity, and projective terms. We have also reviewed a range of contextual effects that indicate that spatial terms mean different things in different contexts. In the final part of the book, we develop the functional geometric framework; in this chapter, we will begin to explore how these multiple constraints come together to shape comprehension and production. A useful place to start is to consider the claim that situation models are required as a means of coordinating the different information sources that contribute to spatial language use. THE NEED FOR SITUATION MODELS: THE GENERAL ARGUMENT Pinning down reference There is no getting away from the fact that meaning is extremely difficult to pin down. As we saw in Chapter 2, prepositions refer to a wide range of

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Page 128 specific geometric relations in the world. The issue of whether or not all of these possible relations are listed in the lexicon, or whether situation-specific meaning is generated pragmatically, has pervaded the lexical semantic literature for quite some time. As we argued earlier, whether one adopts fully or minimally specified lexical entries, most theories are essentially referential in character. The lexical entries for spatial prepositions are taken to be the relations to which the prepositions refer. As we have also seen earlier in the book, grounding language in terms of perception allows one to address the issue of how the processing of spatial relations and of particular spatial terms is related. For example, it is possible to say much more than that the lexical entry for above corresponds to the relation “higher than”; rather, the processing of above is associated with particular computations, perhaps of the type nicely outlined in the attention vector sum model (Regier & Carlson, 2001). So, rather than representing a fixed core meaning, often glossed in terms of a dictionary-type lexical entry, this type of approach grounds language more directly in processing of spatial relations. Now, it is tempting to think that grounding language in perception offers a solution to the problems we have encountered throughout the book. An individual spatial term (e.g., over) is associated with a range of spatial relations. As we argued earlier with reference to spatial template theory, given the range of possible spatial relations associated with individual spatial terms, mapping a template onto a scene or computing a relation using a geometric routine does not resolve the issue of which template or routine is the appropriate one for that context. The argument we will develop here is that what a spatial preposition means in a specific context is a function of information present in the visual scene, knowledge of the objects in that scene, and an appreciation of how those objects are functioning in that particular context. All of these constraints operate together to establish situationspecific meaning. Hence, the range of possible situation-specific meanings for a preposition is going to be a function of the way in which these multiple constraints are put together and weighted within our functional geometric framework. We will discuss how the constraints come together later. First, we consider the general argument that situation models are required as the vehicles in which this can occur. Mental models The idea that human thinking can be explained in terms of the construction and manipulation of models in the mind goes back to Craik’s (1943) book The Nature of Explanation . Craik suggested that we apprehend and reason about our world via internal representations that serve to model reality and, like mechanical devices, they model reality to the extent that they share the same relational structure as the state of affairs being modelled. This means

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Page 129 that models can be used as internal surrogates for the real world, serving both to fill out the details and simulate how the world should change under different circumstances. It took 30 years for Craik’s original ideas about mental modelling to re-emerge in the literature. The contemporary use of mental models as explanatory devices arose from three main enterprises. First, they were proposed as a basis for logical inference (Byrne & Johnson-Laird, 1989; Johnson-Laird, 1983); second, as a means of characterising how we understand simple physical systems and devices (de Kleer & Brown, 1983); and third, as a basis for understanding analogical reasoning in a variety of contexts (Gentner & Gentner, 1983; see also Gentner & Stevens, 1983, for a general discussion). The common denominator in all these accounts was that mental models are bounded representations of reality that fulfil both a representational function and impose constraints on the way we can reason about objects and events. They make the world intelligible by restricting our view of it. In the context of his theory of reasoning, Johnson-Laird (1983) summarised the key principles of mental models thus: Mental models are finite and computable representations constructed from tokens arranged in a particular structure to represent states of affairs. A description of a single state of affairs is represented by a single model even if the description is incomplete or in some way indeterminate. However, mental models can represent indeterminacies if and only if their use is not computationally intractable and hence does not lead to an exponential growth in complexity. Finally, the structures of mental models are identical to the structures of the states of affairs, whether perceived or conceived, that the models represent. So mental models as described by Craik (1943) and refined by Johnson-Laird (1983), de Kleer and Brown (1983), and Gentner and Gentner (1983), have proved to be useful representations in accounting for how we apprehend our world and reason about it. They have two important characteristics. First, any particular domain can be represented according to a variety of different models, each reflecting different perspectives on that domain. Second, the choice of model will constrain our thinking about the particular target domain. It does this in a number of ways, first in terms of the so-called ‘‘ontology” of the target domain (Greeno, 1983). Any mental model needs to represent its target through a mapping between the tokens in the model and actual entities in the domain. Therefore, the tokens correspond to the conceptual entities that can enter into reasoning about that domain. Now the particular choice of tokens and their properties will determine what set of entities in the target are going to be significant. Hence it may severely limit our perspective on that target. This can be illustrated by considering the various models we might construct to represent the spatial arrangement of

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Figure 7.1 An arrangement of angles that can be represented differently according to the spatial mental model that a viewer imposes on the scene (adapted from Greeno, 1983). lines in Figure 7.1. According to one model, this figure might be broken down into three entities reflected in the angles DOB, BOC, and COA; alternatively, it could be represented as the two overlapping right angles DOC and BOA. Depending on which model is chosen, it may turn out to be either very straightforward or impossible to establish certain properties of the figure; for example, whether or not the angle DOB equals the angle COA (see Greeno, 1983). So one way in which models constrain the way we think about things is through imposing a particular “ontology” on the domain we are thinking about. Other ways in which they can affect our reasoning arise from the constraints imposed by the model on the actual mental operations carried out in using it. When we come to consider how models can act as interfaces between spatial language and the scenes it portrays, we will find a number of examples of how the ontology of the domain can affect the nature of the spatial relations we see in that domain. First, we need to discuss more generally how mental models might enter into language processing. Situation models and language processing We introduced mental models in the context of Craik’s original motivation for them as devices to aid thinking about the world. However, mental models also play a crucial role in language interpretation. First, it has been suggested that they function as surrogates for the world portrayed in the text or discourse. Hence they support the interpretation of language divorced from the real-world context in which it is encountered, as when interpreting reference to the characters and events portrayed in a fictional story. The second function is that of acting as an interface between the world being talked about and the language itself (Garrod & Sanford, 1989). We consider each of these functions in turn.

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Page 131 Models as surrogate representations Mental models that are used to represent the world of discourse have been described as discourse models (e.g., Kamp, 1981; Sanford & Garrod, 1998) or situation models (e.g., van Dijk & Kintsch, 1983; Zwaan & Radvansky, 1998). In either case, they serve to integrate information present in the text with information from memory such that the representation of the text as a whole goes beyond what is given just by the meaning of the words and sentences that it contains. In general, the argument for such models is compelling. Zwaan and Radvansky (1998) provide an excellent review of evidence in the case of text comprehension. Let us just consider one example that relates to the use of spatial prepositions. Consider the following two simple texts: (1) Harry put the wallpaper on the table. Then he sat his cup on it. (2) Harry put the wallpaper on the wall. Then he sat his cup on it. Sentence (2) sounds odd because when wallpaper is on the wall, it is in a vertical plane and would not support a cup. If you noticed this, which you will have, then this means you produced a mental model of what the first sentence meant in relation to the real world, and when you integrated the second sentence, there was a problem. The simple point is that situation models are required to explain how we can notice this kind of anomaly so easily. It cannot be explained just by reference to what the words themselves mean. Similarly, Hess, Foss, and Carroll (1995) found that the speed with which the last word in a sentence can be named is a function of the extent to which that word can be integrated into a situation model (rather than, for example, a function of the extent to which it relates to the lexical representations of the nearest words to it in the text). So, situation models are required to integrate information presented in a text. They are also required to explain similarities in how we process information from quite different sources. For example, the coherence of a text relates closely to the coherence of the same series of events presented visually or in auditory form, as has been shown by Gernsbacher, Varner, and Faust (1990). The correlation in comprehension performance for stories presented across a range of different modalities suggests that the same kind of situation model may underlie processing in all these modalities. Situation models have also been invoked to explain how we can integrate information from a variety of different sources. For example, Glenberg and Langston (1992) showed how information from one source (e.g., a picture, diagram, graph) can aid our interpretation of information from another (i.e., linguistic information presented at the same time). They presented participants with texts that described four-step procedures in which

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Page 132 Steps 2 and 3 were to be executed at the same time. For example, writing a paper requires writing a first draft (Step 1), consideration of the structure (Step 2), addressing the audience (Step 3), and proof-reading the paper (Step 4). Consideration of structure and addressing the audience are executed at the same time, but given the nature of texts the steps had to be described sequentially. When the texts were presented with appropriate pictures that showed the middle steps occurring simultaneously, people constructed appropriate mental representations of the procedure (i.e., both middle steps were connected equally strongly, as indicated by priming effects, to the first step and the last step). However, when the texts were accompanied by pictures in which the middle steps were shown sequentially, as in the texts, people tended to construct a mental representation reflecting the structure of the text rather than that of the procedure (i.e., one of the middle steps was more strongly connected to the first step and the other to the last step). Models as interfaces between language and the world The second function ascribed to mental models in language processing is as interfaces between the world being talked about and the language itself. This interface function, which will play an important role in our functional geometric framework, is particularly relevant when we are talking about space. For example, Garrod and Anderson (1987) used a cooperative maze game task to investigate how conversationalists described their locations on a maze. The players had the task of negotiating mazes like those shown in Figure 7.2 presented on different computer screens. The game was so organised that the move options for each player depended on the location of their partner. So to succeed, the two players had to keep abreast of where their partner was located on the maze at all times and this meant that they regularly had to describe where they were on the maze. What Garrod and Anderson found was that players adopted distinct but consistent description schemes to talk about the maze, which they readily classified into four basic types: path descriptions, line descriptions, coordinate descriptions, and figural descriptions. Each of these descriptions treats the maze in a different way, illustrated by the following (describing the position of the box marked with an X on A’s maze, Figure 7.2): • Path description: “See the bottom right, go along two, up one, then go two to the right, that’s where I am”. • Line description: “I’m on the second level, on the far right”. • Coordinate description: “I’m at E five”. • Figural description: ‘‘I’m in the box immediately below the last gate on the right”.

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Figure 7.2 Examples of the mazes used by Garrod and Anderson (1987). This pattern of results can be explained in terms of the use of different situation models. Garrod and Anderson (1987) argued that each description scheme is based on a particular mental model of the maze configuration, which in the case of effective communication would become “agreed upon” by the participants. Like Greeno (1983; see above), they claimed that the mental model has the effect of breaking down the scene into different sets of significant spatial entities—lines, points, regions, or volumes of space—associated with the various objects in the scene and then representing spatial relations between those entities. For example, in a path network model underlying a path description scheme, the maze is broken down into a series of boxes linked together by the actual paths on the maze. By contrast, in a line description model, it is broken down into a set of parallel lines related to each other either vertically (e.g., as rows above each other) or horizontally (e.g., as columns side-by-side). In giving a description, the speaker then has to formulate the spatial relations between these different entities represented in the model, and the nature of the description is going to be constrained by the particular relations between the entities in the model. Note that two locations on the maze can end up in rather different spatial relations depending upon the model adopted. For example, square X on A’s maze in Figure 7.2 is directly above the bottom right square according to a “column” version of the line model, so square X is next to the bottom right square in this model. However, in a path model, the two squares are quite far from each other. In terms of path links, square X is three along, one up and two to the right of the bottom square .

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Page 134 If such models underlie the description schemes used in the maze game dialogues, as Garrod and Anderson claimed, then they should also impose strict constraints on any description, both in terms of what spatial entities are being talked about and how these spatial entities might be discriminated from each other within the description. Indeed, when a pair of players adopted some particular model of the maze configuration, this was observed to have the effect of constraining their locative descriptions to the extent that the “local” meaning of any expression could only be derived through the model itself. Such an example would be the sometimes long-winded and bizarre descriptions, like the path description given above, which were commonly observed among players. The final point that needs to be made about such spatial mental models is that they are not the same as images. As Bryant, Tversky, and Lanca (2000) point out, mental models of space are more abstract and more schematic than images. Furthermore, the spatial relations within or between objects in a mental model of space need not be analogue in the way that they are in an image. For example, the distance between the two maze positions discussed above is not represented in an analogue fashion, otherwise it would have been the same in path and line models. Bryant et al. suggest that an image can be viewed as a special case of a mental model, where the spatial relations are analogue and there is a single perspective; but these are not the kind of models that we invoke in the functional geometric framework. Spatial models need to be more abstract than images to bring together information from the variety of different sources brought to bear in identifying any particular functional geometric relationship. So there is much evidence that language understanding depends on the use of situation models both as surrogate representations (e.g., discourse models) or as interfaces between language and what is being talked about as in the maze game described above. However, arguing that situation models are required is only the beginning; the more difficult task is the one of explaining how such models are constructed. It is to this issue that we now turn. THE FUNCTIONAL GEOMETRIC FRAMEWORK IN ACTION: MULTIPLE CONSTRAINTS AND SPATIAL LANGUAGE COMPREHENSION We have argued that appropriate use of a spatial term depends on multiple constraints associated with the scene being described. We have also seen evidence, summarised in Table 7.1, for a range of types of constraints on the comprehension and production of spatial prepositions. But how are these constraints determined? Before we consider a concrete example, it will help to discuss different levels of structure from which these constraints may emanate.

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Page 135 Table 7.1 Summary of the influence of the three ingredients in the functional geometric framework by preposition Preposition Geometric Extra-geometric dynamic-kinematic routine Extra-geometric conceptual constraints routine In Convex hull Location control Knowledge of specific function (region Manifestations: Predicted (Garrod et al., 1999)Manifestations: Different labels for same object connection or shown (Coventry, 1992, 1998; Ferrier, associated with weighting for different routines calculus) 1996) constraint of position of located object (Coventry et al., 1994; Coventry & Prat-Sala, by reference object. Animacy effects (Feist & 2001; Feist, 2000; Feist & Gentner, 1998; Gentner, 1998) Ferenz, 2000). Context can increase weighting Types of evidence: Alternative control of of routines (Coventry, 1999) located object using attachments such as Types of evidence: Labelling same object using strings to located object (Garrod et al., 1999). different nouns (e.g., dish vs. plate ) (Coventry Independent movement of located object or et al., 1994; Coventry & Prat-Sala, 2001; Feist, reference object, or movement together at 2000; Feist & Gentner, 1998; Ferenz, 2000), or same rate of located and reference objects novel objects named according to function or (Coventry, 1992, 1998; Ferrier, 1996). Effects stuff object is made from (Ferenz, 2000), affect of animacy of located or reference objects acceptability judgements for in. Use of a (Feist, 2000; Feist & Gentner, 1998) functional game context increases appropriateness of in (Coventry, 1999) On Connectivity Location control Knowledge of specific function (region Manifestations: Predicted (Garrod et al., 1999)Manifestations: Different labels for same object connection or shown (Coventry, 1992, 1998; Ferrier, associated with weighting for different routines calculus) 1996) constraint of position of located object (Coventry et al., 1994; Coventry & Prat-Sala, by reference object 2001; Feist, 2000; Feist & Gentner, 1998; Types of evidence: Alternative control of Ferenz, 2000) located object using attachments such as Types of evidence: Labelling same object using strings to located object (Garrod et al., 1999). different nouns (e.g., plate vs. dish) (Coventry Independent movement of located object or et al., 1994; Coventry & Prat-Sala, 2001; Feist, reference object, or movement together at 2000; Feist & Gentner, 1998; Ferenz, 2000), or same rate of located and reference objects novel objects named according to function or (Coventry, 1992, 1998; Ferrier, 1996). Effects what object is made from (Ferenz, 2000), of animacy of located or reference objects affect rating of on (Feist, 2000; Feist & Gentner, 1998)

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Page 136 Preposition Geometric Extra-geometric dynamic-kinematic routine Extra-geometric conceptual constraints routine Over Attention Threatening contact/blocking contact Knowledge of specific function and object Under vector sum Manifestations: Predicted (Coventry et al., association Manifestations : Object association in Above Experimental 2003b) or shown protection of reference fluences degree of deviation from centre of Below evidence object by located object (Coventry et al., mass to functional part for above placements consistent 2001). Predicted (Carlson-Radvansky et al., (Carlson-Radvansky et al., 1999). Object with AVS 1999; Coventry & Mather, 2002) or shown knowledge affects reference frame selection shown by (Coventry et al., 2001) successful interaction (Carlson-Radvansky & Radvansky, 1996; Regier and between located and reference objects. Carlson-Radvansky & Tang, 2000). Objects Carlson Located object in position to interact with functioning non-canonically but which still (2001). reference object influences selection of afford contextual protection exhibit in fluence of Results also reference frame (Carlson-Radvansky & dynamic-kinematic routine (Coventry et al., consistent Radvansky, 1996). Shown (Coventry et al., 2001). Discourse context affects frame of with 2001) or predicted (Coventry et al., 2003b) reference use (Grabowski & Weiss, 1996; Hayward and protection influences selection of reference Grabowski et al., 1993). Tarr (1995) frame and Logan and Sadler (1996) Near Implicit None Knowledge of specific function and object Far scaling association operation Manifestations: Object association and (currently accessibility of reference object by located not object influence acceptability judgements of specified) near (Ferenz, 2000). Qualified distance is affected by functional relationship between objects (Ferenz, 2000). Expected speed of driver and vehicle influences ratings of near (Coventry et al., 2003a) At Implicit None Knowledge of specific function and object scaling association operation Acceptability of at influenced by being in a (currently position to interact, and knowledge that objects not can interact (Coventry, 1992) specified) Between As yet Separation/potential to contact Knowledge of specific function and object unspecified Manifestations: Alternative control of association Manifestations : No empirical (but reference objects reduce acceptability of evidence to date extension of between (Coventry & Garrod, in press). AVS Animacy of reference objects affect possible). judgements of between (van der Zee & Evidence for Watson, in press) geometric acceptability judgements in van der Zee and Watson (in press)

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Page 137 Jackendoff (1996) argues that the two crucial modules for the connection of language and spatial cognition are conceptual structure and spatial representation . Conceptual structure for Jackendoff (see also Jackendoff, 1983, 1990, 2002) is an encoding of linguistic meaning independent of the particular language whose meaning it encodes. Conceptual structure includes information about taxonomic relations (e.g., robin is a kind of bird) and information about the distinction between tokens and types (a specific robin vs. all robins or birds). Of more interest in relation to the functional geometric framework is that conceptual structure contains information about the functions of objects (see also Pustejovsky’s discussion of “qualia” structure: Pustejovsky, 1991, 1995). On the other hand, spatial representation encodes the shapes and parts of objects and must be able to support object identification and categorisation. Also included in spatial representation is information about spatial reference frames and axes. Jackendoff argues that conceptual structure and spatial representation modules share a great deal of structure. Not only do both modules share notions such as physical object and whole–part relations, but both modules share the notions of path and place (see also O’Keefe, 1996). Importantly, Jackendoff also notes that physical motion is central to both conceptual structure and spatial representation. Meaning in Jackendoff’s framework goes beyond a lexical entry in conceptual structure. What many words mean includes information from spatial representation, such as detailed shape information. According to the functional geometric framework, extra-geometric information relevant to the comprehension and production of spatial expressions can be derived from both the conceptual structure and spatial representation systems. Information about the function of objects and how they are expected to interact with each other is represented in the conceptual structure module in line with Jackendoff’s proposals. However, we are proposing that extra-geometric information is also represented in the spatial representation module. This is because dynamickinematic relations such as location control are an integral part of our spatial representation of the world and, as we argued in Chapter 3, are established as part of the perception of realistic scenes. Now imagine looking at a spatial scene containing a toothbrush and tube of toothpaste, such as the one displayed in Figure 7.3. As a viewer one has to decide how best to describe the spatial relation between the tube and the brush. Carlson-Radvansky and Logan (1997) outline a range of steps that one might go through to do this. The first steps are to identify the reference object (e.g., the toothbrush) and to superimpose multiple reference frames on the scene. At that point, a reference frame needs to be selected. From a functional geometric perspective, the key question is how knowledge of what the objects are (i.e., a tube of toothpaste and toothbrush) directs

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Figure 7.3 Is the toothpaste over or above the toothbrush? the application of geometric and dynamic-kinematic routines to the scene. In particular, how it might lead a viewer to describe the tube as over or above the brush when it is placed more or less above the bristles. One possibility is that attentional weightings in the attentional vector sum (AVS) model are biased towards the functional part of the object. Motivation for this comes partly from Lin and Murphy’s (1997) finding that people are quicker and more accurate in detecting that a part is missing from an object when that part is a functional rather than a nonfunctional part of the object. Recall that Carlson-Radvansky et al. (1999) found that, in a placement study, the preferred above placement of the tube of toothpaste was between the functional part of the object and the centre of mass of the object. Now, the fact that the head of the toothbrush is geometrically distinct from the rest of the toothbrush in terms of whole–part relations itself may bias attention to that part. In terms of the AVS model, the computation is affected by the proximal orientation (the shortest distance between the reference and located objects). In this respect, the correlation between form and function (functional parts are frequently asymmetric parts of objects) may allow the spatial representation system to work with shape as a means of changing computations. However, it is unlikely that such asymmetry would be a sufficiently robust cue of functionality to explain the general bias towards a functional part. After all, children’s toothbrushes often have disproportionately large handles.

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Page 139 What is more likely is that identification of the object involves accessing the conceptual system, which indicates the function of the toothbrush, locates the functional part at the head of the toothbrush, and finds this part using the spatial representation module. However, here we still have two possibilities (see Carlson, 2000, for a discussion of these possibilities). The first is that the functional part directs the way in which a reference frame is imposed on the object, such that computation of geometric routines is fully weighted to the functional part (e.g., the bristles). Carlson (2000) argues that this possibility is not correct; according to Jackendoff, spatial reference frames and axes are set via perceptual processes operating on the spatial representation module. Furthermore, the fact that placements in the study of Carlson-Radvansky et al. were between the functional part and centre of mass of the reference object suggests that computations are weighted towards the functional part, but not completely so. Indeed, Regier, Carlson, and Corrigan (in press) argue that function and geometry may cause attention to be allocated to particular parts of objects, and that therefore a single computation (AVS in this case) could account for a range of effects normally considered quite distinct from each other. Furthermore, they present a modified version of the AVS model that maps onto the results produced by Carlson-Radvansky et al. (1999). Although the role of attention in Regier and Carlson’s AVS model is important, it remains to be seen whether the dynamic-kinematic routines also central to the comprehension and production of spatial prepositions can be accommodated within a single geometric computation. Coventry et al. (2001) provide results that cannot be readily explained in terms of attentional bias towards the functional part of an object. Recall, in Figure 5.7, that whether rain was shown to be falling on the umbrella or on the man holding the umbrella influenced the ratings of a range of prepositions. In these cases, the functional part of the umbrella is not misaligned with the centre of mass of the object and, therefore, the weighting towards the functional part of the reference object in the AVS model does not apply. Recall also that whether the object was shown to be fulfilling its function in these studies had an effect on acceptability judgements even when the umbrella was positioned directly above the man’s head. This points to the separate influences of two distinct routines, geometric and dynamic-kinematic, which are applied to the scene, and integrated within a situation model depending on context. Ordinarily, in the context of preparing to brush one’s teeth, the tube of toothpaste needs to be positioned in such a way that squeezing the tube will result in the successful delivery of toothpaste to the bristles of the toothbrush. Thus, in Figure 7.3, the tube of toothpaste can be described as over the toothbrush, although in this scene the tube of toothpaste is not aligned with the centre of mass of the toothbrush, or with the centre of mass of the functional part of the toothbrush. It is the projected changes in position over

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Page 140 time that are important. Although extra-geometric routines to establish changes in position can be approximated using gravitationally weighted vector population encoding not that far removed from the types of computations adopted in the AVS model (Coventry, Richards, Joyce, & Cangelosi, 2003b), the essential difference is that vectors are projected from the located object (e.g., tube) to the reference object (e.g., brush) in these cases. It may be the case that the AVS model can be further modified and extended to accommodate such computations, or that the AVS model forms one of the components in a larger computational framework. We discuss the computation of dynamickinematic routines in more detail in Chapter 9. So another interpretation of the results of Carlson-Radvansky et al. (1999) is that viewers attempt to construct and test the most informative spatial model that associates the tube with the brush on the basis of prior knowledge. The most informative model is the one that supports the strongest inferences about the situation that are consistent with the information present in the scene itself. Such a model will generally correspond to the one that captures the strongest functional relation between the objects in the scene. Given that a geometric routine for the tube being above the brush, rather than to the left of it or below it, affords the best initial fit, the viewer can then apply a dynamic-kinematic routine to test whether the stronger functional relation is appropriate. Confidence in the use of the preposition above , and especially confidence in over, will then reflect the extent to which both the geometric and the extra-geometric routines fit the scene. Therefore, the overall confidence in a spatial relation will be determined by the extent to which the appropriate situation model fits the scene. In the context of an object placement study (used by Carlson-Radvansky et al., 1999), the most informative model is likely to represent a balance between geometric and dynamic-kinematic routines as the task is not explicit regarding the context in which the objects occur. This account explains a second finding from the study of Carlson-Radvansky et al. When the tube of toothpaste was replaced with a tube of oil paint, the misalignment effect was greatly reduced. This would be because prior knowledge does not point to a functional situation model that relates the two. At best the functional model would only be appropriate in a somewhat bizarre situation of an expressionist painter who preferred toothbrushes to regular paintbrushes. Hence, the functional model would not normally be considered the most informative one to fit to that situation. Other data from an earlier study by Coventry et al. (1994), in which the located object was a jug and the reference object was a glass, is also consistent with the model-based account. In this case, the centre of mass of the jug was misaligned with that of the glass, but the jug was in the ideal position for pouring liquid into the glass. Confidence in the use of the description The jug is over the glass was strongly influenced by whether the jug contained liquid or not.

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Page 141 When it contained liquid, confidence in over increased reliably. Again, in the situation where the functional relation was most salient (i.e., when there was fluid in the jug), geometric misalignment was given less weight in the judgement of over. Evidence from other prepositions suggests that routines, both geometric and dynamic-kinematic, can be applied flexibly. With abstract two-dimensional images of the kind used by Regier and Carlson, the AVS model on its own accounts rather well for the data produced by human participants. Without salient relations between objects presented in the image, as in the paint tube/toothbrush examples, there is no need for dynamic-kinematic routines. Consider the picture in Figure 7.4. One might well be unhappy to say that the semi-circle is over the circles. However, if the semi-circle were identified as an umbrella and the circles as a man, over would be seen as an appropriate relation. The data for in and on also indicate that geometric and extra-geometric routines are not always automatically applied to any scene. The marble in the circle in Figure 7.5a does not invite the use of a dynamic-kinematic routine, but the same objects might do so if the marble was moving on a path towards the circle (Figure 7.5b). In this case, judgements of whether the marble is in the circle depend on judgements as to whether the marble is

Figure 7.4 Is the semicircle over the circles?

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Figure 7.5 The marble is in the circle. likely to be in the circle when it comes to rest. Similarly, even in cases where location control is clearly implicated (e.g., real three-dimensional containers), there may be occasions when geometric routines are sufficient in themselves to support a containment model, as when there is topological enclosure of the located object by the referent. Indeed, in the location control studies with in and on that we discussed in Chapter 4, the influence of location control information was reduced when the ping-pong ball was clearly enclosed in the convex hull of the bowl (e.g., Garrod et al., 1999; see p. 77).

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Page 143 Once objects have been identified, the functions associated with those objects in conceptual structure point to the construction of the most informative situation model and, in turn, the application of appropriate geometric and extra-geometric routines. Furthermore, we have seen evidence that the same object, labelled differently, can direct a different routine. ‘‘Plate” in conceptual structure is linked to a support routine, whereas “dish” is associated with a containment routine. It is also important to note that the stereotypical relations between objects must also be encoded in conceptual structure. Various studies have shown that the expected functional relations between objects affect how we talk about where those objects are. Recall that ratings of in go up and down as a function of the object-specific functions of objects (Coventry et al., 1994; Coventry & Prat-Sala, 2001) and projective and proximity terms are influenced by the association between objects (e.g., postman and post box vs. librarian and post box: Carlson-Radvansky & Radvansky, 1996; man and piano vs. cat and piano: Coventry, 1992). In all cases, it is clear that the nature of the objects involved in the scene influence how these routines are applied and weighted. An umbrella with holes in it is not a very good umbrella, and as Coventry et al. (2003b) have shown, the processing of functional relations with such objects is affected. Similarly, with objects that have a stronger protection function (for example, a bigger umbrella), there is a larger effect of function. However, the information in the scene itself can introduce a functional relation. An object does not have to behave as it is expected to in order to function in a particular way. The scene itself, and the context in which the scene occurs, can introduce roles for objects and interactions between objects that are novel. For example, as Coventry et al. (2001) have shown, a suitcase used to protect someone from rain produces the same patterns of effects as an umbrella even though suitcases are not stereotypical rain guards. How the scene itself grabs the attention of the viewer also influences how one talks about where objects are located. In this sense, the notion of meshing of affordance presented by Glenberg (e.g., Glenberg, 1997; Glenberg & Kaschak, 2002; Glenberg & Robertson, 1999, 2000; Kaschak & Glenberg, 2000) is consistent with the functional geometric framework. Objects functioning noncanonically in a visual scene may well point to different objects functioning canonically in conceptual structure. For example, a child in symbolic play is happy to put a book above his or her head and call it an umbrella. The functional geometric framework requires situation models as a means of integrating the multiple constraints we have implicated. And within this framework, meaning does not reside in conceptual structure or spatial representation, but rather in the situation model that represents the integration of the multiple constraints. This allows us to retain the flexibility and gradedness of the “experientialist” account (cf. Lakoff, 1987) without the need to lexicalise every new relation encountered. At the same time, there

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Page 144 are real constraints on what words can mean. What words mean in our framework is not determined by an explicitly stored representation for the word, but rather it drops out of the situational-specifics of the way in which multiple constraints associated with words and visual scenes come together in any particular instance. Although it is tempting to add other possible situation-specific meanings to the range of lexical entries for a single term (as is done with prototype theories), this tactic would be no more than another referential theory of meaning, which we have seen leads our armchair linguists into considerable difficulty. Rather, situation-specific meaning is the output of a situation model, which is where the combined processes of multiple constraints come together. For us the issue is not what words mean, but how situation models are built. TOWARDS WEIGHTING CONSTRAINTS BY PREPOSITION: DELINEATING ROUTINES AND FUNCTIONS BY TERMS We have argued that the viewer attempts to construct and test the most informative model to relate a reference object with a located object. By “informative”, we mean that the model should support the strongest inferences that could be drawn about the scene. However, thus far we have considered the comprehension and production of prepositions in isolation. When choosing a preposition to describe a spatial relation, there are many lexical candidates to pick from. We have seen in the experimental chapters that spatial expressions clearly differ both in terms of the relative importance given to geometric routines, dynamic-kinematic routines, and extra-geometric stored knowledge. The differential weightings, given to prepositions as situation models are assembled, account for the semantic field effects that have been documented in the spatial language literature. For example, Logan and Sadler (1996) report overlaps in the meaning of terms such as above and over using a multidimensional scaling approach. While it is clear that over and above have a greater overlap in terms of geometric appropriateness, as seen in the overlap of the use of these terms, we have also seen that they behave differently with respect to extra-geometric variables. Take in, on, and over, for example. In involves a strong location control relation, whereas on involves a weaker location control relation. With a containment relation, movement is less likely to dislodge the located object than with a support relation. Additionally, we have seen that over involves a location control component, but this is likely to be even weaker still. If this is the case, then the change in prepositional use from one term to another where functional relations are important to a scene may be affected by the strength of relation present. Garrod et al. (1999; see also Garrod, in press) provide evidence that this is indeed the case. In the scenes with ping-pong

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Page 145 balls and a glass bowl we considered in Chapter 4, as confidence in location control weakens, so viewers reduce their confidence in the use of in descriptions. Furthermore, as confidence in in descriptions decreases so confidence in on descriptions increases. When confidence in location control weakens even further, the preferred preposition becomes over. What is interesting about these findings is the way in which viewers tend to adopt the functionally strongest relation consistent with the scene. In other words, they choose the description associated with the strongest functional inferences about the relation that the scene can support. Location control is stronger for containment than it is for support and location control is no longer a primary feature of the over relation. Coventry (1999) also reports some similar results. Recall that the production and acceptability ratings for in to describe the position of a ball suspended from a frame over a container were significantly higher in a game context than in a control context. It was also found that over was affected by the introduction of the functional context but that above was not. While the comprehension and production of in and over both increased in the functional game context described above (see Figure 4.6 in Chapter 4), the use of above decreased, showing that in and over in the functional context behave more similarly than over and above . Ferrier (1996) also reports evidence that in, on, and over are related from a functional perspective. In one condition a video image of a ball resting on top of other balls in a bowl was preceded by a dynamic context in which the ball was first seen floating in mid-air, and then the bowl together with the other balls was moved under it until the ball came to rest on the top of the other balls in the bowl. This was compared with the final stationary scene without any prior dynamic context. Ratings for in in the static case were greater than those for on and over, whereas in the context case ratings for on and over went up, whereas those for in went down. Finally, as we have already seen, Coventry et al. (2001) and Coventry and Mather (2002) have shown that over and under are affected to a greater extent by extra-geometric relations than above and below , whereas above and below are affected to a greater extent by geometric relations than over and under. These data suggest that prepositions may be weighted according to the application of geometric and dynamickinematic routines. If a speaker should choose not to select a functionally strong preposition in what looks like an appropriate context, then this should indicate that there is something unusual about the scene. For example, a man sitting beside a piano about to play is usually described as at a piano, but the preposition near also serves to locate the man. In such circumstances, The man is near the piano might serve some ironic function, such as leading to the implicature that the man is not a good pianist. So, although at and near are both geometrically appropriate, the use of a term that does not require the instantiation of extra-geometric knowledge/

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Page 146 routines leads to a situation model inconsistent with the strongest possible model available to represent the scene. Similarly, The plane is above the target , while geometrically true, indicates that the plane is probably in the wrong position to drop a bomb such that it will hit the target, for example. As we shall see in the next chapter, differences in weightings for geometric and extra-geometric routines between terms that share degrees of similarity are not unique to English. SUMMARY In this chapter, we have argued that various constraints work together to determine the appropriate meaning of a spatial expression in context. We started the chapter by presenting evidence that situation models offer the vehicles by which these multiple constraints come together. Meaning in the functional geometric framework reflects the result of all these constraints coming together in the situation model, which supports the most informative relation between a reference object and a located object. By informative, we mean that the model should support the strongest inferences that could be drawn about the scene. We concluded the chapter by arguing that both objects and individual prepositions are associated with weightings for individual routines, and that understanding the interplay between geometric and extra-geometric routines provides a framework for assessing the similarity between individual prepositions. In the next chapter, we begin by considering the developmental evidence for the emergence of geometric and extra-geometric routines and extra-geometric knowledge of objects and object relations.

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Page 147 CHAPTER EIGHT Cross-linguistic and developmental implications In the previous chapters of the book, we have set out the main components of the functional geometric framework and how these components come together. Our aim has been to provide a general framework. However, the account we have constructed has focused almost exclusively on the comprehension of spatial prepositions in English. Furthermore, only fleeting mention has been given to the acquisition of these terms. In this chapter, we consider how the framework sits with what is known about languages other than English and how language acquisition can be viewed within the framework. In particular, we will examine whether there is any evidence for the use of extrageometric routines in the prelinguistic infant, in other languages, and in the utterances produced by children when they are acquiring a language. We also consider the issue of whether the routines associated with spatial language which are in the spatial representation system are the same routines associated with spatial categorisation and spatial memory. THE PRELINGUISTIC ORIGINS OF THE FUNCTIONAL GEOMETRIC FRAMEWORK Infants have a prelinguistic understanding of spatial relations. Indeed, there is evidence for knowledge relating to both geometric and extra-geometric routines long before children start to produce spatial prepositions. Within the first few months of life, babies are able to distinguish between left and right (Behl-Chadha & Eimas, 1995) and above, below, and between relations

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Page 148 (Antell & Caron, 1985; Quinn, 1994; Quinn, Cummins, Kase, Martin, & Weissman, 1996; Quinn, Norris, Pasko, Schmader, & Mash, 1999). The method of obtaining these results relies on the well-established finding that infants have a tendency to look longer at novel than at familiar stimuli (see Spelke, 1985, for a review). For example, Quinn (1994) habituated 3- and 4-month-old infants to a single diamond presented in different positions above a horizontal bar. Infants were then presented with two diamonds in novel positions, one above the bar and one below the bar. Infants consistently showed a visual preference for the diamond presented in the novel position below the bar, indicating that they had formed a category for above . Initially, however, the relations distinguished are always associated with the particular objects that are used to depict the relations, and it is only a few months later that the relations generalise to all objects in those configurations. Quinn (in press) suggests that object information and spatial information is tightly bound together for young infants, and that it is only when they become older that the “what” and the ‘‘where” information can be properly separated.1 In addition to learning basic geometric relations, infants learn much about the physical properties of objects and the world in which they are found. Much of this information corresponds to the basic ingredients of our functional geometric framework. Let us consider them in turn. Physical properties of objects, such as permanence There is much evidence that object knowledge develops rapidly during the first year of life. Infants aged 2.5–3.5 months show knowledge of an object’s physical properties. Spelke, Breinlinger, Macomber, and Jacobson (1992) habituated infants to a test event in which a ball rolled from left to right across a platform and then disappeared behind a screen (see Figure 8.1). The screen was then removed to reveal the ball resting against a barrier at the far end (right-most part) of the platform. Following habituation, infants were presented with two variants of this scene. In one variant, the physically appropriate one, a second barrier was positioned to the left of the original barrier (and shown to protrude above the screen). The screen was then removed and the ball was revealed at the point where the barrier had stopped its path. In the other variant, the physically impossible scene, when the screen was removed the ball was revealed to be in the same position as in the habituation trials. So in the second variant the ball would have had to pass through the barrier. Infants looked longer at the second 1 The independence of “what” and “where” in older infants raises the question of how object and spatial knowledge comes to be bound together for older children. Some researchers have speculated that it is language which makes this possible (Hermer-Vazquez, Spelke, & Katsnelson, 1999).

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Figure 8.1 Example of types of scene used by Spelke et al. (adapted from Spelke et al., 1992). variant, demonstrating knowledge of two important constraints on object motion: continuity and solidity. Kellman and colleagues (Kellman & Spelke, 1983; Kellman, Spelke, & Short, 1986) also show that 4-month-old infants appear to use the common motion of stimuli above and below an occluder as a cue to perception of unity. When objects move together, they treat objects as a single entity, but when they move independently of one another, they are treated as two different entities. Causality Dynamic causal events of the type discussed by Michotte (1963) have been investigated in early infancy. For example, a direct launching event is one where an object collides with a second object and the second object moves off instantly (just like one billiard ball hitting another and the other moving off). As Michotte originally showed, adults perceive this as one object causing the other object to move. Oakes (1994), Leslie (1984), and Kotovsky and Baillargeon (2000) provide evidence that understanding of such causal relations appears to be present at 7 months (though initially understanding is tied to the objects depicting the relation; see Cohen & Oakes, 1993).

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Page 150 For example, Oakes (1994) presented infants with simple events involving red and blue moving balls. She habituated them to a causal direct launching event (of the type just described), to a non-causal delayed launching event (in which one ball collides with the other, but a delay is present before the second ball moves off), or to a non-causal no collision event (where the first ball moves towards the second ball but does not touch the second ball, yet the second ball moves off). Infants who had habituated to causal events dishabituated to novel non-causal events (either delayed launching or no collision events), and those who had habituated to non-causal events dishabituated to novel causal events. Oakes, therefore, found evidence that young infants responded on the basis of causality. However, with more complex objects, these effects can only be found in slightly older children (at around 10 months; see Cohen, Amsel, Redford, & Casasola, 1998). Similarly, infants around 7 months of age appear to understand the difference between cause and effect (Leslie & Keeble, 1987). Leslie and Keeble found that 7-montholds showed greater dishabituation for reversal of a causal event than for the reversal of a non-causal sequence. However, again this understanding appears to emerge later when complex objects are used (some time between 10 and 14 months; Cohen et al., 1998). Containment Bower (1982) noted that containers hold a special fascination for very young children. E. Clark (1973) found that children play with objects in ways that suggest an understanding of the concepts of containment and support before they learn the words in and on. For example, children, when presented with an inverted glass, turn it round the right way. Freeman, Lloyd, and Sinha (1980) also found that children from 10 months of age made significantly fewer place errors when searching for hidden objects hidden in cups in their canonical orientations compared with when they were inverted. Hespos and Baillargeron (2001) have shown that infants as young as 2.5 months possess expectations about containment events. For example, in one experiment, infants saw an object lowered inside a container with either a wide opening or no opening in its top surface. Infants looked longer at the closed-container event rather than the open-container event. In another experiment, infants saw an object lowered either behind or inside a container, then the container was moved forward and to the side revealing the object behind it. In the condition in which the object was placed inside the container, infants looked longer when the object was revealed than in the condition in which it was placed behind the container. Presumably, the infants realised that the object could not possibly pass through the wall of the container, and hence should have moved with the container to the new location, an early appreciation of the notion of location control. Baillargeon

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Page 151 and colleagues have also shown that 8.5-month infants take into account the width and compressibility of an object when determining whether it can be inserted into a container (Aguiar & Baillargeon, 1998). By the age of 1.5 years children have a sound understanding of containment. Using a preferential looking task, Caron, Caron, and Antell (1988) showed children videotapes of a hand-held cylinder being tilted backwards and forwards. When tilted, the cylinder was revealed to be either a tube (open at both ends) or a can (open at the top but closed at the bottom). Sand was poured into the upright cylinder and was either contained (such that the sand rose above the rim of the cylinder) or not contained (such that the sand poured out the bottom of the cylinder). Children looked more at events that violated the nature of the cylinder (e.g., when the cylinder was a can and the sand fell through the bottom of the cylinder, or when the cylinder was a tube and sand did not pour out the bottom) than events that conformed to the expectation of containment of the can and non-containment of the tube. Gravity and support There is also evidence that infants have emerging knowledge of gravity (Kim & Spelke, 1992). Infants viewed videotaped events in which a ball rolled downward (or upward) while speeding up or slowing down. At 7 months, infants looked longer at test events with inappropriate acceleration. Similarly, when they were shown a stationary object released on an incline, they looked longer when the object moved upwards, illustrating an understanding of gravity. More recently, the same team of researchers found, using a predictive judgement task, that by 2 years of age infants appear to have sensitivity to gravity. Needham and Baillargeon (1993) have also shown that infants aged 4.5 months expect an object to fall when its support is removed. Infants were shown a test event in which a hand either deposited a box on a platform, leaving the box supported by the platform, or put it beyond the platform, leaving the box suspended in mid-air. Infants looked reliably longer at the impossible event where the hand let go of the box and it was suspended in mid-air. Hood (1995, 1998; Hood, Santos, & Fieselman, 2000) also reports a pattern of errors on an object displacement task consistent with a bias towards searching in the gravitational plane. When searching for a ball that was dropped into an opaque tube that formed an “S” bend, 2-year-olds repeatedly searched at the location directly below the bend, although the ball could not travel invisibly across the intervening space. When the object motion was reversed, so that the ball appeared to travel up the tube, or when horizontal trajectories were used, performance was better. This indicates that there is something about falling events that overrides judgements based on physical knowledge of how objects travel along tubes.

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Page 152 There is also evidence that infants detect a violation when one object falls through the space occupied by another object. For example, Spelke et al. (1992) familiarised infants with an object falling to a stage floor; they were then shown a solid shelf, which was placed above the stage. The stage and shelf were then partially occluded by a screen and the object dropped behind the screen. When the screen was removed, the object was revealed either resting on the shelf (possible outcome) or on the stage below the shelf (impossible outcome). Infants looked at the impossible outcome longer than the possible outcome, suggesting knowledge of support. Stereotypic functions of objects There is also evidence for the recognition of familiar object function prelinguistically. Madole, Oakes, and Cohen (1993) found that infants’ ability to attend to and remember object function changes towards the end of the first year of life. Infants were presented with objects to manipulate and explore, and their visual attention to those objects was measured. Initially, the infants were familiarised with a single novel object constructed from plastic building blocks (e.g., a yellow rectangular object that rattled when shaken). Following familiarisation with this object, the infants’ attention to the familiar object and a second novel object was assessed. The novel object differed from the familiar object either in appearance only (e.g., a red round object that rattled when shaken), function only (a yellow rectangular object that rolled when pushed) or both appearance and function (a round red object that rolled when pushed). Children at 10 months of age examined the novel object more than the familiar object when the object differed only in terms of appearance, but not when it differed only in terms of function. However, 14-montholds did notice a change in the object’s function as well as a change in the object’s appearance, suggesting that function starts to become important for infants some time around the end of the first year. Furthermore, Madole et al. (1993) show that children treat function and appearance as independent properties until around 18 months. So, there is evidence that prelinguistic children have a great deal of knowledge of the sort we have assumed in our functional geometric framework. Whether this knowledge develops from a base of innate “core” principles (Spelke et al., 1992; Spelke, Katz, Purcell, Ehrlich, & Breinlinger, 1994), or whether there are constrained learning mechanisms that allow the infant to arrive at important generalisations about objects (e.g., Needham & Baillargeon, 1993), remains to be established. However, it is clear that conceptual knowledge about objects and geometric and extrageometric routines is built up rapidly in the early months of life. Given this evidence, it is tempting to argue that prelinguistic spatial knowledge structures how language is acquired. As Talmy (1983) put it, we can ask whether space structures

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Page 153 language (e.g., H. Clark, 1973; Landau & Jackendoff, 1993; Talmy, 1983) or, alternatively, whether language structures space (e.g., Bowerman, 1996a, 1996b; Bowerman & Choi, 2001; Levinson, 1996b). THE ACQUISITION OF SPATIAL PREPOSITIONS IN ENGLISH It is clear that infants and older children have quite sophisticated prelinguistic knowledge of both geometric and extra-geometric aspects of spatial relations; but is this reflected in children’s use of geometric and extra-geometric routines as they acquire the language of space? Children start to produce spatial terms in the second year of life (e.g., Tomasello, 1987), and the development of spatial language continues throughout the first 8 years or so. The order in which particular spatial prepositions are first understood is remarkably consistent across languages, and begins with the so-called “topological” prepositions in, on, and under (in the second and third years), with proximity terms such as next to and beside occurring from the fourth year followed by projective terms such as behind ( in back of ) and in front of . Initially, projective prepositions are only used when objects have an intrinsic front and back and they begin to emerge when children are around 5 years of age. This is not surprising because it is only around this age that children are first able to identify the sides of objects (e.g., Harris & Strommen, 1972; Kuczaj & Maratsos, 1975). Over the next few years these prepositions come to be used in situations where fronts and backs have to be projected onto objects. The final set of prepositions to emerge are between, over, above , left, and right (e.g., Johnston, 1984, 1985; Johnston & Slobin, 1979; Sinha, Thorseng, Hayashi, & Plunkett, 1994). As Bowerman (1996a) notes, the correspondence between the order of emergence of spatial concepts (e.g., Piaget & Inhelder, 1956) and the order of acquisition of spatial terms (across a range of languages) is striking. It is not our purpose here to examine all the factors that may account for the acquisition of spatial prepositions in English. Many factors are likely to play a role, including the frequency of the words in language, the frequency of words in the speech input from the caregivers of the children acquiring the language (see, for example, Huttenlocher, Haight, Bryk, Seltzer, & Lyons, 1991), the complexity of the syntactic structures individual prepositions are likely to occur in (Durkin, 1981), and the joint attention of the mother and infant (e.g., Tomasello, 1999)—all of which are beyond the scope of the present discussion. However, we will discuss the extent to which acquisition might relate to mappings between prelinguistic concepts of space and distinctions being made in the parent language. Mandler (1988, 1992, 1996) has argued that the prelinguistic child’s conceptualisation of space is derived from an attentive perceptual analysis of

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Page 154 visual scenes that begins when infants start to learn to parse the world into objects. This attentive analysis results in a redescription of the perceptual information being processed, and the result is a set of conceptual spatial invariants that she labels “image-schemas”. Among the first image schemas Mandler points to are containment, contact, and support, and notably those involving moving objects (such as contingent motion). Furthermore, these image schemas provide a facilitatory level of representation that is intermediate between perception and language and thus aids the process of language acquisition. Such image schemas can be regarded as the origin of the different types of visual routines we have outlined. It is then assumed that they become associated with lexical items through the process of language learning. As we shall see shortly, the fact that languages vary in the way they carve up space indicates that the parent language also influences how visual routines are packaged for that language. Our more humble goal here is to examine whether children acquiring language exhibit evidence of the influence of extrageometric routines as well as geometric routines. Research on the development of nouns has revealed that perceptual features of objects and functional features of objects both influence the way in which names are extended to new category members, but exactly when functional information kicks in is unclear. For example, Landau, Smith, and Jones (1998; see also Smith, Jones, & Landau, 1996) showed children and adults novel objects that were given a novel name (e.g., this is a “dax’’). The objects possessed different perceptual features, and also were shown in some cases to have different functions (how the object was “used” was demonstrated). New objects were then presented that possessed the same function as the original object, or the same shape (or both similar shape and similar function). Participants were then asked whether the new object was like a dax (a nonlinguistic categorisation task) or whether the new object was a dax (a linguistic categorisation task). Both adults and children categorised objects in the nonlinguistic task on the basis of functional information when it was available to them. However, whereas adults used functional information to extend object names in the linguistic categorisation task, children (age groups 2, 3, and 5 years) predominantly used perceptual (shape) information. More recently, Kemler Nelson and colleagues (Kemler Nelson, 1999; Kemler Nelson, Frankenfield, Morris, & Blair, 2000; Kemler Nelson, Russell, Duke, & Jones, 2000) have found that children from 2 years of age do extend the names of novel artefacts with novel functions to new objects. They suggest that 2-yearolds name by function when they can make sense of the relation between the appearance and the function of objects. More recently, Smith and colleagues have found evidence that the names of objects are extended on the basis of functional information and that there is a close relationship between form and function (see Smith, in press, for a review). For example, children were presented with labelled objects that

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Page 155 were either tall and thin and moved up and down along the vertical axis or were short and wide and moved along the horizontal axis. When new objects were presented that were either taller and thinner than the original object or shorter and wider than the original object, children as young as 2.5 years extended the names of the objects according to the direction of motion associated with the dimensions of the objects. In other words, when the original object moved in the vertical plane, children extended the name to objects that were taller and thinner than the original object, but when the object moved in the horizontal plane, names were extended to smaller and fatter objects. There is therefore evidence for the early importance of functional information (defined in terms of how those objects are used in all these cases) as a means of extending names to new objects. In relation to spatial prepositions, there has been little direct investigation of the relative influence of functional and geometric information. Landau and Stecker (1990) found that both children (3-year-olds and 5-year-olds) and adults, learning the meaning of novel prepositions ( This is acorp my box ), tended to disregard shape information and focus on position information alone. However, sensitivity to the functions of objects has been shown by E. Clark (1973). She found that children, when asked to put one object in/on another reference object that was either a supporting surface or a container, produced an error pattern that was consistent with an understanding of the functions of the objects involved. When asked to put an object on an inverted container, children aged 1.5–3 years frequently turned the container over and put the object inside the container. However, it is not clear to what extent these results reveal early knowledge of associations between prepositions and canonical objects, or whether they arise from the use of a nonlinguistic strategy under circumstances when the preposition has not been understood. Lynn Richards, in her doctoral dissertation, set out to examine systematically whether the production of spatial expressions by children was influenced by manipulations like those used in the studies with adults reviewed in previous chapters. Richards first pretested children to try to find the youngest age at which they were able to complete the production task. In one study (Richards, Coventry, & Clibbens, in press; see also Richards & Coventry, in press), 80 children aged 3 years 4 months to 7 years 8 months were presented video images of scenes of the type used by Coventry (1992, 1998) and Garrod et al. (1999). The scenes involved objects piled in and on containers and supporting surfaces. Location control was manipulated by using scenes that: (1) depicted located and reference objects moving together; (2) depicted the located object moving independently of the reference object; or (3) presented both located and reference objects as static (see Figure 4.1 in Chapter 4 for examples of the types of manipulations used). The findings were striking. Even in the youngest age group (age 3 years 4 months to

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Page 156 4 years 6 months), children used in as the first (or only) prepositional phrase2 most in the scenes where there was evidence of location control and least in the scenes that provided evidence against location control. These results show that children are sensitive to location control not long after they can reliably produce the prepositions in and on. Richards (2001) and Richards and Coventry (2003b) also report a series of studies examining the influence of functional relations on projective and proximity terms. In one set of studies, children and adults were presented with video scenes showing one source container positioned higher than another recipient container (similar to the scenes displayed in Figure 5.7, bottom pictures). In functional scenes, liquids, or solids (e.g., water or beans) were being poured/dropped from the source container to end up in the recipient container. In nonfunctional scenes, the liquids/solids being poured/dropped were shown to miss the recipient container and fall to the ground instead. Both children and adults were found to produce prepositions denoting the vertical axis (e.g., The teapot is higher than/above/over the cup) significantly more in functional than in nonfunctional scenes. In contrast, proximity terms, which do not denote a specific axis, were the preferred productions for nonfunctional scenes (e.g., The teapot is near the cup). In a further series of studies, Richards (2001) and Richards and Coventry (2003a) tested both children and adults on scenes of the type used by Carlson-Radvansky and Radvansky (1996). Located objects (all people) were depicted at various distances from reference objects. The reference objects always had intrinsic functional parts, and the located objects were either presented facing the functional parts (so that they were in a position to interact with the functional part) or were presented facing away from the functional parts. For example, a librarian was depicted facing towards or away from a bookshelf. Unlike Carlson-Radvansky and Radvansky’s results with adult samples, Richards and Coventry found that children did not use more intrinsic expressions (e.g., the librarian is in front of the bookcase) when the librarian was facing towards rather than away from the bookcase. However, children did differentiate between horizontal and proximity terms as a function of orientation. Children were more likely to use terms specifying the horizontal axis (e.g., the librarian is in front of/across from/opposite the bookshelf ) when the located object was facing towards the reference object and proximity terms when the located object was facing away from the reference object. So we have seen that there is evidence that children, like adults, are influenced by functional interactions in visual scenes when describing the 2 The first words used by children in an expression reveal the attentional focus for the child (for discussion and evidence of this, see for example MacWhinney, 1977; Plumert, Ewert, & Spear, 1995).

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Page 157 relative positions of objects in those scenes across a range of types of spatial relations. However, the use of a production methodology has shown that children often make these distinctions in different ways to adults. Children of the ages tested in the studies by Richards et al. do not have the range and command of spatial prepositions that adults have, but they nevertheless use the language they do have to make the same distinctions as adults. Although further work is needed to examine the comprehension of spatial terms with similar manipulations among younger children, the results nevertheless show that children are extremely sensitive to “what” objects are and how they are interacting when describing the location of objects in visual scenes. FUNCTIONAL GEOMETRY IN LANGUAGES OTHER THAN ENGLISH We have seen that extra-geometric as well as geometric constraints are manifest in the production of spatial expressions in children acquiring English. However, it does not necessarily follow that such constraints will be in evidence across all languages. Although languages differ greatly in the way in which they carve up space, it has often been assumed that perceptual understanding of space is mapped onto the language being acquired. For example, H. Clark (1973) argued that meanings across languages must be similar to the extent that all people are affected by the same biological constraints (e.g., the head is at the top of our bodies, there is front–back asymmetry as a result of where the sensory organs are positioned, there is a common gravitational constraint, etc.). As we indicated in the early pages of this book, one of the most striking features of spatial expressions is the sheer diversity of ways in which different languages carve up the spatial world. This presents a problem for the view that words in the language input are mapped onto non-linguistic concepts alone. Although spatial conceptualisation and categorisation in the prelinguistic child is quite well developed, the idea that such a mapping characterises learning across all languages downplays the considerable cross-linguistic variation that has been catalogued over the last 15 years (see Levinson, 1996a, 1996b, for reviews; see also Munnich et al., 2001). As Levinson (1996b, p. 177) puts it: A number of plausible cognitive science generalisations about spatial conception and language [which] seem to be falsified by a couple of errant studies … it is at least tempting to draw the conclusion that a model of universal conceptual constraints ought not to be invariably in the strong Mendelian style (permutations and combinations of a set inventory) favored, for example, by Chomsky, but rather should sometimes be viewed as a set of filters which may radically under-determine the phenotypic cultural variants.

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Page 158 There is considerable evidence that the words in the specific language to be learned influence semantic development (for excellent reviews and discussion, see Bowerman, 1996a, 1996b; Bowerman & Choi, 2001; Levinson, 1996a). Choi and Bowerman (1991) present evidence to suggest that the language children are exposed to affects the way in which space is conceptualised and categorised. Whereas English expresses path notions (movement into, out of, etc.) in a constituent which is a “satellite” to the main verb (e.g., a particle or preposition), Korean expresses path in the verb itself. In English a video cassette is put in a video case, a lid is put on a jar, an apple is put in a bowl, and an orange is put on a table. By contrast, in Korean the verb kkita is used for tight fit path events (e.g., put video cassette in video case/put lid on jar), whereas nehta is used for loose fit containment relations (e.g., put apple in bowl), and nohta is used for loose fit support relations (e.g., put orange on table). Thus Korean carves up the spatial world according to degrees of fit as much as it does according to containment and support relations. Furthermore, Choi and Bowerman (1991) found evidence that children learning English and Korean, respectively, extend meanings of terms according to the semantic structure of their input language. English children produced in for paths into both tight and loose fit containers and extended their use of in accordingly, whereas Korean children produced kkita for putting objects into tight places, nehta for putting objects into loose containers, and extended their use accordingly. More recently, Choi, McDonough, Bowerman, and Mandler (1999) used a preferential looking task to assess the generalisations made by children learning either English or Korean. By the age of 1.5–2 years, the children in both cases spent more time looking at the language-appropriate aspects of spatial relations. English children looked more at containment scenes than noncontainment scenes on hearing in, whereas Korean children looked more at tight-fit scenes than loose-fit scenes when hearing kkita. So the language the child learns affects the way in which visual routines are packaged for future language use. Bowerman (1996a, 1996b; Bowerman & Choi, 2001) argues that the language being learned actually structures the building of spatial semantic categories; children learn how to structure space for language. Alternatively, Mandler has argued that reliance on the prior organisation of nonlinguistic spatial schemas such as those for support and containment makes some distinctions in a language harder to learn than others. Dutch has two subtypes of support compared with English ( op and aan) and this distinction takes some time for children to learn; but in Spanish containment and support are collapsed into a single linguistic category ( en) that is easier to learn. We concur with Mandler (1992) that the tight fit/loose fit distinction in Korean may be similarly easy to learn as children are likely to be influenced by the dynamic-kinematic routines of location control very early on. As we have seen for English, the use of in occurs significantly

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Figure 8.2 Scenes representing a gradient proposed by Bowerman and Pederson (in preparation; cited in Bowerman & Choi, 2001). more in children’s descriptions when location control is present than when it is absent (Richards et al., in press). Indeed, recently McDonough, Choi, and Mandler (2003) have found that 9- to 14-month-old Korean and English infants categorised both tight containment versus loose support and tight containment versus loose containment, indicating that infants have conceptual readiness for learning location control aspects in either language. Indeed, the dynamic-kinematic routines that are important for English spatial language may well offer a useful means of understanding cross-linguistic variation. Bowerman and Pederson (in preparation; cited in Bowerman & Choi, 2001) have undertaken an examination of how support, containment, encirclement, attachment, adhesion, piercing, and hanging relations are structured across 38 languages from 25 different language families (see also Feist, 2000). Consider the static scenes depicted in Figure 8.2. Bowerman and Pederson found that, although languages differ considerably in the number and range of terms they map onto these situations, languages do not categorise spatial situations in arbitrarily different ways. Rather, Bowerman and Choi (2001) suggest that differences across languages can be represented by an underlying gradient or implication hierarchy. They note that variation is characterised by the number of terms used to divide up the basic situations, as well as where the cases covered by one term end and those covered by a new term begin. However, in no language did they find cases in which there were gaps in the hierarchy of situations (i.e., if a term was used for more than one segment, it only covered adjacent segments). The gradient is

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Page 160 difficult to pin down, but Bowerman and Choi argue that the ordering relates to how easily situations can be construed as similar to prototypical containment (on the right) and support (on the left). Given that the geometric notions of enclosure and contact with a surface, and the extra-geometric notion of location control, are so important in English, we might suggest that a gradient may reflect these three constructs working together. For example, en in Spanish simply collapses all situations involving location control, whether by virtue of enclosure or contact. English differentiates the situations in terms of enclosure (i.e., containment) versus contact (i.e., support) and in terms of degree of location control. Thus, in English one can say the crack is in the bowl or the crack is on the bowl depending on whether the situation is construed in terms of enclosure and location control or in terms of contact (i.e., contiguity with the surface of the bowl). Indeed, Bowerman (1996b) suggests that force dynamics may explain the two different terms in Dutch, op and aan, which map onto the use of on in English; whereas op is associated with situations in which there is no pull towards separation, aan is associated with situations in which there is a pull towards separation. It would be interesting to examine the range of languages where in and on situations are carved up differently, to assess whether multiple constraints are also in operation across these languages. In Spanish, for example, we have some preliminary data that tilting a container away from its canonical orientation weakens judgements of en, although other lexical candidates are not readily available to use in this language (in English in such situations on the bowl becomes appropriate; Coventry, 1992). Coventry and colleagues have also examined whether languages other than English offer the types of contrasts between over/above and under/ below that have been found for English (Coventry et al., 2001). Recall that the comprehension of over and under has been found to be more influenced by extra-geometric routines than above and below , whereas above and below are more influenced by geometric computations. Similar contrasts have been found in Spanish (Coventry & Guijarro-Fuentes, in press) and in French (Green, 2001; see also Vandeloise, 1991, 1994), although there are also some intriguing differences between languages. For example, in a series of experiments Coventry and Guijarro-Fuentes (in press) compared acceptability ratings for over/under/above/below to ratings for the related Spanish prepositions sobre/encima de/debajo de/bajo using similar materials to those used by Coventry et al. (2001; see Figure 5.7 in Chapter 5). For the superior terms sobre and encima de, the results mirrored the findings for over and above . Acceptability ratings for sobre were affected more by functionality (e.g., whether the umbrella is shown to fulfil its function or not) than ratings for encima de. However, no differences in the influence of functionality and geometry were found for the inferior terms debajo de and bajo ; ratings for both terms were strongly influenced by dynamic-kinematic routines.

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Page 161 Additionally, the influence of the manipulation of geometry for superior and inferior prepositions in Spanish was much weaker than for the equivalent terms in English (see also Regier & Carlson, 2002, for a related discussion of differences between English and German). These results suggest that languages differ in the weightings given to geometric and extra-geometric variables, and that there are also differences within languages in terms of how geometric and extra-geometric routines are weighted for specific spatial terms (see Coventry & Guijarro-Fuentes, in press, for discussion). So there is evidence that both geometric and extra-geometric routines play a role in the spatial semantics of languages other than English, although it is too early to say exactly how prevalent this is. Certainly, the earliest prelinguistic concepts to emerge, such as containment and support, both of which have a location control element, are important for the spatial semantics of most if not all languages. LINGUISTIC RELATIVITY AND THE UNDERLYING STRUCTURE OF SPATIAL REPRESENTATIONS FOR LANGUAGE The final issue we turn to in this chapter concerns what is sometimes called linguistic relativity. To what extent do the representations underlying spatial language determine the representations underlying nonlinguistic spatial judgements or vice versa? In the framework we have outlined there is a flexible interface between conceptual representation and spatial representation. Yet there are many who believe that there is a single spatial representation system that underlies both spatial language and spatial representation. As we have seen, some researchers have argued that spatial language reflects universal nonlinguistic spatial representations (e.g., Bryant, 1997; H. Clark, 1973; Hayward & Tarr, 1995; Landau & Jackendoff, 1993; Talmy, 1983). Others, on the other hand, have argued that spatial language can in fact shape spatial representation (e.g., Levinson, 1996a, 1996b; Pederson, Danziger, Wilkins, Levinson, Kita, & Senft, 1998). There are two main sources of information to which we can turn to resolve the issue: cross-linguistic studies and neuropsychological studies. Although a wide range of languages seem to have terms for support and containment situations, when it comes to projective terms languages differ more radically from each another. For example, Indo-European languages use terms for left and right that depend on the reference frame adopted. Left can refer to one’s own left side in an egocentric frame, or to the left of an object being viewed from in front. In the latter case, this would be on the viewer’s right side. However, in several languages, such as Arandic (Pama-Nyungan, Australia) and Guugu Yimithirr (North Queensland, Australia), terms like these do not exist. Instead, there are terms that only locate directions

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Page 162 or sides using an absolute frame of reference (like north, south, east, and west) in both small-scale (e.g., to describe the positions of objects on a desk) and in large-scale settings (Levinson, 1996a, 1996b; Pederson et al., 1998). Because these languages differ from Indo-European languages so radically, Brown and Levinson (1993) and Pederson et al. (1998) set out to examine whether the structure of the language also affects the encoding of nonlinguistic spatial relationships. Both teams of researchers administered a series of recognition, recall, and transitive inference tasks to speakers of a range of languages that either use projective prepositions (like English and Dutch) or only absolute reference frame terms. For example, participants were shown spatial arrangements and were requested to make judgements about what constituted the “same” spatial arrangement by either reproducing the arrangement after moving position or by selecting a drawing from a range of drawings that matched the original layout. They found that speakers of Tzeltal, for example, performed the nonlinguistic tasks using an absolute frame of reference, whereas speakers of English and Dutch would often use a relative frame for the same tasks. Thus it would appear that language may bias the conceptual coding of nonlinguistic spatial relations, suggesting the possibility that spatial representations underlying spatial language and spatial judgements may be the same. This would be consistent with the idea that viewers use the same kind of spatial mental model to perform nonlinguistic spatial tasks that they use when encoding spatial relations in the language. However, the relativist effects must be interpreted with some caution. It is likely that participants in such tasks may use language as a means of encoding spatial relations and, therefore, the results may be more in line with a weaker version of relativity (e.g., Slobin’s thinking for speaking hypothesis; Slobin, 1996). For example, Tzeltal speakers may have encoded a spatial scene by noting that an object is south of another object. Furthermore, more recent studies have drawn attention to some methodological issues relating to these studies. Li and Gleitman (2002) found that the differences found in the studies of Pederson et al. and Brown and Levinson can be found in a range of circumstances not related to language differences. Munnich et al. (2001) suggest that the relationship between spatial representation for language and spatial representation for nonlinguistic spatial tasks is rather more complex. Using a slight modification of the tasks used by Hayward and Tarr (1995), they tested English, Korean, and Japanese speakers’ language and memory skills for the locations of objects. They found similar organisation across the three languages in terms of axial structure, but differences between languages in the organisation of contact/ support (like Pederson & Bowerman; see above). However, the results for the memory task revealed a similar influence of axial structure and contact/ support for all speakers. Munnich et al. (2001) conclude that spatial language and spatial memory may rely on the same spatial properties, but

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Page 163 that the systems may still be independent (see also Crawford, Regier, & Huttenlocher, 2000). Furthermore, they suggest that the similarity between the systems may arise as a consequence of negotiating the same spatial world (see also Shepard, 1994). Another approach to understanding the relationship between spatial representation for spatial language and spatial representation for spatial memory is to examine processing from a neuropsychological perspective. Given the established influence of the language being acquired, and the differences that exist between languages, the development of linguistic knowledge may require constructing new categories that go beyond those required for nonlinguistic spatial categorisation. As Kemmerer and Tranel (2000) suggest, it is therefore possible, or even likely, that children build new, language-specific representations of categorical spatial relationships in response to the linguistic input they are exposed to. Indeed, Kemmerer and Tranel (2000) provide some preliminary evidence that these two types of representation are independent. They performed an assessment of the linguistic and perceptual/ cognitive representations of spatial relationships in two brain-damaged patients, revealing a double dissociation between linguistic and perceptual representations of spatial relations. One patient (with a right hemisphere lesion involving various cortical and subcortical regions) performed poorly on tests of (nonlinguistic) visuo-spatial abilities, but well on tests involving the comprehension and production of spatial prepositions (including both topological and projective terms). The other patient (with a left hemisphere lesion involving other cortical and subcortical areas) performed poorly on the linguistic tests but well on the visuo-spatial tests. These results (see also Kemmerer, 1999), together with those of cross-linguistic studies, suggest that the relationship between spatial representations for spatial language and spatial representation for nonspatial tasks is complex. We concur with Munnich et al. (2001) that there are at least likely to be a set of common constraints operating on both spatial language and spatial representation, although it remains to be seen whether these systems are completely independent. SUMMARY In this chapter, we have examined the evidence that infants are able to make distinctions revealing knowledge of both geometric and extra-geometric factors underlying spatial relations. Furthermore, although preliminary in nature, it would appear that children acquiring language are affected by both sets of constraints. We have also seen that, although languages differ considerably in the way that they carve up space, there is still a degree of regularity across languages. We have suggested that extra-geometric as well as geometric routines provide a way of understanding these regularities and

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Page 164 differences. Our primary concern in this book has been to try to understand how speakers of English comprehend and produce spatial prepositions, but the functional geometric framework can be applied to a wide range of languages. Although languages differ in the way in which geometric and extra-geometric routines might be packaged, fundamental constraints like gravity and the geometric and dynamic-kinematic routines associated with concepts like support and containment are in evidence across all languages. However, the balance between geometric and extra-geometric factors has yet to be tested in a wide range of languages. It remains an exciting avenue for future exploration.

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Page 165 CHAPTER NINE Extensions, links, and conclusions In this book, we have presented a functional geometric framework by which to account for the meaning of spatial prepositions. The three components in the title of the book, saying, seeing, and acting, all play a role in the framework. When describing a particular spatial scene, the speaker chooses expressions that map onto relations in a situation model of that scene that are consistent with the outputs of both geometric routines reflecting how we see the world and extra-geometric routines reflecting how we can act on that world. How these routines are assembled depends on knowledge of the objects involved and memory for relations between those objects. In this final chapter, we consider how the functional geometric framework sits with other recent approaches to language understanding and, in doing so, pick up issues given only a fleeting mention earlier in the book. THE FUNCTIONAL GEOMETRIC FRAMEWORK, EMBODIMENT, AND SITUATED ACTION Within the framework we have outlined, the meaning of a spatial expression does not simply derive from the addition of the fixed meanings of the preposition together with the meanings of other elements in the sentence (e.g., nouns and verb). Rather, its meaning is constructed and is associated with the strongest situation model that can be established given the ingredients we have outlined.

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Page 166 The idea that meaning is constructed as a result of putting together multiple constraints is consistent with recent eye-tracking studies showing that linguistic and visual information both contribute to the construction of situation models on line (e.g., Chambers, Tanenhaus, Eberhard, Filip, & Carlson, 2002; Tanenhaus, Spivey-Knowlton, Eberhard, & Sedivy, 1995). For example, in series of studies reported by Chambers et al. (2002), participants were positioned in front of a table on which a range of objects was placed. The task for participants involved responding to spoken commands, such as ‘‘ Put the cube inside the can ”. Chambers et al. found that eye movements on hearing the preposition inside immediately fixated on the can. Furthermore, in a second experiment when containers of various sizes were used, when inside was heard participants fixed on the container that was the appropriate size to contain the cube. They argue that the results provide evidence for the notion that the processing system rapidly integrates linguistic and nonlinguistic constraints, including situation-specific information relevant to communicative goals. The idea that meaning is constructed as a result of putting together multiple constraints also fits with recent work on embodiment, and in particular the work of Glenberg and colleagues (e.g., Glenberg, 1997; Glenberg & Robertson, 1999, 2000; Kaschak & Glenberg, 2000; see also de Vega, Rodrigo, Ato, Dehn, & Barquero, 2002) and that of Barsalou (e.g., Barsalou, 1999). Glenberg and colleagues have proposed that the meaning of a sentence is constructed by indexing words or phrases to real objects or perceptual analogue symbols for those objects, deriving affordances from the objects and symbols and then meshing the affordances under the guidance of syntax. Barsalou (1999) also places similar emphasis on perceptual representation for objects and nouns in his perceptual symbol systems account. For Barsalou, words are associated with schematic memories extracted from perceptual states that become integrated into what Barsalou terms simulators (see also Grush, in press). As simulators for words develop in memory, they become associated with simulators for the entities and events to which they refer. Furthermore, once simulators for words become linked to simulators for concepts, Barsalou argues that words can then control simulations. Central to this notion is the idea that language comprehension has as much to do with preparation for situated action as it has to do with extracting propositions from sentences (Barsalou, 1999). In this respect, our functional geometric approach to the meaning of spatial prepositions is similar to the approaches of Barsalou and Glenberg. Common to these accounts is the notion that words are associated with a range of types of perceptual information. For example, knowing what an object is requires knowing what one does with it, and therefore its representation should reflect how you can interact with that object, a representation that can prepare you for situated action.

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Page 167 Whereas cognitive linguistics places central emphasis on space as the fundamental building block of conceptual structure, Glenberg and colleagues (Glenberg, 1997; Glenberg & Kaschak, 2002; Glenberg & Robertson, 1999, 2000; Kaschak & Glenberg, 2000) have argued that action is the fundamental building block. For example, Glenberg and Kaschak (2002) have found action–sentence compatibility effects similar to the action potentiation effects reported by Tucker and Ellis (1998; see Chapter 3, p. 64). Participants made judgements about whether sentences were sensible or not by depressing a key (“yes” or “no”) requiring a movement towards or away from the body. Glenberg and Kaschak found that responses requiring an action opposite to the direction of the action depicted in the sentence led to slower responses than when the two were compatible. For example, “close the drawer” judgements were significantly slower when the “yes’’ response required a movement towards the body rather than a movement away from the body (and so compatible with the movement required to close the drawer). Just as dynamic-kinematic routines are required for the meaning of spatial expressions, the results from Glenberg and Kaschak suggest that dynamic-kinematic routines are also going to be important in understanding action statements. However, while cognitive linguists have placed central emphasis on space, and Glenberg and colleagues place central emphasis on action, in the functional geometric framework it is how space, action, and conceptual knowledge “mesh” together (using Glenberg’s terminology) that underpins the construction of the situation-specific meaning of spatial expressions. COMPUTATIONAL MODELLING AND THE NEURAL CORRELATES OF SPATIAL LANGUAGE COMPREHENSION AND PRODUCTION It may be helpful to indicate the level of explanation offered by the functional geometric framework. We have argued that situation models are the vehicles where multiple constraints reflecting both geometric and extrageometric factors combine to produce a specific meaning. However, we are neither claiming that situation models are necessarily required as a specific part of an architecture in a computational model of spatial language processing, nor are we suggesting that an examination of the brain structures involved in spatial language processing will eventually reveal a specific brain area where a situation model can be identified. Rather, the functional geometric framework is intended as a framework somewhere between the computational and algorithmic levels of explanation (cf. Marr, 1982). It is quite possible that situation models are an epiphenomenon of subconceptual processes (Barsalou, 1999; Smolensky, 1988) within a constrained connectionist framework. Therefore, the functional geometric framework is best

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Page 168 regarded as an abstract/theoretical framework that specifies the information sources relevant for spatial language processing. Currently, Coventry, Cangelosi, Joyce, and Richards (2002, in progress) are developing a computational model for spatial language comprehension and production that implements the multiple constraint satisfaction in the functional geometric framework and maps onto past and new empirical data. The approach introduces cognitive-functional constraints by extending Ullman’s (1984, 1996) notion of visual routines to include operations on dynamic rather than static visual input (cf. Cavanagh, Labianca, & Thornton, 2001). For example, Figure 9.1(a) illustrates an example video processed by a “what + where” code (see Joyce, Richards, Cangelosi, & Coventry, 2002; see also Edelman, 2002); that is, the input consists of an array of some 9 × 12 activations (representing retinotopically organised and isotropic receptive fields) where each activation records some visual stimulus in that area of the visual field. In addition to the “field” representation, a distributed object identity code is augmented. These codes were produced by an object representation system (Joyce et al., 2002; based on Edelman’s, 1999, theory) using the same videos. In Figure 9.1(b), we show such a coding for the liquid in (a). The distributed object code (bottom left of Figure 9.1b) is appended to each input field. The connectionist model then consists of a predictive, time-delay connectionist network similar to Elman’s (1990) simple recurrent network (SRN). Figure 9.2 shows the network as an Elman SRN, but “folded’’ about the hidden layer. So, the network is given one set of activations as input that feedforward to the hidden units and, simultaneously, the previous state of the hidden units is fed to the hidden units. The hidden units feedforward, producing an output that is a prediction of the next sequence item and then, using the actual next sequence item, backpropagation is used to modify the weights to account for the error. The end point of the training is that the network can “replay” the properties of the visual episode that was learned and, given a cue, can predict how positions of objects will change over time. Figure 9.3 shows the results of such a test (compare this with the actual sequence shown in Figure 9.1b). In essence, the model is able to provide the predictions and simulations required for the dynamic-kinematic routines in the functional geometric framework (see Joyce, Richards, Cangelosi, & Coventry, 2003, for discussion). One of the assumptions in the computational model we have described, and one of the implications of the framework we have adopted in this book, is that multiple areas of the brain are likely to be associated with spatial language comprehension and production (see Chapter 3). Furthermore, we would expect to find differential activity of these areas associated with differing degrees of activation of geometric and dynamic-kinematic routines. Despite the overwhelming evidence for the importance of extra-geometric factors on the comprehension and production of spatial prepositions sum-

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Figure 9.1 (a) An example of a video sequence used by Joyce et al. (2003). (b) An example field coding for the sequence shown in (a). marised above, studies that have examined the neural correlates of spatial language processing have focused exclusively on geometry. For example, O’Keefe (1996; see also O’Keefe, 2003; O’Keefe & Nadel, 1978) presents an analysis of the meaning of spatial prepositions derived from cognitive map theory that was originally developed to account for how neural coding of space in the rat hippocampus could support spatial memory. O’Keefe and

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Figure 9.2 Schematic representation of the predictive, time-delay connectionist network implemented by Joyce et al. (2003).

Figure 9.3 Sequence recalled by the network (compare with Figure 9.1b).

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Page 171 Nadel (1978) argued that entities are located by their spatial relationships to each other in a cognitive map. These relations are specified by three variables corresponding to places, directions, and distances bound together as vectors. Each vector is based upon the direction and distance of a place relative to the observer at a certain time. Originally, O’Keefe and Nadel (1978) claimed that such a system is able to account for the spatial behaviour of rodents and is consistent with neuro-anatomical studies of the rat hippocampus. However, O’Keefe also extended the basic theory to account for human spatial representation. Whereas the cognitive map system in rodents was distributed across both hippocampi, in humans the system is thought to reside in two related systems. While the right hippocampus deals with nonlinguistic representations of space, the left hippocampus mediates the mapping of spatial language onto a spatial representation like that on the right. In particular, O’Keefe claims that the vector machinery of the cognitive map theory can be used to define the meaning of various spatial prepositions (see also Zwarts, 1997, 2003; Zwarts & Winter, 2000). While O’Keefe’s model is attractive, it doesn’t take into account the myriad of extra-geometric influences that affect the comprehension and production of spatial prepositions. Within the functional geometric framework, O’Keefe’s work provides a possible account of the geometric routines important for spatial language processing. However, the hippocampus is not the only area that has been implicated in spatial language comprehension and production. There is evidence that the retrieval of words denoting spatial relations is dependent on the structures in the left parietal and frontal regions (e.g., agrammatic aphasics often exhibit an impaired use of prepositions; Friederici, 1985; Tesak & Hummer, 1994). Furthermore, the parietal and frontal regions have also been shown to be involved in the processing of space and motion (Ungerleider & Mishkin, 1982). More recently, Damasio et al. (2001), using PET, found that naming spatial relations and naming actions was associated with activity in the left frontal operculum and left parietal cortices, but not in the left infero-temporal cortices (IT) or right parietal cortices (associated with naming objects). However, whereas naming actions was also associated with activity in the lateral temporo-occipital cortices related to motion processing (specifically area MT), no such activity was found when naming spatial relations. But the scenes used by Damasio et al. were rather restricted, and they did not systematically vary the prepositions presented with the same scenes. Indeed, Kourtzi and Kanwisher (2000) present the first evidence of increased middle temporal and medial superior temporal (MT/MST) activation over baseline when viewing static images that imply movement (e.g., a picture of an athlete in running pose or a sea wave in mid-air). They suggest that motion processing is mediated by high-level processes. Following on from this, we might expect that scenes depicting spatial relations requiring the instantiation of dynamic-kinematic

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Page 172 routines may similarly show MT/MST activation, perhaps further mediated by the language task underway. For example, a static image of a container beginning to pour liquid positioned higher than a bowl (e.g., the first picture in Figure 9.1a) could be described as being over the bowl, above the bowl, or near the bowl. If a task involves judging the appropriateness of over/ above , one might expect that motion processing is essential to project the path of the liquid to assess whether the objects will interact successfully. However, with the same scene in the context of a near/far judgement, motion processing may be less relevant. Understanding the neural correlates of spatial language comprehension and production and developing computational models is currently in its infancy (but see the pioneering work of Regier, 1996). This is likely to be an important avenue of research in the next few years. METAPHORICAL USES OF SPATIAL PREPOSITIONS AND UNDERLYING MODELS One of the original motivations for the functional geometric framework was another issue that we have not addressed in any detail in the book so far. It concerns the origin of spatial metaphor (see Garrod & Sanford, 1989). Spatial prepositions are extremely productive metaphorical devices. Statements such as the following are commonplace: Jane wanted to complain, but she felt it was beneath her. Harry was in a bad mood. Joan had been on social security for years. Mary felt under the weather. The prevalence of spatial metaphors and extended uses of spatial prepositions has led some to argue that spatial representations are somehow basic and, therefore, act as productive vehicles for metaphor (Lakoff & Johnson, 1980). However, to what extent do the metaphorical interpretations depend upon the geometry of the underlying spatial relations as opposed to extra-geometric factors of the kind assumed in the functional geometric framework? In other words, is spatial representation basic because of its geometry or because of the spatial functions associated with that geometry? O’Keefe (1996; see also O’Keefe & Nadel, 1978) presents an interesting analysis of the metaphorical extensions of spatial prepositions such as below , under, beneath , and over derived from the cognitive map theory we discussed above. The vector machinery of the cognitive map theory can be used to define the meaning of various spatial prepositions. For example, for vertical prepositions relations are determined primarily by a single “vertical” axis, the z axis. In the simplest case (e.g., below ), if some place A is below another place B , then the vector from the observer to A must be greater in the

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Page 173 z axis than the vector from the observer to B . More complex vertical prepositions (e.g., under) require an additional orthogonal x axis, which can be used to reflect the extent of the located object that is directly below the reference object. This is required to explain how we can say such things as The chair on the right is further under the table than the chair on the left. In this case, the difference between the locations of the two chairs does not reflect a difference in the z axis, but rather it reflects differences in the overlap of the x axis between each chair and the table. For other types of prepositions, additional axes can be introduced into the system. For example, path uses of prepositions, such as the use of from and to in Mary went from the study to the dining room, require an orthogonal time axis t . In principle, any orthogonal axis can be added to the system to capture any spatio-temporal relation between two or more places. But, how can this cognitive map theory be applied to the metaphorical use of spatial prepositions? O’Keefe (1996) discusses two metaphorical domains to which the vertical prepositions can be applied: influence and social status. Consider the following uses of below , beneath , and under: She was acting below ( beneath ) her station. She was acting under his orders. *She was acting under her station. *She was acting below his orders. To understand how these prepositions express the relations they do, O’Keefe assumes that people can be ordered on a status dimension, analogous to the “vertical” z dimension. Hence, for someone to act beneath their station means that their actions correspond to acts that are lower on the status dimension than the position normally associated with that person. However, the examples also show that there is something else going on here, because below is not interchangeable with under. As a result, O’Keefe introduces yet another “vertical” axis, which corresponds to something like influence. He then argues that there are two slightly different uses of under with respect to influence that correspond to the two following spatial uses: under the widening sky and under the table. By analogy we have: under the aegis of and under the influence of . The difference in both cases relates to the presence or absence of the second x dimension, which was mentioned above to explain comparative uses of under (e.g., one chair being more under a table than another). Note that it is possible to say June was more under the influence of John than Sally was, but not *Harry was more under the aegis of the king than John was. Hence, the metaphorical uses of under and below correspond to the spatial uses but with the physical z and x axes being mapped onto either status or influence. O’Keefe (1996) even goes so far as to offer a “spatial”

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Page 174 treatment of causality in relation to cognitive map theory. In the theory, causality is associated with the influence of something over an event using a similar influence axis related to a complex spatio-temporal representation. From the functional geometric point of view, O’Keefe’s treatment of metaphor is interesting in that he recognises the importance of extra-geometric factors such as influence and control. According to the functional geometric framework, we should expect to find extended uses of this kind. After all, we have argued that extra-geometric factors such as “location control’’ are central to the meaning of many spatial prepositions. The main difference between our account and that of O’Keefe is that such extended uses are treated as direct extensions of the extrageometric components of the meaning of the terms rather than as novel metaphorical uses. As Garrod and Sanford (1989) pointed out, many if not most extended uses of spatial prepositions, such as in and on, do not make much sense in relation to the purely geometric component of their meaning. In other words, it is not clear what being in a bad mood has to do with the geometry of enclosure or what being on social security has to do with the geometry of contact. Yet, the first makes sense in relation to the mood exerting control over one’s behaviour and the second makes sense in relation to the notion that social security is serving as a financial support. In fact, one would expect the extra-geometric aspects of the meaning of these prepositions to be particularly effective as metaphors. In Chapter 3, we argued that extra-geometric components of meaning underpin many of the spatial inferences that can be drawn on the basis of these relations. In other words, location control and support are particularly useful for making predictions about how objects will behave with respect to each other in the real world. It is just such inference potential that should make the prepositions productive as metaphorical vehicles. For example, in the case of being on social security, we can infer that if the social security is removed the person would suffer an economic fall. THE FUNCTIONAL GEOMETRIC FRAMEWORK AND OTHER SYNTACTIC CATEGORIES Our focus in this book has been to provide a framework for the treatment of spatial prepositions as opposed to other spatial expressions. However, other spatial terms are also likely to require this treatment. For example, the importance of contextual factors and how objects are conceptualised has been shown for dimensional/referential adjectives (e.g., Bierwisch & Lang, 1989; Goy, 2002). For example, someone 1.9 metres tall (6 feet 2 inches) would be described as a tall person, but not as a tall basketball player. Poles can be described as being high, tall, or long, but a tower can only be described as being tall or high, and people can only be described as being tall.

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Page 175 Nonspatial terms also fall within the more general framework. For example, the idea that quantifiers like a few , some, many, and lots of somehow refer to a number of objects that are easily quantifiable has been challenged by a battery of empirical findings that show that the number referred to varies dramatically as a function of a range of contextual factors. As Moxey and Sanford (1993, p. 108) have argued, “the extent to which some possible interpretation is paramount will depend on the current situational context”. For example, expected frequency effects for quantifiers are well known. To visit the cinema often represents more times per year than to visit the USA often (Newstead & Collis, 1987). This suggests that expected rates may be used as a standard against which frequency expressions are calibrated. Consider also Moxey and Sanford’s (1993) example of some people in front of the fire station versus some people in front of the cinema. Our expectations suggest that large numbers of people should be outside the cinema, but not outside the fire station. Of particular interest with respect the functional geometric framework are a range of effects on quantifiers to do with relative dimensions of objects. Hormann (1983) originally found that the size of an object influences the quantifier used to describe a number of those objects. For example, a few crumbs means more than eight, but a few shirts means about four. Similarly, a few large cars means a smaller number than a few cars . More recently Newstead and Coventry (2000) have shown that the relative size of objects influences the appropriateness of quantifiers to describe a quantity of objects (balls) in a container (a bowl). They varied the size of balls and bowl and found that high magnitude quantifiers are more appropriate when there is a low size differential (i.e., large bowls in a bowl) and low magnitude quantifiers are more appropriate when there is a large size differential (e.g., small balls in the same size of bowl). The range of effects with quantifiers seems to mirror the results found with prepositions quite closely. One intriguing possibility is that the extra-geometric conceptual knowledge we have identified as being important for prepositions may also be required to establish the situation-specific meaning of a range of terms across syntactic categories. In the case of quantifiers, there is some preliminary evidence to suggest that this possibility might be the case. Newstead and Coventry (2000) presented participants with simple pictures of bowls containing a number of balls, ranging from 3 to 21. They varied the size of container and balls, such that with large balls and a small container when the number of balls reached 9 the balls started to overflow the top of the container (similar to the high piles of ping-pong balls used by Coventry, Garrod, & Ferrier and described in Chapter 4). Participants had to rate the appropriateness of sentences of the form There are a few/several/ many/lots of balls. Newstead and Coventry found that, when the balls started to overflow the rim of the container, although the number of balls increased,

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Page 176 the acceptability judgements for quantifiers such as several and many actually went down. Similar influences were found when the container was tilted. Although quantifiers are about number, it would seem that the extra-geometric dynamic-kinematic relation is so central to such scenes even judgements about number are affected. The results with quantifiers suggest that the same extra-geometric parameters may underlie the meaning of a number of syntactic categories. Recall that Morrow and Clark (1988) found similar effects for the verb approach (see Chapter 6). It remains to be established whether these results can be generalised to a wider range of syntactic categories. CONCLUSIONS In this book, we have set out a functional geometric framework that we believe provides the starting point for an understanding of the meaning of spatial prepositions. The framework brings together into a single explanatory space a number of empirical results and theoretical assertions that we think need to be viewed together if we are to understand the language of space. Establishing the meaning of a spatial expression is a process that calls on links (or “meshing” in Glenberg’s terminology) between stored object (extra-geometric) knowledge, attentional processing of the visual scene, geometric routines, extra-geometric dynamic-kinematic routines, and weights for these parameters associated with individual prepositions. Exactly how these multiple constraints come together is an important avenue for future research. Furthermore, understanding how the multiple constraints might operate will require computational modelling and further investigations of the neural correlates of spatial language processing. Currently, work on the relationship between spatial language and perception is a hotbed of activity. We are sure that algorithmic and implementational realisations of the functional geometric framework cannot be far away.

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Page 191 Author index Aguiar, A., 151 Allen, J. F., 40 Amsel, G., 150 Anderson, A., 132–134 Antell, S. E., 148, 150–151 Armstrong, S. L., 29, 34 Ato, M., 166 Aurnague, M., 40 Baillargeon, R., 149–152 Barquero, B., 166 Barsalou, L. W., 13 Behl-Chadha, G., 147 Bennett, B., 38, 40–42, 79 Bennett, D. C., 6, 8, 22, 24, 32–33 Bertamini, M., 66 Bierwisch, M., 174 Bingham, G. P., 65–66, 69 Blair, E., 154 Bloom, P., 100 Boroditsky, L., 5–6 Bower, T. G. R., 150 Bowerman, M., 4, 153, 158–160, 162 Breinlinger, K., 148–149, 152 Brown, J. S., 129 Brown, P., 9, 162 Brugman, C., 5, 21–22, 28–34 Bryant, D. J., 46, 134, 161 Bryk, A., 153 Burgess C., 5 Burroughs, W. J., 117 Byrne, R. M. J., 129 Cadwallader, M., 117 Campbell, S., 52, 54, 77–79, 84–86, 121, 135, 142, 144, 155 Cangelosi, A., 109, 136, 140, 143, 16–170 Caramazza, A., 103 Carey, D. P., 63 Carlson, G. N., 10, 166 Carlson, L. A., 34, 39, 46, 48–50, 54, 58, 66–67, 99–102, 110, 115, 128, 136, 138–139, 141, 160 Carlson-Radvansky, L. A., 46, 59, 64, 97–102, 107, 109–110, 112, 136–140, 143, 156 Carmichael, R., 52, 54, 80, 81–82, 88, 103, 135–136, 140, 143 Caron, A. J., 148, 151

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Page 192 Caron, R. F., 151 Carroll, P., 131 Casad, E., 30 Casasola, M., 150 Cavanagh, P., 169 Chambers, C. G., 10, 166 Cheng, J., 66, 69 Choi, S., 153, 158–160 Cienki, A. J., 83 Clark, E. V., 150, 155 Clark, H. H., 8, 22–23, 33, 55, 114–115, 118–119, 123, 153, 157, 161, 176 Clibbens, J., 155, 157, 159 Cohen, L. B., 149–150, 152 Cohn, A. G., 38, 40–44, 53, 57, 68, 79, 88 Collis, J., 175 Cooper, G. S., 16, 18, 20 Corrigan, B., 139 Couclelis, H., 92 Covell, E. R., 110 Coventry, K. R., 29, 32, 52, 59, 65, 74–76, 79–84, 86–88, 102–109, 111, 116, 119, 121–122, 135–136, 139–140, 143, 145, 155–157, 159–161, 168–170, 175 Covey, E. S., 59, 64, 102, 110, 112, 115, 136, 138–140 Craik, K., 128–130 Crangle, C., 40, 58 Crawford, L. E., 100, 163 Creem, S. H., 62 Crowther, M., 116, 136 Cui, Z., 41 Cummins, M., 148 Dalimore, J., 121 Damasio, A. D., 63, 171 Damasio, H., 63, 171 Danziger, E., 161–162 de Kleer, J., 129 de Vega, M., 99, 166 Dehn, D. M., 166 Diwadkar, V. A., 117–118 Dosher, B. A., 100, 157, 162–163 Duke, N., 154 Dumais, S., 5 Durkin, K., 153 Eberhard, K. M., 10, 166 Edelman, S., 168 Ehrlich, S. M., 152 Eimas, P. D., 147 Ellis, R., 64, 167 Elman, J. L., 168 Eschenbach, C., 92 Ewert, K., 156 Faust, M. E., 131 Faust, R. R., 100 Feist, M. I., 62, 79, 81, 83, 88, 135, 159 Ferenz, K. S., 82, 116–118, 135–136 Ferrier, G., 52, 54, 76–79, 83–86, 121, 135, 142, 144–145, 155, 175 Fieselman, S., 151 Filip, H., 10, 166 Fillmore, C. J., 10, 22, 96 Fodor, J. A., 29 Foss, D. J., 131 Frankenfield, A., 154 Franklin, N., 99 Freeman, N. H., 150 Freyd, J., 66, 69 Friederici, A. D., 56, 97, 171 Gale, N., 92 Gapp, K.-P., 49 Garnham, A., 92 Garrett, M. F., 100 Garrod, S. C., 12, 52, 54, 59, 76–86, 88, 103, 121–122, 130–136, 140, 142–144, 155, 172, 174–175 Gentner, D., 5, 79, 81, 96, 129, 135 Gentner, D. R., 96, 129 Georgopolous, A. P., 49 Gernsbacher, M. M., 131

Gibson, J. J., 52 Gleitman, H., 29, 34 Gleitman, L., 29, 34, 162 Glenberg, A. M., 5, 13, 30, 131, 143, 166–167, 176 Glucksberg, S., 30

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Page 193 Goldstone, R. L., 117 Golledge, R. G., 92 Goodale, M. A., 62, 63 Gooday, J., 38, 40–42, 79 Gotts, N. M., 38, 40–42, 79 Goy, A., 174 Grabowski, J., 111–112, 136 Grabowski, T. J., 63, 171 Graf, R., 97 Green, B., 103 Green, D., 160 Greeno, J. G., 129–130, 133 Grush, R., 166 Guijarro-Fuentes, P., 160–161 Haight, W., 153 Halberstadt, J., 117 Harnad, S., 5, 30 Harris, C. L., 32 Harris, L. J., 97, 153 Hawkins, B. W., 30 Hayashi, M., 153 Hayward, W. G., 47, 58, 100–101, 136, 161–162 Herndon, R. W., 100 Hermer-Vazquez, L., 148 Herrmann, T., 112, 136 Herskovits, A., 18, 22, 24–28, 33–34, 43, 52, 61, 95, 119–120 Hespos, S. J., 150 Hess, D. J., 131 Hichwa, R. D., 63, 171 Holcomb, P. J., 100 Holyoak, K. J., 117 Hood, B. M., 151 Hormann, H., 175 Horton, W. S., 30 Hummer, P., 171 Humphrey, G., 62 Huttenlocher, J., 100, 153, 163 Inhelder, B., 153 Irwin, D. E., 97–99 Jackendoff, R., 4, 6–8, 10–11, 22, 34, 37, 55, 63, 69, 92, 96, 114, 137, 139, 153, 161 Jacobson, K., 148–149, 152 Jakobson, L. S., 63 Janda, L., 30 Jeannerod, M., 64, 69 Jiang, Y., 99 Johansson, G., 65 Johnson, J. R., 153 Johnson, M., 5–6, 28, 30, 172 Johnson-Laird, P. N., 11, 18, 20–21, 33, 52, 55, 81, 88, 95, 112, 114, 118, 129 Jones, K., 154 Jones, S. S., 154 Joyce, D. W., 109, 136, 140, 143, 168–170 Kamp, H., 131 Kanwisher, N., 171 Kaschak, M. P., 143, 166–167 Kase, J., 148 Katsnelson, A. S., 148 Katz, G., 152 Keeble, S., 150 Kellman, P. J., 149 Kemler Nelson, D. G., 154 Kemmerer, D., 163 Kessler, K., 97 Kettner, R. E., 49 Keysar, B., 30 Kim, I. K., 151 Kintsch, W., 131 Kita, S., 161–162 Klatt, S., 115 Kotovsky, L., 149 Kourtzi, Z., 171 Kreitzer, A., 32 Kuczaj, S. A., 153

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Labianca, A. T., 168 Labov, W., 80 Lakoff, G., 4–6, 10–12, 21–22, 28–35, 48, 143, 172 Lamme, V. A. F., 44 Lanca, M., 134 Landau, B., 4, 6–7, 22, 34, 37, 55, 63, 69, 100, 114, 153–155, 157, 161–163

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Page 194 Landauer, T., 5 Lang, E., 174 Langacker, R. W., 10, 28, 114 Langston, W. E., 131 Lattanzi, K. M., 59, 64, 102, 110, 112, 136, 138–140 Lee, T. S., 44 Leech, G. N., 16, 18, 20 Leslie, A. M., 149–150 Levelt, W. J. M., 56, 92, 94, 95, 97–98, 100 Levinson, S. C., 8–9, 92–93, 100, 153, 157–158, 161–162 Li, P., 162 Lin, E. L., 138 Lindkvist, K. G., 24 Lindner, S., 30 Lloyd, S., 150 Logan, G. D., 12, 34, 39, 46–49, 58, 99–102, 136–137, 144 Lund, K., 5 Lyons, J., 6 Lyons, T., 153 Macko, K. A., 62 Macomber, J., 148–149, 152 MacWhinney, B., 156 Madole, K. L., 152 Mah, W. A., 117 Mandler, J. M., 153, 158–159 Maratsos, M. P., 153 Margolis, E., 29, 34 Marr, D., 51, 92, 167 Martin, E., 148 Mash, C., 148 Mather, G., 32, 103–104, 116, 136, 145 McCloskey, M., 103 McDonough, L., 158–159 McNamara, T. P., 117–118 Medin, D. L., 34, 117 Michotte, A., 5, 52, 57, 65, 69, 149 Miller, G. A., 11, 18, 20–21, 52, 81, 88, 95, 111–112, 114, 118 Miller, J., 11 Milner, A. D., 63 Minsky, M., 44 Mishkin, M., 6, 62, 171 Morris, C., 154 Morrow, D. G., 114–115, 119, 123, 176 Moxey, L. M., 175 Mumford, D., 44 Munnich, E., 100, 157, 162–163 Murphy, G. L., 34, 138 Nadel, L., 92, 100, 170–172 Naylor, S. J., 100 Needham, A., 151–152 Newstead, S. E., 175 Norris, C. M., 148 O’Keefe, J., 92, 120, 137, 170–174 Oakes, L. M., 149–150, 152 Pantzer, T., 66, 69 Papert, S., 44 Pasko, R. N., 148 Pederson, E., 159, 161–162 Perenin, M. T., 63 Peterson, M. A., 100 Piaget, J., 153 Plumert, J. M., 156 Plunkett, K., 153 Ponto, L. L. B., 63, 171 Prat-Sala, M., 81, 87–88, 104–109, 111, 135–136, 139, 143, 145, 160 Proffitt, D. R., 62 Purcell, S. E., 152 Pustejovsky, J., 10, 33, 137 Pylyshyn, Z. W., 29 Quinn, P. C., 148 Radvansky, G. A., 101, 109, 131, 136, 143, 156

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Randell, D. A., 41 Redford, M. A., 150 Regier, T., 5, 12, 34, 39, 45, 48–50, 54, 58, 66–68, 100–102, 128, 136, 138–139, 141, 160, 163, 172 Retz-Schmidt, G., 8, 10, 92 Rice, S., 32

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Page 195 Richards, L. V., 102, 104–109, 111, 136, 139–140, 143, 145, 155–157, 159–160, 168–170 Robertson, D. A., 5, 13, 30, 143, 166–167 Rodrigo, M. J., 99, 166 Romero, R., 44 Rosch, E., 29, 117 Rosenblum, L. D., 65, 69 Roth, E. M., 29, 34 Russell, R., 154 Sadalla, E. K., 117 Sadler, D. D., 12, 34, 39, 46–49, 58, 100–102, 136, 144 Sandhagen, H., 24 Sandra, D., 32 Sanford, A. J., 12, 52, 54, 83, 130–131, 172, 174–175 Santos, L., 151 Schmader, T. M., 148 Schmidt, R. C., 65, 69 Schober, M. F., 92 Schwartz, A. B., 49 Schwartz, D. L., 66 Searle, J. R., 22–23 Sedivy, J., 166 Seltzer, M., 153 Senft, G., 161–162 Sewell, D. R., 29 Shen, Y., 30 Shepard, R., 163 Shoben, E. J., 29, 34 Short, K. R., 149 Sinha, C., 150, 153 Sitnikova, T., 100 Slack, J., 100 Slobin, D. I., 153, 162 Smith, L. B., 154 Smolensky, P., 167 Spear, S. J., 156 Spelke, E. S., 148–149, 151–152 Sperber, D., 23 Spivey-Knowlton, M., 166 Staplin, L. J., 117 Stecker, D. S., 155 Stevens, A. L., 129 Strommen, E. A., 97, 153 Suppes, P., 40, 58 Talmy, L., 5, 10–12, 22, 34, 52, 54–56, 114, 152, 161 Tanenhaus, M. K., 10, 166 Tang, Z., 109, 136 Tarr, M. J., 47, 58, 100–101, 136, 161–162 Taylor, H. A., 92, 100 Taylor, J. R., 22 Tesak, J., 171 Thornton, I. M., 168 Thorseng, L. A., 153 Tobler, W., 92 Tomasello, M., 153 Tranel, D., 63, 163, 171 Tucker, M., 64, 167 Tversky, B., 92, 99–100, 134 Ullman, S., 39, 43–46, 48, 67, 68, 169 Ullmer-Ehrich, V., 52 Ungerleider, L., 6, 62, 171 van Dijk, T. A., 131 Vandeloise, C., 12, 52–54, 116, 160 Varner, K. R., 131 Vighetto, A., 63 Watson, M., 120–121, 124, 136 Weiss, P., 112, 136 Weissman, S., 148 West, R., 100 Wilkins, D., 161–162 Wilson, D., 23 Winter, Y., 171 Wittgenstein, L., 29

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Wood, F. T., 24 Zee, E. van der, 100, 120, 121, 124, 136 Zimmer, H., 99 Zwaan, R. A., 131 Zwarts, J., 171

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Page 197 Subject index Above, 8, 9, 45–46, 48, 58, 66, 95, 97, 100–113, 136, 138, 140, 144–146, 153, 156, 160, 172 Acquisition of language, see Language acquisition Action-sentence compatibility effects, 167 Across , 30, 156 Adjectives, 11, 174 Ad hoc categories, 29 Affordances, 30, 52, 64, 143, 166–167 Agrammatic aphasia, 171 Algorithmic level of explanation, 167 Along , 8 Analogical reasoning, 129 Approach, 114–115, 119, 176 Arandic, 161 Artificial Intelligence, 12, 16 Astern, 6 Astronauts, 56–57 At, 24–25, 59, 61, 69, 113, 118–120, 123, 136 Attention, 44, 49, 139, 152, 156, see also Attention vector Sum (AVS) model Attention Vector Sum (AVS) model, 39, 45, 48–51, 53–54, 58, 67, 100–101, 128, 136, 138–141 Background conditions, 22–23 Base representation, 43 Behind , 8, 22, 26, 59, 92, 95, 111–112, 153 Below, 9, 48, 95, 103–109, 136, 145, 160, 172–173 Beneath, 172 Berber, 159 Beside, 153 Between , 59, 113, 120–124, 153 Biological motion, 65 Bounding box, 100 By, 61 Cardinal directions, 9, 92 Causality, 149–150, 174 Centre-of-mass, 49, 101 Children’s understand of spatial relations, see Prelinguistic spatial concepts Classification of prepositions, 6–11

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Page 198 Cognitive linguistics, 5, 12, 16, 28, 30, 35, 48, 167 Cognitive map theory, 170–174 Coincidence situation, 95–96 Computational modelling, 48, 167–170, see also Connectionism Computational theory level of explanation, 51, 167 Conceptual structure (CS), 137, 139, 143 Connection, 40, 135 Connectionism, 12, 39, 45, 167–170 Containment, 4, 150–151 Contextual scaling model, 117–118 Contiguity, 20, 84 Converses/converseness, 22, 94 Convex hull, 41, 43, 45, 60, 81, 135 Convexity, 40–41 Core sense/core meaning, 12, 16, 22, 128 Cross-linguistic variation, 147, 157–164 Decoding and encoding problems, 12, 22 Deixis, see Reference frames, deictic frame and Reference frames, relative frame Dialogue, 132–134 Dictionary theories of meaning, 12, 16, 128 Dimensional adjectives, 174 Dimensional prepositions, 7 Directional prepositions, 7, 8 Discourse models, 131, 134, see also Situation models Distance, 49, 101 Distance estimation, 117–118 Dorsal pathway, 62–63 Down, 4 Dynamic-kinematic routines, 12–13, 55–59, 73–80, 84–89, 101–109, 117, 123, 127, 137–141, 144–145, 158–160, 164, 167, 170, 172, 176 Dutch, 4, 158–160, 162 Dynamics, 40, 65–67, 69 Ecological approach to vision, 52 Embodiment, 13, 28–30, 33, 165–167 Emotions, expressions of, 5, 30 Encounter situation, 95–96 Event-related potentials (ERPs), 99–100 Experientialism, 12, 143 Eye tracking studies, 166 Family resemblances, 28 Far, 8, 113–119, 123, 136 Figure, 10 Finnish, 4 For , 6 Force dynamics, 53–54, 68 French, 116, 160 Full specification of lexical entries, see Minimal versus full specification of lexical entries Functional geometric framework, 6, 12–13, 24, 35, 39–40, 51, 54–62, 67–70, 91, 112, 124, 127, 134–146, 148, 165–167, 174–176 Functional relations, 52, 64 Generative lexicon, 33 Geometric routines German, 111, 161 Goals, 166 Grammatical uses of prepositions, 6-7 Gravity, 9, 54, 56, 58, 92, 107, 151–152 Grazing line, 49, 101 Ground, 10 Guugu Yimithirr, 161 Hippocampus, 171 Human motion, 65 Ideal meanings, 24–28 Image schemata, 30–33, 154 Imagery, see Mental imagery Implication hierarchy, 159 Instance links, 32 In, 4, 6, 8, 10, 12, 15–18, 21–22, 26–28, 37 –41, 45, 47, 51–54, 56–63, 67–70, 73–84, 88–89, 113, 118, 135, 141– 142, 144–145, 153, 155–156, 172, 174

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Page 199 In front of , 10, 59, 69, 92, 95, 101–102, 111–113, 153, 156 Into , 4, 63 Inside , 44, 166 Japanese, 159, 162 Kinematics, 40, 65–67, 69 Korean, 158–159, 162 Landmark, 10 Language acquisition, 57, 147 nouns, 154–155 prepositions, 57, 153–157 Language of thought, 29 Language production, 155–157 Large-scale space, 162 Left, see to the left of Linguistic relativity, 161–164 Local uses of prepositions, 6–7 Located object, definition of, 10 Location control, 13, 51–53, 57, 59–60, 67, 74–80, 84–89, 121–123, 135, 137, 144, 156 Locative adverbs, 11 Locative prepositions, 8, 10 Maze game descriptions, 132–134 Meaning chain analyses, 32 Memory, 162–163 Mental imagery, 28, 65, 69, 134 Mental maps Mental models, 67, 95, 112, 128–134, see also situation models Meshing, 143, 167, 176 Metaphor, 5, 11, 13, 28, 172–174 Metonymy, 28 Minimal versus full specification of lexical entries, 12, 24, 32–33, 35, 128 Motor planning, 63–64, 69 Multi-dimensional scaling, 48, 144 Naïve physics, 103 Neuropsychology, 13, 62–63, 68, 163, 167, 170–172 Non-literal language, see Metaphor Near, 8, 61, 113–119, 123, 136, 145, 156, 172 Next to, 153 Normal situation types, 24 North, 9, 93 Nouns, 6 Object knowledge, 59–62, 80–83, 88–89, 109–113, 135–136 Object permanence, 148–149 Object recognition, 63, 168 Of, 6 On , 4, 6, 8, 11, 18–23, 26–28, 37, 47, 52–54, 56, 58–59, 61–63, 66–67, 69–70, 73, 84–88, 113, 118, 135, 144– 145, 153, 155–156, 172, 174 Opposite, 156 Out , 4 Outside, 44 Over, 5, 10–11, 21–22, 28–33, 37, 47–48, 58, 64, 69–70, 100, 103–109, 111–112, 136, 138–141, 144–145, 153, 160, 172 Particles, 11 Perceptual symbol systems, 166–170 Perspectives, 92, see also Reference frames Point of view, see Reference frames Polish, 62, 82 Polysemy, 4–5, 12, 30–33, 48 Positron emission tomography (PET), 63, 171 Pragmatic ‘‘near” principles, 24, 26, 28 Preferential looking paradigm, 148, 151, 158 Prelinguistic spatial concepts, 13, 57, 62, 147–153, 164 causality, 149–150 containment, 150–151 gravity, 151–152 object function, 152–153 object permanence, 148–149 support, 151–162

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Page 200 Primary object, 10 Priming paradigm, 99 Principle of canonical orientation, 95 Projective prepositions, 7–8, 13, 58, 91–112, 127, 143 Proximal orientation, 49, 101, 138 Proximity prepositions, 7–8, 13, 113–124, 127, 143 Prototypes, 29–30, 32, 34, 48, 64, 144, 160 Qualia structure, 137 Qualitative calculi, 40, 43, see also Region connection calculus Quantifiers, 175–176 Reference frames, 8–10, 56, 91–100, 106–109, 161–162 activation and assignment, 91, 97–100 classification of, 8–10, 92–96 cross-linguistic differences, 161–162 specific absolute, 8–9, 91–100, 106–107, 109 deictic, 8–9, see also Reference frames, specific, relative environment-centred, 8–9, see also Reference frames, specific, relative intrinsic, 8–9, 91–100, 106–107, 109 object-centred, 8–9, see also Reference frames, specific, intrinsic relative, 8–9, 91–100, 106–107, 109 viewer-centred, 8, 91, see also Reference frames, specific, relative Reference object, definition of, 10 Region Connection Calculus (RCC), 38, 40–43, 68, 79–80 Relational prepositions, 8, 10 Relativity, see Linguistic relativity Relevance, 23–24, 26 Representational momentum, 66 Right, see to the right of Routines, see visual routines Salience, 24, 26 Sapir-Whorf hypothesis, see Linguistic relativity Satellite-frames languages, 11, 158 Scale, 114, 117–118, 136 Schematisation, 61 Secondary object, 10 “Semantic” versus “pragmatic” representations, 64 Sense shifts, 26 Shape, 154 Similarity links, 32 Simulators/simulations, 166 Situation models, 13, 114, 123, 127–134, 140, 143–144, 146, 165–167 Small-scale space, 162 South, 9 Spanish, 4, 11, 158–161 Spatial indexing, 47 Spatial inference, 55–56, 112, 129 Spatial metaphors, see Metaphor Spatial representation (SR), 137, 162–163 Spatial templates, 12, 39, 46–49, 128 Structure mapping principle, 96 Support, 4, 20, 151–152 Symbol grounding problem, 5, 30, 34 Syntactic boundaries, 10–11 Temporal prepositions/expressions, 5, 10, 30 Theme object, 10 Thinking for speaking hypothesis, 162 To , 8 To the left of, 3, 8, 10, 48, 93–94, 97, 102, 153 To the right of , 3, 8, 9, 48, 93–94, 97, 153 Tolerance, 24, 26, 43 Topological prepositions, 7, 8, 13, 73–89, 123, 127 Trajector, 10 Transitivity, 20–21, 43, 55, 94

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Page 201 Transformation links, 32 Truth conditions, 12 Typicality, 24, 26 Tzeltal, 9, 10, 162

Under , 16, 103–109, 136, 145, 153, 160, 172–173 Up, 3 Use types, 24–28, 119–120 Vectors, 49 Ventral pathway, 62 Verbs, 10-11 Visual routines, 39, 43–45, 48, 59, 67, 158, 168 “What” and ‘‘where” systems, 6, 35, 55, 62–64, 68–69, 148, 168

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