JOURNAL OF S EMANTICS AN INTERNATIONAL j OURNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE MANAGING EDITOR: REVIEW EDITOR:
PET ER BoscH (IBM Germany) BART GEuRTS (Univ. ofTilburg)
ASSI STAN T EDITOR: T1BORK1ss(IBMGermany) EDITORIAL BOARD:
PET ER BoscH (IBM Germany) SIMON C. GARROD (Univ. of Glasgow) BART GEURTS (Univ. ofTilburg) PAUL
H oP P ER ( Carnegie Mellon Univ., Pirrsburgh)
LAURENCE R. H oRN (Yale Universiry) STEPHEN ISARD (Univ. of Edinburgh)
HANS KAMP (Univ. o f Srurtgarr) LEO G. M. NooRDMANN (Univ. ofTilburg)
Ros A. VAN DER SANDT (Univ. ofNijmegen) PIETER A. M. SEUREN (Univ. of Nijmegen)
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D. WILSON (Univ. College, London).
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JOURNAL OF SEMANTICS Volume 9 Number 3
SPECIAL ISSUE: PRESUPPOSITION PARTr
Guest Editors: Rob A. van der Sandt, Henk Zeevat
C ONTENTS HENK ZEEVAT AND RoB vAN DER SANDT EDITORIAL INTRODUCTION
I
79
IRENE HEIM
Presupposition Projection and the Semantics of Attitude Verbs ROBERT E. MERCER Default Logic: Towards a Common Logical Semantics for Presupposition and Entailment
ALLAN RAM sAv
Presuppositions and WH-Clauses
18 3
223
journal
© N.I.S.
Foundation ( 1992)
Editorial Introduction
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This is the first special issue at the Journal ofSemantics on presupposition. Most of the contributions in chis and the following issue derive from a presupposi tion workshop organized within the DANDY project (Esprit Working Group 3 3 1 s on Dialogue and Discourse). The workshop was motivated by a desire to bring together some recent developments in presupposition theory and artificial intelligence. Presupposition has been a major theme in semantic theorizing since its original introduction by Frege and its subsequent revival by Strawson. Until recently, two ways of thinking were dominant. Some authors took presupposi tion to be a logical notion. Presuppositions were taken to be chose inferences which survive under negation, a property which had to be explained in terms of truth and entailment. Since such a notion of presupposition resists treatment by means of classical two-valued logic, it was assumed that the mere existence of presuppositions forced us to adopt some non-classical logic in order to give an adequate semantics for natural language. Others, inspired by Grice's work, took presupposition to be a wholly pragmaric notion. On this view no deviation from classical logic was called for. Conversational principles and contextual information were supposed to determine the erratic behaviour of presuppositions in various contexts. One of the most extreme consequences drawn was that the notion of presupposition could be eliminated altogether. Presuppositional inferences were taken to be special cases of conversation implicatures. Gricean maxims and contextual information thus had to bear the explanatory burden. When it was noted chat presuppositions behave in a non-standard way not only under negation, but behave in a similarly problematic way under ocher embeddings, the focus of research changed. Most of the reserach in presupposi tion theory centred around the so-called projection problem: what happens to presupposition requirements when their triggers are embedded in various non entailing environments? In the 1970s this resulted in the emergence of several theories of presupposition projection. Karttunen developed a theory which was based on the notion of contextual satisfaction. Gazdar presented his cancella tion account. Retrospectively Karttunen's theory can be seen as a precursor to current dynamic accounts, while Gazdar's system can be seen as a precursor to approaches which handle pragmatic phenomena in terms of default inheritance and non-monotonic logics. Various theoretical developments in the 1980s gave a new impetus to presupposition theory. One of these was the development of various theories of discourse representation and ocher dynamic approaches to natural language
180
Editorial Introduction
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semantics. The other was the trend in computational linguistics and artificial intelligence to handle certain pragmatic processes which seemed to elude logical treatment up to then by means of non-monotonic inference systems. Three streams of new developments around presupposition deserve special mention. The first of these is the discovery of certain similarities between the treatment of anaphoric pronouns and presuppositional phenomena. Though it muse be admitted chat an awareness of these similarities is present both in Kartrunen's work (there are strong relations between his work on presupposi tion and his pioneering studies on discourse referents) and in its further devel opment by Heim, arguments for the superiority of an anaphoric analysis appear later. Kripke(as reported by Soames) noted chat presuppositional elements like 'too', 'again', or 'stop' may be in some way anaphorically related co other ele ments in discourse. A technical argumentation that nearly any presupposition inducer can be treated as an anaphoric expression is found in van der Sandt, who also provides an integrated treatment of presupposition and anaphora in discourse representation theory. The second stream consists of more computational work done around presuppositions. Though we found it hard to lay our hands on speakers having running systems, che phenomenon of presupposition (like other pragmatic forms of inference) is considered co be a frontier in computational linguistics. Integration of presuppositions promises to be of practical importance in interfaces co computer applications carrying out certain casks, as task preconditions naturally correspond with che linguistic notion of presupposi tion. They are also expected to play a role in human computer interaction where they can be used to diagnose communication failure by mismatch of shared presuppositions. The third stream brings together che logical analysis of defaults, the phenomenon known as presupposition cancellation, and that of 'global' accommodation, which turns out co be a default strategy as well. This rapproche ment is part of a growing number of applications of non-monotonic systems co linguistic phenomena, like tense, discourse structure, genericity, and others. The contributions in chis first part of che special issue in some ways each represent one of these streams. Heim's paper addresses the much neglected problem of presupposition projection in attitude contexts. The point of departure is her previous reinterpretation of Karccunen's theory. According co chis theory presupposi tions can be conceived of as definedness conditions, i.e. they determine to which contexts the context change potential of their triggering sentence can be applied. She chen explains Karttunen's intuition chat presuppositional con structions in various specialized attitude contexts trigger presuppositions in the beliefs of the subject of che attitude. The account of presuppositional behaviour in attitude contexts is a rather radical elaboration of Stalnaker's ideas. It is
Henk Zeevat and Rob van der Sandt 181
HENKZEEVAT
ROB VAN DER SANDT
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shown that much can be achieved in a possible world framework that has been suggested not to be amenable to analyses of this type. Mercer defends the inferential view on presupposition. He takes Gazdar's idea that presupposition projection should be handled by some kind of 'cancellation' mechanism as his starting point, but develops this idea along rather different lines. Instead of viewing presuppositions as some kind of content that may or may not be defeated by conflicting pragmatic information, he develops the idea that presupposition is some kind of non-monotonic inference to be treated in a suitable kind of default logic. The logic taken as starting point is Reiter's default logic. One of the basic claims is that once we expand our notion of logical inference to include non-monotonic ones, certain parts of pragmatics can be directly integrated in the logical paradigm. Ramsay's paper is directed towards the computational problem of how to integrate the syntax and semantics of presuppositions in a single formal framework. In order to achieve this goal he introduces a very powerful higher order language, which serves as the language of semantic interpretation. The theory is based on the assumption that meaning should be conceived of as a relation between information states. Presuppositions act as constraints on the situations in which the content part of the formula can be interpreted. The main part of the paper is devoted to an analysis of different WH-constructions showing that these can be treated by a simpler syntax than is commonly employed.
© N.l.S. Foundation (1992)
journal ofSemantics 9: 1X3-22 1
Presupposition Projection and the Semantics of Attitude Verbs IRENE HElM
MIT
Abstract
representative instances of this generalization from suitable assumptions about the lexical
semantics of attitude predicates. The enterprise is carried out in a framework of context change semantics, which incorporates Stalnaker's suggestion that presupposition projection results from the stepwise fashion in which information is updated in response to complex utterances. The empirical focus is on predicates of desire and on the contribution of counterfactual mood.
I I NTR ODUC T I O N How are presuppositions projected in propositional attitude sentences? For example, given that Patrick sells his cello presupposes that Patrick owns a cello, what does (I) presuppose? (I) Patrick wants to sell his cello. At first sight, (I) likewise seems to presuppose that Patrick owns a cello. But then, it can also appear without contradiction in the context of(2). (2) Patrick is under the misconception that he owns a cello, and he wants to sell his cello. Karttunen (I973b, I974) concludes that {I) presupposes, not that Patrick owns a cello, but rather that Patrick believes he owns a cello. This projection behavior is not peculiar to the verb want , but generalizes, according to Karttunen, to all other non-factive verbs of propositional attitude. (He cites believe , think , expect , fear, intend, suspect , assume, and hope as further examples ( 1 973b: 4). Explicitly excluded, beside factives, are verbs of saying.) They are all subject to the following rule (his (2 1 ) ( 1 974: 1 89) with trivial changes). (3) If a is a verb of propositional attitude, then a context c satisfies the presuppositions of 'aaj> ' only if Ba(c) satisfies the presuppositions of � ; where 'Ba(c)' stands for the set of beliefs attributed to a in c.
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Karttunen observed that, if the complement of an attitude sentence presupposes p, then that
sentence as a whole presupposes that the attitude-holder believes p. I attempt to derive some
Ill4
Presupposition Projection and the Semantics of Attitude Verbs
Together with the rule for and ( 1 974: 1 8 5):
(4) Context c satisfies the presuppositions of'¢ and tp' just in case
(i) c satisfies the presuppositions of¢ , and (ii) the context that results from c by the assertion of ¢ satisfies the presuppositions of tp.
some additional conversational principle to the effect that, unless it has been indicated otherwise, [Patrick] can be assumed to share the speaker's beliefs. In other words, there is a natural spill-over from [c] to [BPatrick(c)]. Consequently, in situations where nothing has been said about[Patrick's] beliefs, one tends to think that, if the presuppositions of[( I)] are satisfied, they are satisfied by virtue of the speaker's tacit assumption that [Patrick] shares his beliefs. (t973b: 6)
I think that Karttunen's proposal was basically right, in its description of the facts as well as in its theoretical conception. 1 In fact, the present article does nothing more than spell it out in somewhat greater precision. This should make it easier to assess its merits and the objections against it. Section 2 introduces the theoretical framework. Sections 3 and 4 examine the semantics ofverbs of belief and of various types of desire verbs in reports of realistic as well as counter factual desires. Section s elaborates a bit more on the reasons why attitude verbs should superficially appear to be holes rather than filters. In the examples below, I will use a variety of presupposition triggers, in particular definite descriptions (to which I here give a classical, Fregean, analysis) and too. I assume, perhaps simplistically, that for the purposes of this paper there is no relevant difference between the various kinds of triggers. I have nothing original to say about where presuppositions come from in the first place, what the set of triggers is, and what presupposition exactly each trigger contributes.
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(3) accounts for the intuition that (2) as a whole presupposes nothing. To presuppose nothing means to place no particular requirements on the initial context; in other words, a sentence presupposes nothing iff every possible context satisfies its presuppositions. Given (3) and (4), this is predicted for (2): whatever the initial context may have been like, the first conjunct creates from it an intermediate context in which Patrick is attributed the belief that he owns a cello, and that intermediate context thus satisfies the presuppositions of the second conjunct. But what about the intuition that ( 1 ) in isolation commits the speaker to Patrick's owning a cello? Karttunen speculates that this is attributable to
2
P RE S U PP O S I T I O N P R OJE C T I O N I N C O N TE XT C H A N GE SEMA N T I C S
(s) For any context c, c + it is raining - (w E c: it is raining in w}.
The CCPs of complex sentences are determined compositionally on the basis of the CCPs of their pares, so for cruchfunctional connectives, for instance, we have semantic rules like the following (where \ is set-theoretic complementation). (6) c +not¢ = c\(c + ¢).
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The framework I will employ, basically a radical elaboration of ideas of Robert Stalnaker, is characterized by four central assumptions.2 First, the meaning of a sentence is its context change potential (CCP). (By 'sentence', I mean not j ust a string of words, but a full structural description at the level of Logical Form (LF).)3 A CCP is a function from contexts to contexts. Contexts are here identified with states of information, which in turn are construed as sets of possible worlds,4 and the change effected by the CCP of a sentence consists of updating that information by what the sentence says. Second, not only complete (matrix) sentences have context change potentials, but so do embedded sentences down to atomic clauses, and the CCPs of complex sentences are compositionally determined by the CCPs of their constituents. Third, the presuppositions of a sentence are requirements on the context, that is, they determine which contexts its CCP can be applied to. Whenever a sentence presupposes something, it must be evaluated in a context chat already entails chat presupposition.5 These requirements are uncancellable; under certain conditions, a context may be fixed up to meet them, but never the other way round, i.e. never is the requirement waived or weakened to make it more easily met by a given context.6 Fourth (as a consequence of the previous three assumptions, and as already urged by Stalnaker ( 1 97 3, 1 974) and Karccunen ( 1974) ), the phenomena of so-called presupposition projection are just a by product of the way the CCP of a complex sentence is composed from the CCPs of its pares. Let me illustrate chis with concrete examples and at the same time make it a bit more precise. Suppose (unrealistically) we start with the 'empry'7 context, where nothing is presupposed yet. This is W, the set of all possible worlds. Imagine chat in this context W, there occurs a (successful) assertion of the atomic sentence it is raining . The result will be a new context, a subset of W, which contains just those worlds where it is raining. More generally, the CCP of it is raining is the instruction to conjoin (that is: intersect) whatever the current context may be with the proposition chat it is raining. I use the notation 'c + ¢' co designate the result of executing the CCP ofLF¢ on the context c.8 The CCP of(che LF of) it is raining can thus be defined as in (s).
1 86
Presupposition Projection and the Semantics of Attitude Verbs
(7) c +John's cat is hungry is defined iff c � {w: John has a unique cat in w}; where defined, c +John's cat is hungry = (w E c: John has a hungry cat in w} 'Presupposition projection', according to this theory, arises from the way the definedness conditions of the CCPs of elementary sentences affect those of the CCPs of bigger constituents. For instance, (6) is really an abbreviated version of the following more explicit rule: (8) c + not rj> is defined j ust in case c + rj> is, in which case c + not rj> c\(c + rj> ). -
and so the combined effect of (7) and (8) is to predict that not Uohn's cat is hungry] (presumably one of the Logical Forms of John's cat isn't hungry) also presupposes that John has a unique cat. More generally, (8) predicts negation to be a 'hole' in the sense ofKarttunen ( 1 973a). Notice that the spelled-out rule in (8) is, in a sense, fully recoverable from the abbreviated version of (6):9 the added top line states j ust what it takes for the expression to the right of the equation sign below to denote a context-no more and no less. This is always so when we are dealing with the lexical entry of an item (such as here not) that doesn't contribute any presuppositions of its own. Only items that are themselves presupposition-triggers have in their entries additional, non-recoverable, defmedness conditions. The fuller rule format of (8), while more explicit and therefore easier to use in proofs, has the dis advantage of superficially obscuring the difference. Below I will often use a compromise between the two formats: include the recoverable conditions, but in brackets.
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If you apply the CCP of not [it is raining ] (the LF of it isn't raining ) to W, what you get by (6) and (s) is the set of all worlds in which it isn't raining. Actually, things are a bit more complicated, since so far we have disregarded presuppositions (taking it is raining , simplifying perhaps, to be an example of a sentence that presupposes nothing). The definition of the CCP of a sentence is supposed to encode not just its content but also its presupposition. The CCP of a sentence without any presupposition will be a total function from contexts to contexts (like the one defined in (s) ), but in general CCPs are partial: they are defined only for those contexts that satisfY the presuppositions of the sentence in question. For example, John's cat is hungry presupposes that John has a unique cat, and this is reflected in the fact that the CCP of this sentence is only defined for contexts that entail that John has a unique cat. (The entailment relation between contexts is the subset relation.)
Irene Heim 187
3
BEL I E F REPORTS
Now what would it mean to give an account within this framework of presupposition projection in attitude reports? Well, the central task is evidently to specify appropriate lexical entries for the attitude predicates, i.e. to give appropriate definitions of the CCPs of sentences of the form 'a believes¢>', 'a wants ¢> , etc. Once these CCPs are defined, the projection behavior of presuppositions originating with the complement sentence ¢> is thereby determined. So what we must do is write definitions of the form (9). '
�
.
.
.
Let us begin by recapitulating the standard possible worlds semantics of believe , as found, e.g., in Hintikka ( 1 969). A sentence like ( w) ( 1 0) John believes that it is raining. is true in a world w iff it is raining in every world w' that is doxastically accessible forJohn to w. What does 'doxastically accessible' mean? It means this: world w' is doxastically accessible for person x to world w iff w' is compatible with the beliefs that x holds in w. This familiar analysis is our starting point, and we now try to recast it faithfully in our context-change framework. First, a technical convenience: accessibility relations(binary relations among possible worlds) correspond one-to-one to accessibility assignments(functions from worlds to sets of worlds): 10 ( 1 1 ) Let R � W X W. Then fR is chat function from W to g;(W) such that, for any w E W, fR(w) = {w' E W: wRw'}. For instance, to the relation of doxastic accessibility for John corresponds the following functionDox1 ('Dox' for 'doxastic' and T for John'):
( 1 2) For any w W, e
Dox1(w) = [w' E W: w' conforms co what John believes in w}.
The choice, has, of course, no substantive import, but we will save space in our CCP-definitions below by directly referring to these accessibility functions instead of the corresponding accessibility relations. Notice that the values of. accessibility functions are the same kind of thing as contexts, namely sets of possible worlds, and as such are suitable arguments for the CCPs of sentences a fact that will be exploited in our rules below. So how does the assertion of a belief-sentence like ( w) affect the context? What information does it convey, what possibilities does it rule out? According
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(9) For any context c, c + a believes¢> is defined only if. . . Where defined, c + a believes¢>
188 Presupposition Projection and the Semanrics of Attitude Verbs
to the standard analysis just sketched,(Io) tells us about the world we are in that it is a world accessible from which (more precisely: doxastically accessible for John from which) are only worlds in which it is raining. In other words, ( 1 0) informs us that we are in a world w such that it rains in every element of Doxj(w). So the CCP of ( 1 0) has to be an instruction to eliminate from the original context all but the worlds which fulfill this condition on w. It must be this: (I 3) For any c, c +John believes it is raining =(w E c: for every w' E Dox1(w), it is raining in w').
( 1 4) For any set X � W: it is raining in every w' E X iff X + it is raining =X. In other words, the sets of worlds throughout which it is raining are precisely those that map onto themselves under the CCP of it is raining . Why? Because if it is already raining in every element of a set of worlds X, then eliminating from X any non-rain-worlds won't change ic Whereas, if a set does become genuinely smaller by eliminating non-rain-worlds from it, then it must be a set which didn't already have rain throughout. Thus (I 3) becomes (Is). ( I s) For any c, c +john believes it is raining =(w E c:Dox_,(w) + it is raining Doxj(w)). =
From this it is easy to generalize to arbitrary complements(and subjects):11 (I6) For any c, c +a believes¢ =(w E c:Doxa(w) + ¢ =Doxa(w)) The general format of this rule will recur elsewhere, �nd it will be more transparent if we use an abbreviation: if c is any context, ¢ any LF, let 'c +¢ =same' express the condition that c + ¢ =c. So we can render (I6) as (I7).
(I7) For any c, c +a believes¢ =(w E c:Doxa(w) + ¢ =same).
For arbitrary choices of¢, of course, we can no longer take the well-definedness of'Doxa(w) + ¢'for granted. For certain choices of rj>, a and w it might happen that Doxa(w) is not in the domain of the CCP of ¢. In other words, (I7) implicitly contains a definedness condition that is brought out into the open in the following fuller rendition:
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Now we must figure out how this CCP is determined compositionally, by the interaction of a general rule for structures of the form 'a believesrj>' on the one hand and the CCP of the complement it is raining on the other. A first step towards isolating the contribution of each is to express the condition that it rains throughoutDox1(w) in terms which make explicit reference to the CCP of it is raining. It turns out (given (s) above) that the following equivalence holds:
Irene Heim 189
(I 8) For any context c,
[c + a believes � is defined iffDoxa(w) + � is defined for each w e c]. Where defined, c + a believes � ={w e c:Doxa(w) + � = same].
( 19) John believes that Mary is here, and he believes that Susan is here too. Before we can get started, I must fill in a brief sketch of my treatment of too. Relying on Kripke,12 I assume that too is implicitly deictic or anaphoric, sort of like in addition to x, where the intended reference of x is disambiguated at Logical Form by means of a referential index. In the salient construal of ( I 9), for instance, too means 'in addition to Mary' and is therefore coindexed with Mary in the preceding clause. Also, too associates with focus, and this too is represented at LF, by means of the customary subscripted 'F'.O So the LF of(19), under the reading we want to consider, is (2o). (2o) John believes that Mary1 is here, and he believes that SusanF is here too1• The general rule for the interpretation of too is (21).
(21 ) ¢[a ] tooi presupposes Xj ¥a F
&
�[xi] ·
Transposed into the context change framework and applied to the example at hand, this amounts to (22). (22) For any c, c + SusanF is here too1 is defined iff Mary is here in every world in c. Where defined, c + Susan F is here too1 ={we c: Susan is here in w}.
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Now our first proposal is in place and we can look at its predictions about presupposition projection. If the complement � in (1 8) has non-trivial presuppositions, i.e. a genuinely partial CCP, then what does this imply for the CCP of a believes¢ ? The answer can be read right off ( 18): if the CCP of ¢ makes non-trivial demands on its input context, then so does the CCP of a believes � . If the CCP of � is defined only for contexts that entail a certain proposition p, then the CCP of a believes � is defined only for those c all of whose elements w map onto Doxa(w) that entail p. Only for those c, in other words, which entail that a believes p. (Recall the definition in (12): 'Doxa(w) entails p' means nothing more and nothing less than that a believes p in w.) What we predict, then, is simply (a special case of ) Karttunen's generaliza tion: if¢ presupposes p, then a believes� presupposes that a believes p. We rhus expect to be able to account at least for the data that most directly supported Karttunen's view, e.g. the fact that a sequence of two belief reports in which the content of the complement of the first entails the presupposition of the complement of the second makes a smooth discourse with no presuppositions as a whole. Let us calculate through an example of this kind to see exactly how this works.
1 90
Presupposition Projection and the Semantics of Attirude Verbs
The rule for the connective and, of course, is(23)(c£ Karttunen's(4) above). (23) (c + ¢ and tp is defined iff c + ¢ and(c + ¢) + tp are defined.] Where defined, c + ¢ and tp = (c + ¢) + tp .
(24) c' := c +john believes Mary, is here {w E c: Mary is here in all w' E Doxj(w)) We have left to show that c' + he believes Susanp is here too1 is defined. By rule (I 8) this is so iffDox1(w) + Susan F is here too1 is defined for every w E c'. Let w be an arbitrary w E c'. It follows by (24) that Mary is here in all w' E Doxj(w). According to(22), this in turn guarantees the definedness ofDox1(w) + Susanp is here too1• End of proo£ This calculation should have made clear just how the utterance of the first conjunct of (2o) is responsible for the fact that the second conjunct's presuppositional requirement is satisfied by the intermediate context against which it is evaluated. (And mind you, it is satisfied , not cancelled , even though it superficially may appear so!) For a contrasting case, where presupposition filtering does not occur and in fact the discourse is deviant, consider(2s). 1 4 (25) John doubts that Mary1 is here and/but believes that SusanF is here too1. That(25) doesn't make sense is predicted if we assume that doubt means(or at least implies) something like not believe. After the first conjunct in(25), we then have a context for all whose elements w Dox1 (w) fails to entail Mary's being here. So not only isDoxj(w) + Susan is here too1 not guaranteed for every such w to be defined, it is actually guaranteed to be undefined for all of them. 15 I don't mean to suggest that the present analysis is unique in providing an account of the unacceptability of(2s). The same prediction is made by anyone who assumes every presupposition to be also an entailment of the minimal sentence that carries it.16 Given this assumption, the two conjuncts of (25) simply have incompatible contents, and this suffices to explain the deviance.
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What we want to show is that(2o) as a whole presupposes nothing. This means that any context (even the completely information-less W) is in the domain of the CCP of (2o). So what we have to show is that c + (2o) is always defined, regardless of any special properties of c. Here is the proof Let c be an arbitrary context �W. By rule(23), c + (2o) is defined just in case both c + John believes Mary, is here and (c + john believes Mary, is here) + he believes Susanp is here too1 are. We first show that c + john believes Mary, is here is defined. This follows trivially by rule (I 4) from the fact that Mary, is here has no presuppositions, i.e. a CCP that is always detlned. We also know from rule (I 8) what c + John believes Mary, is here (henceforth abbreviated as c') is, namely:
Irene Heim I 9 I
Notice, however, that this simpler explanation doesn't generalize to slightly more complex examples like (26). (26) John doubts that Mary1 is here. He believes that if SusanF were here too1 there would be dancing.
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This use of too is likewise deviant, but the content of complement of the second sentence, viz. that there would be dancing if both Mary and Susan were here, is not at all incompatible with Mary's being absent. The present analysis covers this case along with (25) (provided that the conditional inherits the pre supposition of its antecedent, as standardly assumed; see below). The reader may have been wondering how our rule (I8) relates to Karttunen's rule (3), which I cited in the introduction. There is an obvious respect in which(3) says less than (I8)(and in which all of Karttunen's rules say less than ours):(3) does not tell us what the outcome of incrementing a context by a believes � is; it merely states the prerequisites of the incrementation operation. So it could at best be equivalent to the first half of (I8), the definedness conditions(the part in brackets). But is it equivalent even to that? There is a superficial discrepancy: ( I 8) requires the CCP of� to be defined for each of a set of contexts, namely all theDoxa(w) for each w e c, whereas(3), in effect, requires it to be defined for the single context Ba(c). What is the relation between Karttunen's Ba and our Doxa? Karttunen defines Ba(c) as the set of beliefs attributed to a in c. So, construed as a set of propositions, Ba(c) - {p � W: c entails that a believes p}, or more explicitly: Ba(c) - {p � W: Vw e c: a believes p in w}. Rewriting this in terms of the doxastic accessibility function: Ba(c)- {p � W: Vw e c: Doxa(w) � p}. Now if we form the set of worlds in which all the propositions in this set are true, what we get is U wecDoxa(w). In other words (abstracting away from extrinsic differences): whereas I required the CCP of � to be defined for each Doxa (w) for w e c, Karttunen required it to be defined for the union of them all. But to the extent that definedness of the CCP of � for a context is a matter of that context entailing a certain proposition(as in the cases of interest, where� has a purely presuppositional CCP),17 then the two requirements obviously come to the same thing: a proposition is entailed by each element of a set iff it is entailed by its union. So my proposal is not in conflict with Karttunen's, but can be seen as an elaboration of it.18 Thus far, we are following in Karttunen's footsteps and, indeed, if we restrict our attention to verbs of belief, our predictions fully mirror his. But differences show up when we extend the same treatment to other attitudes, say to the desire verb want . According to the standard Hintikka-sryle analysis we took as a starting point, the rule for want should look just like that for believe, except with a different accessibility relation substituted. Here it is buletic accessibility
192 Presupposition Projection and the Semantics of Attitude Verbs
that is relevant, so the pertinent accessibility function is Buli w - {w' E W: w' conforms to what John wants in w). (27) [c + a wants¢ is defined iff Bula(w) + ¢ is defined for each w E c.] Where defined, c + a wants¢ ={w E c: Bula(w) + ¢ =same). The predictions implied by (27) diverge from Karttunen's in two ways, one good and one bad. First, the good news. (27) predicts correctly what happens in sequences of two desire reports, like (28) or(29) below.
In these examples, the presupposition originating with the last complement clause also gets 'filtered out': they are felicitous and require no initial presup positions. (28) makes sense without committing the speaker to the assumption that Patrick believes he has or will ever have a cello, and (29) also doesn't presuppose that John believes Fred will come. 19 Karttunen's rule (3) fails to account for this, but (27) predicts it straightforwardly. In fact, (27) derives the following generalization: if¢ presupposes p, then a wants¢ presupposes that a wants p. This is a welcome result for want-want sequences, but-and here comes the down side-it is not suited to capture the analogous filtering effect in believe-want sequences like our initial example (2) or(3o) below. (3o) John believes that Mary 1 is coming, and he wants SusanF to come too1• These were better taken care of with Karttunen's generalization that a wants¢ presupposes that a believes p.
4
DE S IRE REP ORTS A ND C OU N TERFAC TUAL I TY
We just saw that the straightforward treatment of desire predicates in (27) fails to account for the ease with which a preceding belief-report can help satisfy the presuppositional requirement of the want-complement, as in (2) and(3o). The problem is that the sets Doxa(w) and Bula(w) (for a given w) may in principle stand in any relation whatsoever, i.e. they may be mutually disjoint, they may overlap, one may be a subset of the other, or vice versa. After all, which worlds I deem desirable has nothing to do with which I consider candidates for actuality. So there is no way we can be sure, e.g., in the evaluation of(30), that just because all of John's belief-worlds have Mary corning in them, this should also be so in all his desire-worlds. Now it is no news to anybody who has thought about the semantics of want-
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(28) Patrick and Ann both dream of winning cellos. Ann would like one for her own use. Patrick wants to sell his cello for a profit. (29) John wants Fred1 to come, and he wants JimF to come too1•
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4.1 A
conditional semanticsfor desire verbs
The analysis of desire verbs I want to pursue here is sketched in Stalnaker ( 1 984: 89): 'wanting something is preferring it to certain relevant alternatives, the relevant alternatives being those possibilities that the agent believes will be realized if he does not get what he wants.' An important feature of this analysis is that it sees a hidden conditional in every desire report. A little more explicitly, the leading intuition is thatJohn wants you to leave means thatJohn thinks that if you leave he will be in a more desirable world than if you don't leave. The main task in implementing this idea is to spell out the conditionals in the above paraphrase. For this I employ a version of the semantics that Lewis ( 1 97 3) proposed for counterfactual conditionals and Stalnaker ( 1 968) for conditionals in general.2° The key concept here is that of comparative similarity among worlds, and the basic idea is that a conditional if�, tp is true in a world w iff tp is true in all �-worlds maximally similar to w. (By a ·�-world maximally similar to w', we mean a world in which � is true and which resembles w no less than any other world where� is true.) The meaning of want , as indicated by the paraphrase above, can now be described as follows: (3 1) 'a wants � ' is true in w iff for every w' E Doxa(w): every �-world maximally similar to w' is more desirable to a in w than any non--¢-world maximally similar to w'. (3 1 ) instructs us, for every belief-world, to compare the set of its closest � alternatives to the set of its closest non--¢-alternatives. In effect, however, one of these two sets of'alternatives' will always be the singleton ofjust w' itself if� is true in w', it is the former set, otherwise the latter. So another way of stating these cruthconditions is in the following disjunctive form: For every belief
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sentences that the primitive treatment in (27) has other defects as well (see below for examples). So it may be a good idea to cast around in the literature for a more sophisticted semantic analysis and then see if that perhaps helps with the presupposition projection facts. This is what I have tried to do. In the i deal case, there would have been some independently motivated analysis out there that only needed to be routinely transposed into the context change framework and then would have automatically gotten the projection facts right. Unfortunately, that wasn't quite what I found. But by combining insights from various sources, I have come up with something that does, I hope, throw some light on what the projection behavior of desire verbs has to do with their truthconditional semantics, even though not all the choices I had to make were determined by independent evidence.
194 Presupposition Projection and the Semantics of Attitude Verbs
(32) (a) Nicholas wants a free trip on the Concorde. (b) Nicholas wants a trip on the Concorde. The prediction of our rule (31) conforms to Asher's intuition: (32b) is false because many of Nicholas's doxastic alternatives in which he flies on the Concorde (in fact, all to which he assigns a high degree of subjective probability) are such that he flies for $J,ooo there and is therefore worse off than in minimally differing worlds where he doesn't fly at all. Yet this does not prevent(J2a) from being true: those(relatively unlikely) belief-worlds where he does get a free trip are better than similar worlds where he doesn't, and the ocher (more likely) belief-worlds, where he doesn't fly, or flies and pays, are each worse than otherwise similar free-ride-worlds. Stalnaker(1984: 89) discusses a different type of counterexample to the same inference pattern: 21 'Suppose I am sick. I want to get well. But getting well entails having been sick, and I do not want to have been sick. Suppose there was a murder. I want to know who committed the murder. But my knowing who committed the murder entails that the murder was committed, and I never wanted the murder to have been committed.' These fallacious inferences, too, would have been validated by the old rule(27): ifl get well in all the worlds that conform to my desires, then I have been sick in all the worlds that conform to my desires. What does the new rule (31) predict for these examples? We would like to show that it allows for the premise, I want to get well, to be true and the conclusion, I want to have been sick , to be false at the same time. Here is how this
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world w', either� is true in w' and w' is more desirable than its closest non-¢ alternatives, or else � is false in w' and w' is less desirable than its closest � alternatives. When a sentence like I want you to call me o n Monday i s used, there typically are doxastic alternatives where you do call me on Monday as well as those where you don't. For it to be true, then, each of the former must be more desirable than minimally different ones where you don't call, and each of the latter less desirable than minimally different ones where you do. Independently of my present concern with presupposition projection, what motivation is there for this semantic analysis? In what respects is it more successful than the primitive treatment in(27)? First, the new rule, unlike the old, no longer predicts that when� entails tp, a wants � therefore entails a wants tp. This is welcome in light of certain intuitively fallacious instances of this inference pattern. Here is an example I owe to Asher(1987): imagine that Nicholas is not willing to pay the $J,ooo that he believes it would cost him if he flew to Paris on the Concorde, but he would love to fly on the Concorde if he could get the trip for free. Under these circumstances (J2a) is true, yet (32b) is false, despite the fact that taking a free trip on the Concorde, of course, implies taking a trip on the Concorde.
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(33) I want to teach Tuesdays and Thursdays next semester. Suppose this sentence is intuitively true as spoken by me today. Is it therefore the case, as the old rule(27) would have it, that I teach Tuesdays and Thursdays next semester in all the worlds that are compatiblewith everything I desire? No. In worlds that are compatible with everything I desire I actually don't teach at all. But if this is so,(27) predicts {3 3) to be false, and likewise for the majority of want-sentences that we accept as true in everyday conversation. Rule (3 1 ) has no such problem: as it happens, I believe that I will teach (a regular course load) next semester. This means there are no doxastically accessible worlds in which I don't teach at all. In all doxastically accessible worlds, I either teach Tuesdays and Thursdays, or else I teach the same load on different weekdays. Among these, the former are more desirable than the latter, and this makes (33) true by (3 I ). 4.2
CCP and presupposition projection
Supposing that the analysis of desire reports in (3 1 ) is on the right track, what form will it take in context change semantics? Let me approach this question via a detour and look first at the CCP of indicative conditional statements. 4.2.1 Excursion: context change with indicative conditionals
First, a few technical devices and abbreviations. The relation of comparative similarity among worlds can be encoded by a family of selection functions; for each world w, there is a selection function Sim.v from propositions to propositions which maps each p to the set of p-worlds maximally similar tow. (34) Sim.v(p): {w' E W: w' E p and w' resembles w no less than any other world in p}
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can be. There are basically three kinds of worlds: w 1, where I am healthy all the time; w2, where I am sick first and then get well; and w3, where I am sick and stay sick. In terms of their desirability to me in the actual world w0, they are ordered as follows: w1 is better than w2, which is better than w3• My beliefs in w0 are such that I believe that I have been sick, i.e., w2, w3 E Dox1{w0) but w1 � Dox1{w0). Now in w2 I get well and the closest world where I don't is w3, which is less desirable. And in w3, I don't get well and the closest world where I do is w2, which is more desirable. Hence I want to get well is true in w0 . On the other hand, in both w2 and w3 I have been sick, but these are not better(rather: worse) than the closest world, w1, where I haven't been. So I want to have been sick is false in w0• For a related point, consider a statement like (3 3).
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In a truthconditional semantics, where each sentence� expresses a proposition [[¢] ] , the semantic rule for conditionals can now be stated as follows: E [[if� 1/J]] iff Siffiw([[�])) � [[ 1/J]]. ' When we try to transpose this into the context change framework, the main hurdle is to find a proposition that will serve as the argument for the selection function. We can't just make reference to 'the proposition expressed by �'; rather, we get a proposition only by applying the CCP of� to some argument. What should that argument be? An often voiced intuition is that it is the main context, i.e., the input context to the CCP of the whole conditional. Compare, e.g., Stalnaker ( 1 975: 276): 'when a speaker says ifA, then everything he is presupposing to hold in the actual situation is presupposed to hold in the hypothetical situation in which A is true.'22 This suggests the following CCP definition: (3 5 )
w
Suppose, for example, Mary calls us and tells us she is calling from a phone booth. So it is part of our common ground c that Mary is in the phone booth. Ifl now say Ifjohn is in the phone booth . . ., the hypothetical situations I am asking you to consider are all situations where John and Mary are in the phone booth together, as opposed to those where he is there instead of her. For instance, if I continue . then the door doesn't close , this will in effect give you information about how the size of the booth relates to the combined volume of Mary and John, and it won't tell you anything about how John's size alone relates to the booth's. This interpretation is forced even if worlds with two people in a phone booth at once are relatively far-fetched in comparison to the worlds in c; in other words, if the selection function is such that the closest worlds withJohn in the booth that it would pick out for any w e c are worlds where he is there alone. So it is not (or at least not necessarily) a property of the similarity relation that leads us to consider worlds with John added to Mary rather than worlds where he replaces her. Rather, it seems to be due to the fact that, in evaluating this conditional, the selection function must apply to a proposition that retains all the information in c along with that contributed by the antecedent. Rule (36) guarantees this. (36) also makes welcome predictions about presupposition projection in condi tionals. In particular, it directly derives the familiar generalization23 that conditionals inherit the presuppositions of their antecedents. In our terms: unless c + � is defined, c + if�, 1/J won't be either. And it also derives the fact that presuppositions of the consequent which are entailed by the antecedent get 'fil tered out'. (This is because the CCP of 1/J is applied to Siffiw(c +�) and this, by the general definition of selection functions, is a subset of c + �.) 24 .
.
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(36) c + if�, 1/J - {w E c: Siffiw(c + �) + 1/J -same)
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to want
Now we return to the analysis of want. The truthconditional-semantics version from (3 1 ) above is reformulated below: (3 7) w E [[a wants�n iff for every w' E Dox" (w), Si�.([[�]])
(38) (a) For any w, w', w" E W, ' w
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Apart from the notation employed in the previous section, this uses an abbreviation for the ranking of possible worlds in terms of desirability.
1 9� Presupposition Projection and the Semantics of Attirude Verbs
choice of c. The first part of the proof parallels the one regarding (2o) in the section on belief reports: we establish that c +John believes Mary1 is here (=: c') is well defined for all c and equals {w e c: Mary is here in all w' e Dox1(w)) (see (24) above). It remains to demonstrate the definedness of c' + he wants SusanF to be here too1• By (39), we must show that Dox1(w) + SusanF to be here too1 and Dox1(w) + not [SusanF to be here too1} are defined for all w e c', which (by the not rule (8) and the too-rule (2 1)) means that, for each w e c', Mary is here in all w' e Dox1 (w). But this we have just shown.
the context change version (39) of our analysis of want loses one of the welcome predictions of the truthconditional version in (3 1 ). Recall again Stalnaker's concern with blocking the inference from I want to get well to I want to have been sick (and from I want to know who committed the murder to I want the murder to have been committed). I showed above how (3 I ) made the premise true and the conclusion false bec;mse I believe that I have been sick. In the same scenario, (39) unforrunately predicts the conclusion to be trivially true instead of false. Ifl believe in w that I have been sick, then Dox1(w) + not [PRO to have been sick} is empry, and so is Siffiw· applied to it. Since it is trivially true that all the worlds in the empry set are worse than any others, this suffices to make the conclusion true. Stating the problem more generally, (39) predicts that, w�enever a believes� or believes not� , it trivially follows that both a wants� and wants not ¢ . A narural move to prevent these trivial truths is to make all selection functions undefined for the impossible proposition.25 In other words, amend (34) above to (4o) below. As it stands,
(4o) p is in the domain of Siffiw only if p of 0; where defined, Siffiw(p): = {w' e W: w' e p and w' resembles w no less than any other world in p) With (40), (39) implies, in effect, that want-sentences have an additional presupposition (above and beyond those projected from the complement according to Karrrunen's generalization), namely that the subject does not believe the complement nor its negation. More formally, c + a wants � will be undefined whenever Doxa(w) + � = 0 or Doxa(w) + � = Doxa(w). Regarding Stalnaker's fallacious inferences, (39) still doesn't predict the same as (3 I ). When the premise is true, (3 I ) allowed the conclusion to be downright false; (39) only allows it to be a presupposition failure. This disagrees with Stalnaker's stated judgment, but for his examples, at least, I think it is quite defensible. I want to have been sick (as well as I want not to have been sick , or its more colloquial Neg-Raising variant I don't want to have been sick) is a strange
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4.2.3 Amendments
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(4 I ) Qohn hired a babysitter because) he wants to go to the movies tonight. (42) I want this weekend to last forever. (But I know, of course, that it will be over in a few hours.) These observations are a serious threat to the present analysis, and I am persuaded at least by (4 I ) that a genuine modification is called for. To see what I have in mind, consider briefly the semantics of a related verb, intend , which displays the behavior of want in (4 I ) even more strikingly. What one intends is typically, notj ust occasionally, something that one is convinced will happen. So our rule for want, generalized as it stands to intend, would systematically predict presupposition failure for perfectly appropriate intend-sentences. But the correct rule, I think, is only a little bit different. What seems to be going on when we assess someone's intention is that we don't take into account all his beliefs, but just those that he has about matters unaffected by his own future actions. More precisely, what should take the place of Doxa in the rule for intend is the following accessibility function Fa :28 (43) For any w E W: Fa (w) = (w' E W: w' is compatible with everything that a in w believes to be the case no matter how he chooses to act} Fa(w) is always a superset ofDoxa(w). If we substitute Fa for Doxa as we adapt our want -rule (39) for intend, we no longer predictjohn intends togo to the movies to be a presupposition failure just because John is convinced he will in fact go. (We would only predict it to be inappropriate ifhe were convinced he'll go no matter how he chooses to act. This prediction seems right.) The substitution also implies different predictions for presupposition projection, in fact, a subtle departure from Karttunen's generalization. No longer do we predict that (44) presupposes just that Patrick believes he has a cello tomorrow, but that it
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sentence indeed to use for someone who takes for granted that she has been sick.26 One would much rather say I am glad that I have been sick or some such thing, with afoctive desire predicate. Stalnaker too spontaneously avoids want as he further comments on the murder-example: 'Given that there was a murder, I would rather know who committed it than not know. The question of whether or not I look withfovor on thefoct that there was a murder-whether I am glad that it happened or wish that it had not-does not arise in that context' (I 984: 89; emphases added). (This raises the question of how these other desire-predicates differ from want, which I will take up below.)27 Still, even if you agree that Stalnaker's examples are appropriately classified as infelicitous rather than false, it doesn't seem right that one can never speak of wanting things one is convinced will happen or convinced won't happen. (4 1 ), for instance, certainly does not suggest in any way that John has the slightest doubt about where he will be tonight, nor do we have difficulty making sense of utterances like (42).
2.00
Presupposition Projection and the Semantics of Attitude Verbs
presupposes, more specifically, that he believes he has a cello independently of what he does . (44) Patrick intends to sell his cello (right now).
4·3·4 Further predictions about presupposition filtering
Rule (39) captures Karttunen's generalization so 'well' that it also shares its more dubious and downright inadequate predictions. As for the latter, (39) loses the one thing that was nice about (27), namely the prediction that presup positions are filtered in want-want-sequences, such as (28) and (29) (repeated here). (29) John wants Fred 1 to come, and he wants JimF to come too 1 • Supposing that (as the felicity of the first conjunct requires, by our present analysis) the possibility of fred not coming is compatible with John's beliefs, the CCP of the second conjunct is not defined for its context. I have no solution to this important problem. All I can do is point out that under the present perspective it falls together with an analogous type of counterexample to Karttunen's generalization about conditionals.3 1 (4S) is likewise fully accept able, though predicted a presupposition failure by rule (36). (4S) If Mary1 comes, we'll have a quorum. If SusanF comes too 1 , we'll have a majority. The only way to treat this case-and thus the analogous one in (29)-that I know of is by invoking accommodation of an inexplicit restriction.32 Once this mechanism is invoked, of course, the question arises to what extent it could also have been employed to yield some of the predictions that I took pains to
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This is certainly plausible for the example at hand, and I hope that a closer look at the data will bear it out in general.29 Returning now to want and example (4 1 ), I suggest that want has a reading more or less equivalent to intend and this is what we witness here. Probably this is not really an ambiguity but indicates a broader sort of vagueness. But this question is just one of numerous loose ends that I am leaving here. What about (42)? I am even less sure how to respond to this example. One strategy might be similar to the one I just rook with (4 1 ): maybe for some reason not all the subject's beliefs are taken into account here either, but only a subset too weak to imply that Monday is right around the corner. Alternatively, (42) might be seen as reporting the attitudes of a mildly split personality.30 The reasonable part of me knows and is resigned to the fact that rime passes, but the primitive creature of passion has lost sight of it. Another loose end.
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make follow directly from the CCP definitions.33 A serious exploration of this alternative must await another occasion. Another prediction shared with Karttunen's original proposal is worth noting: the order of believe and want is not interchangeable if we want the presupposition of the second complement to get filtered. While (2) presupposes nothing, the same is not predicted for (46). (46) Patrick wants me to buy him a cello, although he believes that his cello is going to take up a lot of space.
(4 7) (a) Fred believes that his wife will buy him a car. He hopes that it will be a Porsche. (b) ?Fred hopes that he will get a Porsche. He believes that his wife will buy it for him. (c) *John wants to have a Porsche. He believes his mother will buy it for him. Supposing that the pronouns on the intended anaphoric readings would be E-Type pronouns, equivalent to the definite descriptions the car his wife will buy him , the Parsehe he will get (have), the acceptability of these pronouns turns on the satisfaction of the corresponding definite description's presuppositions. In this light, (47a-c) support our prediction. On the other hand, Asher accepts (48), and Cresswell ( I 988) offers (49). (48) John wants a woman to marry him. He believes he can make her happy. (49) Susan wants a pet. She believes she will look after it. Both authors comment that the meaning of the believe-complement here is an implicit conditional: John believes that, if a woman marries him, he can make her happy, and Susan believes that, ifshe gets a pet, she will look after it. So once again, we must invoke accommodation (modal subordination). I would like to note, however, that certain examples of an analogous form do seem to fit transparently with our (i.e., Karttunen's) analysis. Suppose I had to miss the last set of the Wimbledon women's final because of a hairdresser's appointment, so I don't know who won, though I do know the game is over and decided by now. In such a situation, I might say (so) (so) I want Gabriela to have won.
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Does intuitive judgment bear this prediction out? Not srtikingly so, but (46) does seem a bit less good than (2) or (28). The same pattern shows up in the following judgments from Asher ( I 987) (the judgments pertain to the possibility of an anaphoric reading for it while the intended antecedent (a car, a Porscl1e) has narrow scope with respect to the first atti rude verb):
202 Presupposirion Projection and rhe Semanrics of Arrirude Verbs
However, it would be strange to continue as in ( s I ), even though-in analogy with the examples above-this should be just another way of saying that I am convinced that Steffi cried ifGabriela won.34 (s I ) *. . . and I am sure that it made Steffi cry hard. So there do seem to be some limitations (however obscure) on the availability of accommodated restrictions and, when these apply, the workings of the CCPs themselves are seen more directly and tend to confirm the present approach. 4·3
Counterfoctual andJactive desire predicates
(52) John wishes he would teach on Tuesdays. (52) cannot be analyzed as meaning that John teaches on Tuesdays in his most desirable belief-worlds; to the contrary, it suggests that he doesn't teach on Tuesdays in any ofhis belief worlds. Nevertheless, presuppositions triggered in the complements of wish -sentences appear to be satisfied by previous believe sentences. (53) is just as felicitous as (3o). (53) John believes that Mary1 is the only one here, and he wishes SusanF were here too 1 • If we did insist on interpreting wish here with a doxastic modal base, i.e., followed essentially our rule for want from above, we could not provide an adequate interpretation for (s 3): after processing the believe-sentence, we would have a context c' such that for all its elements w, Dox1(w) entails that Mary is
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Want-sentences are felicitous in contexts where it has already been established that the subject believes the presuppositions of its complement. Hence the naturalness of sequences like (2) and (3o). Our current analysis suggests that this is so because of a fact about the meaning of want: want-sentences are interpreted with respect to a doxastic modal base: to want ¢ means to find the ¢ -worlds among the worlds compatible with one's beliefs more desirable than comparable non-¢ -worlds compatible with one's beliefs. Thus the truth of a want-sentence never turns on the desirability of any worlds which contradict the subject's beliefs. Therefore, if only such non-belief-worlds violate the presuppositions of ¢ , we can be guaranteed that we won't need to consider them in evaluating a wants ¢. Apart from the subtler doubts we already raised above, there is a rather obvious reason why this explanation cannot be right. If we consider a wider range of desire predicates, we find that the m�ority of them do not require or even permit such doxastic modal bases. This is particularly clear in an example like ( 52), where the use of wish with the irrealis mood35 suggests strongly that John is pessimistic, perhaps that he is even certain he won't teach Tuesdays.
Irene Heim 203
here and nobody else is. According to rule (39) with amendment (40), c' + he wishes SusanF were here too1 would then always be undefined. This is because Dox1(w) + SusanF were here too1 is empty for all w E c', and thus not in the domain ofSi�.36 In short, (39) would predict the second sentence of(53) to be inappropriate whenever the first has been accepted, and this is clearly wrong. Counterfactual desire reports like those involving wish + irrealis comple ment are not the only ones that create problems. Our present analysis of want also fails to generalize to theJactive members in the family of desire predicates. Consider (54). (54) John is glad he will teach on Tuesdays.
(s s) John1 thought he 1 was late and was glad that BillF was late too 1 • Consideration of such an extended range of desire predicates suggests that our current analysis of want constitutes at best a special case. How come, then, the facts about presupposition projection are exactly the same for those other desire predicates as for want? Not only does a preceding belief-sentence satisfy the presuppositions of the subsequent desire-complement: (s6a,b) presuppose nothing as a whole; but we also spontaneously accommodate the assumption that the subject believes the presupposition when we hear (s7a,b) out of context. (s6) John believes Mary1 is coming, and (a) he is glad SusanF is coming too 1 (b) he wishes SusanF were corning too 1 • (57) (a) Patrick is glad he sold his cello. (b) Patrick wishes he had sold his cello. If the modal base for these verbs is not doxasric, then why should the presuppositions of their complements be satisfied just because the subject is known to believe them? We have no guarantee of this.
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The predicate be glad, like all facrive desire predicates, introduces a pre supposition to the effect that the subject believes in the truth of its comple ment.37 Again, this trivializes the truthcondirions that would be predicted for (54) if we simply used the same rule (39) as for want. This rime, it is the set to the right of
20�
Presupposition Projection and the Semantics of Attitude Verbs
4 . 3 . 1 Excursion: counterfactual conditionals
It is instructive to see that a similar dilemma arises with presuppositions in the antecedents of counterfactual conditionals. We couldn't just use the same rule (36) for them that we gave above for indicative conditionals, because their antecedents are typically inconsistent with the common ground and they would thus come out undefined. But what should we use instead of c in (36) to apply the CCP of ¢ to? Most discussions of counterfactuals in the literature suggest that it should just be W, i.e., a context devoid of all information.38 That way, the CCP for subjunctive conditionals would be as in (5 8). c
+ if¢ would tjJ = {w E c: Silllw(W + ¢) +
tjJ
= same)
But then we have an unwelcome prediction: counterfactuals whose antecedents have presuppositions should never be interpretable,39 because the modal base, being W, can't have the required entailments. It is surprising, then, that counterfactuals with presuppositional antecedents are so common and that they seem perfect under the same condition that their indicative variants are, viz. when the previous (primary) context entails the presupposition. For instance, when it is already in the common ground that Mary attended, that seems to license (6o) as much as (59). (59) IfJohn attended too, . . . (6o) IfJohn had attended too, . . . These examples suggest that the antecedent of a counterfactual is not really added to an 'empty' context, but to one which is in some sense a revision of the common ground c. It results from c by suspending some of the assumptions in c; i.e., it is a superset of c. But since the specific purpose of the revision is to create an input context for the CCP of the antecedent, there are limits to what can be suspended: presuppositions required by the antecedent must stay. Let's assume, for concreteness, that the result of the revision is always the biggest (- least informative) context within those limits.40 This leads to the following definition. (6 1 ) For any context c, LF ¢ : rev¢ (c), the revision ofcfor¢ , is U {X C W : c C X and X + ¢ is defined} . The CCP definition for counterfactual conditionals can then be given as in
(62).41
(6 2)
c
+
if¢ would tjJ - {w E c: Silllw(rev; (c) + ¢) +
tjJ -
same)
(62) solves our dilemma regarding the inheritance of presuppositions from the antecedents of counterfactuals. Not in a particularly exciting war, of course; I
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4· 3 .2 Back
to
wish
and be glad
I want to propose that wish and be glad have the same core semantics as want, but there is a difference that is analogous to that between indicative and subjunctive conditionals. To get the inruitive idea, recall our initial conditional paraphrase forjohn wants you to leave: John thinks that if you leave he will be in a more desirable world than if you don't leave. If we try to construct similar paraphrases for sentences with wish and be glad, here is how they come out: John wishes you were gone means John thinks that if you were gone he would be in a more desirable world than he is in because you are not gone'.John is glad you are gone means John thinks that because you are gone he is in a more desirable world than he would be in if you were not gone.' The common pattern is apparent, and the differences are in the choice of indicative vs. subjunctive mood and of if vs. because.
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have simply stipulated the appropriate constraint on the revision process in (6 I ). At any rate, it follows directly from (6 I ) that rev9 (c) will entail the presupposi tions required by � if and only if c does!2 For our purposes, where we restrict attention to CCPs whose definedness conditions are purely presuppositional,43 this means that rev9 (c) + fjJ is defined iff c + � is. Given (62), it then follows that a context is in the domain of the CCP of a counterfacrual conditional only if it is in the domain of the CCP of its antecedent. In other words, counterfacrual conditionals inherit the presuppositions of their antecedents. Let me close this excursion with a remark on the effect of presuppositional requirements in the antecedent of a counterfacrual's truth conditions. Recall the context where Mary is presupposed to be in the phone booth. We noted above that an indicative if-clause like IfJohn is in the phone booth . . . in this context amounts to the supposition that both John and Mary are in the booth. This is otherwise for a minimally different subjunctive if-clause: If we say If john WERE in the phone booth , then it depends on the acrual facts and the selection function whether the hypothetical situations under consideration have both people in the booth or have John there instead of Mary. . . . then Mary would be outside is a felicitous and possibly true continuation. (As opposed to the deviant indicative variant IfJohn IS in the phone booth, then Mary is outside. This is acceptable only if we are ready to conclude that Mary's being in the phone booth isn't presupposed after all.) This difference, of course, is predicted by (62). But what is also predicted is that ifwe add to the subjunctive antecedent a too, as in Ifjohn were in the phone booth too . . . , then the meaning is in a certain respect more like that of the indicative again: no matter what the selection function and facts of the world, we only get to consider hypothetical worlds with both people in the booth together. So Ifjolm were in the phone booth TOO, then Mary would be outside is also deviant.44
206 Presupposirion Projecrion and rhe Semanrics of Arrirude Verbs
So what should the CCP definitions look like? The counterfactual conditional in the paraphrase for the wish -sentence, together with what wejust said about counterfactual conditionals in the last section, suggests the following minimal variant of the rule for want: c + a wishes � = {w E c: for every w' E Doxa(w): Silllw{rev91 (Doxa(w)) + �)
(6 3)
c + a wishes � = {w E c: for every w' E Doxa(w): Silllw·(rev91 (Doxa(w)) + �)
w'}
The paraphrase of the glad-sentence, on the other hand, has the counterfactual on the opposite side of 'more desirable than', so this is where we should substitute rev9 (Doxa(w)) for Doxa(w) in (jg). And because of factivity, i.e., the fact that a's beliefs can be assumed to entail �. we can this time simplify the left side. The result is (6s).
(6 s)
c + a is glad � = {w E c: for every w' e Doxa(w): w'
Silllw·(rev91 (Doxa(w)) + not �)}
Presupposition projection from the complements of wish and beglad sentences, of course, works as desired now. (64) and (6 5) both imply (by reasoning parallel to that above) that the CCPs of a wishes/is glad � will be defined for an initial context c iff Doxa(w) + � is defined for all w e c-Karttunen's generalization. Recall, e.g., our dilemma with (5 3). Our context c' after processing the believe sentence was c' = {w: Mary and nobody else is here in all w' E Dox1(w)}. For each such w E c ' , what can we say about revsusall-,-werr-hm·-t"" (Dox1 (w))? By definition of the revision process, this set is not so big as to indude any world where Mary isn't here, and so we can be assured that the CCP of SusanF were here too1 is defined for it. The whole incrementation process thus goes through smoothly, and the presupposition filtering in (s 3) is accounted for.
s W H Y D O A T T I T U D E VERBS APPEAR TO BE H O L E S ? Why is i t that a sentence like (66), uttered in isolation, seems to presuppose that it actually was raining, rather than merely that John believes so?
(66) John believes that it stopped raining.
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s . I De re
readings
If a presupposition trigger in the complement clause is not really interpreted in the scope of the attitude verb, then it will be unsurprising on any theory that the relevant presupposition must be satisfied or accommodated in the main context. Take, for instance, the existence and uniqueness presupposition associated with the italicized definite description in (67}. (67) John thought that the person who was going to kill him had come to read the gas meter. In the salient reading of (67), this definite is interpreted de re. Analyses of this phenomenon vary, but somehow or other they all imply that it is the speaker of (67), notJohn, who is 'responsible' for the definite description. For concreteness, assume a Quine-Kaplan-Lewis analysis of de re reportS along the following lines.48 (68 ) There is an acquaintance relation D such that (i) John bore D to the person who was going to kill him, and (ii) John thought that whoever he bore 0 to had come to read the gas meter.
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Observations of this sort led Gazdar to conclude that attitude verbs are essentially holes (with apparent exceptions due to cancellation).46 For us as for Karttunen, they are filters (as a matter of their intrinsic semantics), and such hole-behavior is unexpected. Let us be clear about what exactly the problem is. There is no dispute about the interpretation of (66} in contexts where it is presupposed that John believes it had been raining. This presupposition-as our analysis predicts and as everyone agrees-suffices to make (66} interpretable and nothing else is accommodated. What, however, if it isn't yet presupposed that John believes it was raining? Then something must be accommodated. What will this be? Our analysis as it stands, it would seem, leads us to expect the minimal accommodation required to make the sentence interpretable. This would be accommodation of the assumption thatjohn believes it to have been raining. But in point offact, we spontaneously accommodate something else, namely that it had infoct been raining. So there is a prima facie discrepancy between the observed facts and our (Karttunen's) predictions. The purpose of this section is to consider some independent factors on which we might blame these facts without abandoning our basic analysis. I will consider two hypotheses in particular:47 first, that all cases where attitude verbs seem to be holes result from de re construals of (a constituent containing) the presupposition trigger. Second, a version of Karttunen's 'spill-over' story cited in the introduction.
208 Presupposition Projection and the Semantics of Attitude Verbs
5 . 1 .2
De re construals for other presupposition triggers?
When we move beyond definite descriptions, we have to clarify, on a case-by case basis for each type of presupposition trigger, what a de re reading would even consist in. To the extent that the constructions in question can be analyzed as involving covert definite descriptions, this is relatively easy.49 Take, e.g., the presuppositions of aspectual verbs like stop. Uncontroversial instances of de re readings like in (67) are harder to come by here, but they can be found if one looks. (69) John thought I had stopped proof-reading. By (69) I could conceivably mean that John thought of the activity of mine that was in fact a proof-reading, but that he may not have recognized as such, that it had stopped. For instance, John may have seen me from a distance and thought I was reading a magazine, then (after he had looked away) heard my step, at which point he concluded I must have stopped reading the magazine. In fact, I was proof-reading my article and continued doing this even as I was walking around. To be a true report about John's attitudes in this story, (69) would have to be represented along the following lines: (7o) There is an acquaintance relation D such that (i) John bore D to my proof-reading, and (ii) John thought that the activity he bore D to had stopped. Here I have, in effect, treated the -ing-complement of stop as a definite description of a process. A verifying value for D in our scenario could be the
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However this is implemented in detail, the definite description is outside the atritude complement in this paraphrase, and it is only to be expected that its presupposition must be entailed by the common ground. Nothing is asserted or presupposed about whether John believes there is somebody that will kill him. (The invited inference here is, of course, that he lacks this belief, but the sentence itself doesn't say one way or the other.) Now it is quite uncontroversial that some cases of apparent presupposition inheritance from an attitude complement-such as in this salient reading of (67)-should be explained away in this manner. But would it be plausible to speculate that all presuppositions that percolate to the top from what seems to be a complement-internal trigger are really riding piggy-back on a de re construal of their trigger (or an expression containing it)? There are at least two prima facie obstacles to such a claim. First, the notion of a de re reading does not so obviously generalize to presupposition triggers other than definite descrip tions. Second, one would be committed to the view that de re readings are ceteris paribus always preferred over de dicto readings, which contradicts superficial evidence. Let's take a closer look at each of these two points.
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209
relation that person x bears to activity y if x observed such and such visible manifestations of y (i.e., the visible manifestations of my proof-reading that John perceived when he looked). So analyzed, (69) evidently presupposes that I had infoct been proof-reading, and ir doesn 'r presuppose rharjohn thought I had been. But what about presupposition triggers like again , even, or the too in many of our examples throughout this article? What might it mean for an occurrence of one of those to receive, or be part of a constituent that receives, a-de re construal? Here is an example which might help us clarify this question and where such a construal might be independently motivated. Imagine two kids talking to each other on the phone: Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(7 I ) John: I1 am already in bed. Mary: My parents think IF am also1 in bed. The point about example (7 I) is that it is quite clearly felicitous even if Mary's parents cannot be assumed to have any beliefs about John. Mary is not committed to the presupposition predicted by Karttunen, i.e., that her parents believe John to be in bed.5° I bring up this example here because it seems promising to try to account for its apparently exceptional projection behavior by analyzing Mary's utterance along the lines of a de re paraphrase like (72). (72) Of the property of also being in bed, my parents think that I have it. The idea behind this paraphrase is that 'the property of also being in bed' (more accurately here: 'the property of [PROF also1 being in bed]') is just another way of describing the property of being in bed, and that it is a description which fits that property only contingently: it is true of itjust in case John happens to be in bed. And since the latter is a fact known to Mary but unknown to her parents, she, but not they, can describe it in those words. This would have to be worked out further, and I am not convinced it is the right approach to this type of example,5 1 but it deserves consideration. 5 · 1 . 3 A general preference for
de re readings?
Suppose we can overcome the first obstacle and posit plausible de re construals for all kinds of presupposition triggers. Would this amount to an alternative explanation of Gazdar's observation that when attitude reports with presup positional complements are presented out of context, we always accommodate the presupposition in the main context? Not all by itsel£ We would have to defend the further claim that de re readings are ceterisparibus preferred wherever there is a choice between a de re and a de dicto construal. Without this assumption, we would merely predict that presuppositions sometimes percolate
8
·
2IO
Presupposition Projection and the Semantics of Attitude Verbs
(73) Does Ralph think that the man he saw at the beach is a spy? Evidently the de dicto reading, because the spontaneous answer (given the facts of Quine's story) is: 'No, he thinks that the man he saw at the beach is a pillar of the community.' Despite these initial deterrents, I think that a basic preference for de re readings may be defensible. Here is how. First, I propose a slight refinement of the standard de re analysis:52 replace existential quantification over acquaintance relations by reference to a contextually salient particular acquaintance relation. For instance, (67) means (74) rather than (68). (74) (i) John bore D to the person who was going to kill him, and (ii) John thought that whoever he bore D had to come to read the gas meter; where D is the acquaintance relation supplied by the utterance context. Like all context-dependency, the selection of an appropriate acquaintance relation for the interpretation of a given utterance of a de re belief report depends on a miscellany of pragmatic factors. Sometimes general background knowledge plays the major part, as when we hear (67) and somehow guess that the intended D is the relation of visual contact between John and his killer as he lets him into the house. But it is plausible that the speaker's description of the res will usually be one important factor among others, and in the absence of other clues often the decisive one. This implies that, everything else being equal, the speaker's decision in (73) to refer to Ortcutt as 'the man Ralph saw at the lieach' (rather than as 'Ortcutt' or 'the man he saw in the shadows') will bias the hearer towards the assumption that the intended acquaintance relation between Ralph and Ortcutt is the one established in the beach-encounter. And with this disambiguation, Ralph thinks the man he saw at the beach is a spy is false, even though read de re. Another way of summarizing the suggestion I just made is this: there is not really just one de re reading (for a given constituent), but there are many-one
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to the top, and we would expect this to correlate with independent clues in favor of a de re reading (such as the overall plausibility considerations that encourage us to flesh out the story in (67) in such a way that John is an unsuspecting murder victim). Now common wisdom certainly has it the other way round: de dicto readings are the unmarked choice. For one thing, this is what you'd expect under standard analyses relying on quantifying-in, polyadic homophones of the attitude verb, or another such special mechanism to generate the de re reading; de dicto readings are somehow simpler and conceptually prior on all these approaches. Moreover, it seems to be confirmed by intuitive judgment. For instance, what is the unmarked reading of(73)?
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2I 1
5.2
Other people's beliefS and the nature ofaccommodation
Recall the problem as we stated it with respect to sentence (66). When this sentence is uttered in a context where it isn't yet presupposed thatJohn believes it had been raining, then we spontaneously accommodate the presupposition that it had (in fact) been raining. Suppose (in distinction to the alternative hypothesis of the preceding section) that the LF of (66) is what it appears to be, with the presupposition trigger genuinely in the scope of believe. And suppose further our account of the CCP of (66) is correct, i.e., it is defined exactly for those contexts in which it is presupposed chatJohn believes it had been raining. Then we have a double puzzle of sorts: accommodating the presupposition that it had in fact been raining is predicted to be neither necessary nor sufficient to tum the context into one for which the CCP of (66} is defined. Yet, in practice it seems to be sufficient as well as highly preferred (if perhaps not downright necessary). Why? Pare of the answer, if our analysis is at all to be saved, has to be that we actually accommodate at once both the presupposition that it has been raining
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for each acquaintance relation that the context might supply. And some of those many, namely those where the acquaintance relation happens to include the subject's awareness that the res fits the same description used by the speaker, are very similar to the de dieto reading: more precisely, they entail it. In a way, I am blurring the distinction between de re and de dicta readings. But that may not be such a bad thing.53 More often than not, the two are impossible to tell apart in practice anyway. When we hear somebody say thatJohn thinks his dog is sick, do we understand thatJohn takes himself to be in a world where the dog he has there is sick, or do we rather understand that John ascribes illness to his dog under some acquaintance relation or other? Under ordinary circumstances, where people know whether they own dogs, are acquainted with their dogs, and rarely encounter them unrecognizably disguised, one is true ofJohn just in case the other is. So we couldn't really tell whether we construe the utterance de dicto and infer the truth of a de re reading, or the other way round. The present proposal, which implies that the unmarked reading is a de re reading that entails the de dicta reading, is equally compatible with our intuitions about those ordinary cases. And it also accounts for (73), where it looked at first like we prefer de dicta . This is all very sketchy. I am not yet ready to really endorse the view that de re construals are ceteris paribus preferred wherever possible, and that all pre supposition inheritance from the complements of attitude verbs is due to this preference. But I think it is not a hopeless line to pursue. In the next section, I sketch an alternative which likewise strikes me as promising, and I will nor attempt to choose at this point.
212
Presupposition Projection and rhe Semantics of Artirude Verbs
6 C O NCLU S I O N Kartrunen ( 1 974: I 8 8), having classified complementizable verbs into a number of subgroups according to their permeabiliry for presuppositions of their complements, wrote: 'These distinctions are of course not arbitrary but presumably follow from the semantics of verb complementation in some man ner yet to be explained.' What sort of an explanation was he hoping for? Presu mably the kind that Stalnaker (1 974, I98 5, and elsewhere) proposed explicitly for the connective and and sketched for conditionals and belief-predicates. In the case of and, this was a simple and satisfying explanation indeed ( 1974: 2 Io I I): Karrrunen defends the following [generalization]: . . . the presuppositions of a conjunction are the presuppositions required by either of the conjuncts, minus any required by the second conjunct which are entailed by thefirst . . we can explain [rhis) generalization without postulating ad hoc .
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and the presupposition thatJohn believes so. For without the latter, the CCP of (66) just wouldn't be defined. This is consistent with intuitive judgment in so far as we certainly wind up assuming that John believes so when we accept (66).54 So the puzzle can be restated this way: why is it somehow easier to accommodate both that it rained and that John thought so at once, than to accommodate the latter alone? It is useful here to recall a general point about accommodation:55 assump tions to be accommodated are supposed to be uncontroversial and unsurptis ing. One may explicitly assert controversial and surprising things (in fact, one should), but to expect one's audience to accept them by way of accommodation is not good conversational practice. So when we hear (66) out of the blue, we know two things: first, as a matter of the semantics of this sentence, we know that it requires the presupposition that John believes it was raining. Second, we know that the speaker takes this to be uncontroversial and unsurprising. Now why would it be unsurprising that John has such a belief? The most natural guess is that it would be unsurprising because it was in fact raining and John was in an appropriate position to find out. Of course, these are not the only possible conditions under which someone might form a belief that it was raining; but they are the most normal conditions. Therefore, if accommodation is generally accompanied by a suggestion of unsurprisingness, then it is not so puzzling that these are the conditions which we spontaneously imagine to obtain. (This, I think, is what Karttunen had in mind in the passage I quoted in the Introduction.) Again, I am not confident that this is the right story, but it is prima facie plausible, and it gives us another way of maintaining our semantic analysis in spite of superficial appearances that attitude reports inherit the presuppositions of their complements.
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21 3
semantic or pragmatic rules. The explanation goes like this: . . . when a speaker says something of the form A and B , he may take it for granted that A . . . after he has said it. The proposition that A will be added to the background of common assumptions before the speaker asserts that B . Now suppose that B expresses a proposition that would, for some reason, be inappropriate to assert except in a context where A , or something entailed by A , is presupposed. Even if A is not presupposed initially, one may still assert A and B since by the rime one gets to saying that B , the contexr has shifted, and it is by then presupposed that A .
The analogous generalization about conditional statements is explainable on equally simple assumptions. Here we need first the assumption that what is explicitly supposed becomes (temporarily) a part of the background of common assumptions in subsequent conversation, and second that an if clause is an explicit supposition. Again, Karttunen's generalization is derived from these obvious assumptions.
What exactly is the role of supposing the antecedent in the overall context change, i.e., why is it necessary to do so in order to calculate the information conveyed by the whole conditional? What does this supposing amount to when the conditional is a counterfacrual? What else happens after the supposition of the antecedent, in particular, what do we do with the consequent? In short, unlike the earlier story about and, this description of the CCP of if leaves a lot unsaid, and it is not so immediately evident how it should be completed in such a way that it predicts both the informational content of conditionals and their presuppositions. The following description of the CCP of believe , though still not complete,56 is more nearly so (Stalnaker 1 988): What Phoebe believes, or is assumed to believe, may be different from, or incompatible with, what a speaker talking about Phoebe's beliefs believes or assumes. The relevant derived context will be . . . the set of all possible situations thar might, for all the speaker presupposes, be compatible with Phoebe's beliefs. This set of possible situations is the derived context for interpreting the clauses that are intended to express the contents of Phoebe's beliefs . . . All of the ways that ordinary contextual information constrains and guides the interpretation of assertions . . . will also be ways in which derived contexts constrain and guide the interpretation of embedded sentences which ascribe or deny beliefs . . . [for example], presupposition requirements: Just as 'Harry regrets accepting the bribe' is appropriate only in a context in which it is presupposed that a bribe was offered, and that Harry accepted it, so the statement 'Phoebe believes that Harry regrets accepting the bribe' requires a derived context in which it is presupposed that a bribe was offered and Harry accepted it. That is to say, it must be presupposed-taken by the speaker to be common ground-that Phoebe believes that a bribe was offered, and that Harry accepted it.
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The mere commonplace that asserting ¢ and 1/J consists of asserting first ¢ and then 1/J was sufficient to explain presupposition projection in conjunctions. In our terminology: one nai"ve look at and reveals what its CCP is and that this CCP makes the correct predictions. That, of course, was an exceptionally easy case. Already the case of the conditional is much less obvious, notwithstanding Stalnaker's optimism in the following passage (1 974: 2 1 1 ):
2 1 4 Presupposition Projection and the Semantics of Attitude Verbs
But numerous questions arise here as well when we try to extrapolate to other attimde verbs. Well, I tried to complete these sketches, and it turned out to be harder than I thought. I had to set my sights low and got around only to two or three of the many verb types that Karttunen included in the classification referred to above. Even with those two or three, I barely scratched the surface and left many open problems and dangling stipulations. I set out to support the hypothesis that all presupposition projection was just a by-product of an independently plausible account of context change. I don't know if I have done more to support it than to cast doubt on it, but at least I have given it more concrete shape.
This article is a substantially revised descendant of a manuscript written in the fall of 1985 at the University ofTexas at Austin and circulated under the ride 'Presupposition projection and anaphoric relations in modal and propositional attitude contexts'. It owes an obvious debt to the writings of Robert Stalnaker and a less visible but equally important one to conversations and co-teaching with Hans Kamp. IRENE HEIM Department ofLinguistics and Philosophy, MIT 2oD-219 Cambridge, MA 02139 USA
N O TE S 1 The main challenge was the alternative theory of Gazdar (1 979), which relies heavily on cancellation of presupposi tions. See Soames (1 979, 1 982, 1 989) for critical discussion of that approach, as well as (more recently) van der Sandt (1989) and Zeevat (1991). 2 I follow here primarily the theory of Heim ( 1988: chapter 3. 1 98 3). The frame work of van der Sandt (1 989, 1 990), based on Discourse Representation Theory (Kamp (198 1 ) ), is very similar and prob ably equivalent in all respects relevant to this article. All current versions of such theories are descendants, in some sense, of the approach to presupposition projec tion that was urged by Stalnaker (1973, 1974) and Karttunen (1974). Or whatever grammarical level(s) is (are) relevant to semantic interpretation. ..
4 Karttunen takes a context to be a set of logical forms (1 974) or a set of proposi tions (1973b). In that sense, a context is not identical to a set of worlds, but it uniquely determines one, namely the set of worlds where all its elements are true. Stalnaker ( 1 979) calls this the context set. For our purposes, there is no need to distinguish between different contexts that determine the same set of worlds, so we might as well identify contexts with their context sets. The general framework leaves open that the definedness of a CCP might depend on properties of the input context other than the fact that it has certain entail ments. I don't know if there are actual instances of this. In this article, at any rate, I only consider sentences whose CCPs have what I call 'purely presupposirional'
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Acknowledgements
Irene Heim
6
7
9
10 II
12
I3
14
Is
16
I7 I8
Karrrunen (I974: I 84), agree with Kripke, but the existential version some how became more widespread.) A problem which I set aside here: unlike only and even , too sometimes associates with a 'focus' that couldn't possibly be prosodically prominent because it ts phonetically null. For instance, we are forced to this analysis for one of the readings ofJohn wants to come too , the one where it means that John wants it to be the case that he comes in addition to so and-so. Given the semantic rule in the text, the representation for this reading must bejohn wants {PROF to come too). (If we designate the overt NPJohn the focus, too must be attached in the marrix clause, and the meaning is that John, in addition to so-and-so, wants to come, which is also present but different.) The deviance is, of course, only under the construal indicated, with too disambigu ated as 'in addition to Mary'. If there is an alternative antecedent instead of Mary available, the sentence may be fine. For this reason, it is not even possible to rescue the example by accommodation. What we would have to accommodate to ensure definedness, i.e. that John believes Mary to be here, conrradicts what we have just been explicitly told. This assumption follows directly under 'semantic' accounts of presupposition (3valued or with truth-value gaps), and it is also part of Gazdar's { I 979) theory. See note S· Stalnaker's (I988) notion of the 'derived context' for believe-sentences also corres ponds to the union of the Dox0(w) across c; in fact he explicitly defines it this way: 'The relevant derived context will be determined by the basic context in the following way: for each possible siruation in the basic context, Phoebe will be in a definite belief state which is itself defined by a set of possible siruarions-the ones compatible with what Phoebe believes in that possible siruation. The union of all the possible belief states will be the set of
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8
definedness conditions. These are the sentences ¢ for which there is some proposition p such that, for any c, c + ¢ is defined iff c entails p (including sentences with 'no presuppositions', in which case the p in question is W). Thus what I mean by 'uncancellability' is, in the terminology of Soames (1 989). that there is no 'de jure accommodation'. Any accommodation there might be is 'de facto accommodation'. By an 'empty' context, I mean one that is empty of any information. In other words, it is the set W of all possible worlds-not the empty set 0 ; hence the quotation marks. (The terminology makes literal sense when contexts are construed as sets of propositions, and that's where it comes from.) This corresponds to Karrrunen's (1974) 'c v [¢ }'-recall that he takes contexts to be sets 0f logical forms. This is · not to be confused with my rash claim in Heim (198 3) that CCPs are fully predictable from truthconditional pro perties, for which I was rightly taken to task by Soames (I989) and Mats Rooth (personal communication m a letter dating from 1986). See Hintikka (I 969) and Lewis { I 97J: 7). This formulation of the rule is due to Hans Kamp (personal communication, Sarurday afternoon, November 9, I985, Cognitive Science Center seminar room at the University of Texas, Austin). See below for discussion of how it relates to Kartrunen's rule (3). Kripke (I 990; and as cited in Soames (I989: note 54)). A common alternative assumption is that too rriggers an existen tial presupposition, e.g. SusanF is here too would presuppose that someone other than Susan is here. But Kripke has argued persuasively that this is not quite correct and that words like also , too , again (and maybe many other presupposition rrig gers) have an essentially anaphoric deictic semantics. (Some older rrearments, e.g. Green {I968) as cited in
21 5
2 1 6 Presupposition Projection and rhe Semanrics of Artirude Verbs
20
21 22 23 24
u[Siffiw(c + ?): w E c) to be a proper subset of c + ?25 This is acrually what Stalnaker does, but in his case, he is forced to it by Stalnaker's Assumption, which we did not adopt. 26 In the murder example, Stalnaker spon taneously changes tense: 'I never wanted the murder to have been committed.' But, of course, the question of what I wanted in the past, before I knew that the murder had been committed, is quite separate. (39) has no difficulty with the possibility that a wants ? is true or false at one rime and then a believes ¢ is true at a later rime. Nor is there a problem, of course, with wanting ¢ before one comes ro believe ¢. I didn't want him to do it, but I saw he was doing it anyway is fine, but this is presumably because the reference rime of the want-clause precedes that of the see clause. Such an example does not show that ' a wants ¢' and ' a believes -¢' can be true at the same time. Likewise; it is not a counterexample to our analysis that I can say coherently: I know he is in and I want him out. Here it is important to make the reference times of the embedded clauses explicit: this sentence says that I know that he is in now and I want him to be out in the immediatefuture. (In other words, the complements of the two clauses are not negations ofeach other.) Complements of want always have a fururate interpreta tion. (Perhaps this is a general property of .for-infinitivals; see, e.g., Stowell 1 982.) 27 One may object to my reanalysis of Stalnaker's judgments as follows: if we have to say which one of the two sentences I want to have been sick and I want not to have been sick is true, we have a firm intuition that it is the latter. What little strangeness there may-be in both of them does not impede this judgment, but our current proposal does not account for it, because it predicts exactly the same status-undefined-for the two sentences' CCPs. I am not sure how best to respond to this objection. Perhaps what is going on here is that we tacitly reinterpret these -
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19
all possible siruarions that might, for all the speaker presupposes, be compatible with Phoebe's beliefs. This set of possible situations is the derived context for interpreting the clauses that are intended to express the contents of Phoebe's beliefs.' But Stalnaker also does not give a rule that actually specifies the outcome of the context change effected by a belief sentence. As far as I can see, one cannot write such a rule without referring to the individual sets Dox0(w) rather thanjust to their union. The significance of this type of counter examples to Karttunen is heightened by the fact that ir seems to support Gazdar: his mechanism of cancellation by a conflicting conversational implicature covers (28) along with (2). My version here is actually a cross between the two authors' versions. I depart from Lewis in making the Limit Assumption, but I don't make what Lewis calls Stalnaker's Assumption. In other words, I assume that for each world w and each contingent proposition p there is a non-empty set of p-worlds which are maximally similar to w, but this need not be a singleton. Evidently, it is important either to justify these choices or show that my aims in this paper do not really depend on them. I must leave both to future work. Similar examples were also discussed by Janet Dean Fodor (1 979). Stalnaker goes right on to say that this is a specific property of indicative, as opposed to subjunctive, conditionals. See below. See, e.g., Kanrunen (1 973a, 1 974). (36) is not fully equivalent to the standard rule for presuppositions of conditionals: it predicts that a presupposition of tp may in principle get filtered away even though not entailed by c + ?, as long as it is enrailed by u[Siffiw(c + ?): w E c). I am unable to give a concrete example of diverging predictions, however, because it is not intuitively clear to me at present what a context c has to be like in order for
Irene Heim 2 1 7 sentences with something like the seman tic rule for factive and counterfactual desire predicates (see below) and base our rtuthvalue judgments on this reinterpre tation. 28 (4 3) suppresses the temporal parameter. Taking that into account, we would have:
receive no semantic interpretation at all; I treat it as a mere surface phenomenon (analogous to, say, case on an NP), and only the superordinate verb that governs it is a semantic unit. (Likewise, the mood
for any w e W, time t, F.(w, t) - {w' e W: w' is compatible with everything that a
marking in the antecedent of a counter
in w at t believes to be the case no matter how he chooses to act after t).
redundant;
29 There is a problem:
cello tomorrow
Patrick intends to sell his
is predicted to presuppose
could
have
decided to sell it today, in which case he wouldn't have one tomorrow anymore. This must be fixed somehow by restrict ing the relevant actions to those at or after the reference time of the complement.
factual
conditional only
is
the
semantically counterfactual
modal-would or m ight -in the consequent is interpreted.) I don't thereby mean to deny, of course, that the lexical items which govern the irrealis mood form a natural semantic class. 36 An alternative might be to undo the amendment in (4o) and return to (3 4).
Then c' +
he wishes Susanp were here too1
would always be c' again. Still, the
truthconditions for ( 5 3 ) would be trivial
c£ Lewis (1986: 34-5)·
3 1 As I was reminded by Carl Pollard
ized, so this is not a way out. 3 7 By the usual definition of factivity, it
(personal communication); (45) is his
moreover presupposes that the comple
example.
ment is in fact true (not just believed to be
32 As in Roberts' treatment of modal sub ordination. See Roberts ( 1 989, 1 9 9 1 ). 3 3 This is, in effect, the proposal of Cresswell ( 1 988).
particularly easy to read as containing covert restrictions. Or perhaps there is a blurring of indicative and counterfactual mood in the future. 3 5 What I mean here by the 'irrealis mood' is, in morphological terms, homophon ous with the past tense, except for the 1 st and 3rd persons singular of the verb
was.
tion on the grounds that one can say
Mary, who was under the illusion that it was Sunday, wasglad that she could stay in bed (Klein 1 97 5 , as cited in Gazdar things like:
??john preftrs for you to have already received his letter, even though he is sure you were very upset by it. Perhaps will-sentences are
34 Another example of this kind:
whose irrealis forms are
so by the subject)-though some have argued against that stronger presupposi
be,
were rather than
It seems to be the same mood that
shows up in the antecedents of counter factual conditionals. Wherever I refer to the verb wish from now, I mean the wish that governs a tensed complement clause in the irrealis. (As opposed to, say,
( 1 979: 1 22)). What matters here is only the assumption that presupposes
at least
a
that
is glad that ¢ a believes ¢.
which has not, t o my knowledge, been disputed. 38 For instance, Kratzer ( 1 9 8 1 : 69) proposes that the modal base for counterfactual conditionals is 'empty'. 39 Except perhaps by way of local accom modation in the sense of Heim ( 1 98 3 ). 40 An alternative assumption would be that it is just some context within these limits, and other contextual clues determine which particular one it is for each given utterance of a counterfactual conditional. This would then be yet another source of
wish
vagueness, on top of that already due to
irrealis mood itself (i.e., the suffix of
don't see at this point how this option
+ infinitive, which I disregard here.) The
the flexibility of criteria for similarity. I
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that he will have a cello tomorrow no matter how he acts. But he
30
non-concatenative morpheme that real izes it on the embedded verb) will
2 1 8 Presupposition Projection and the Semantics of Attitude Verbs 44 This deviance is, ofcourse, unsurprising if every presupposition is also an entailment of the minimal sentence that carries it (as in Gazdar 1 979), because this assumption alone suffices to predict the sentence to be contradictory. But notice that we get rhe same deviance in slightly more complex cases, such as ifjohn weren't also in thephone booth, Mary would be outside. john is also in the phone booth may both presuppose and entail that Mary is, but not (John is also in the phone booth) presumably only pre supposes it. 4 5 Why exactly should we be allowed to take this for granted? One possibility is to stipulate a further felicity condition in sentences of the form a wishes � , namely that they fit only in contexts where it is presupposed that a believes not �· Alter natively, we might explore weaker con ditions analogous to Stalnaker's proposal for subjunctive conditionals; c£ n. 4 1 . So {63) might not always reduce to {64), but it will in typical contexts. 46 Unlike Karttunen, Gazdar (1979) works with a theory according to which pre suppositions are cancellable. Specifically, they get cancelled whenever they con tradict an assertion, conversational implicature, or other presupposition of the same or preceding sentence(s). This is what he claims happens in (2). The initial sentence of this text, Patrick is under the misconception that he owns a cello, entails that Patrick does not have a cello, hence conflicts with the potential presupposi tion of the subsequent sentence, and thus cancels it. In other cases, a conversational implicature or otherpotential presupposi tion might be responsible for the cancella tion. 47 There may be other factors;- e.g., other wise non-factive verbs might sometimes have factive readings. I don't know whether this occurs with attitude verbs though. It does seem to happen with verbs of saying. Take Gazdar's example (i). (i) The salesman didn't tell me that my camera was suitable for color too.
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could be empirically distinguished from the one adopted in the text. 4 1 As David Dowry (personal communica tion) reminded me, (62) and (36) do nor predict that we must use a subjunctive conditional when the antecedent is presupposed to be false and an indicative one otherwise. A closer look reveals that we predict one direction of this generali zation: if the antecedent is incompatible with the common ground, the indicative conditional is infelicitous and only the subjunctive one is permitted. (This follows because of the amendment in (40), which makes the selection function undefined for the inconsistent proposi tion.) On the other hand, nothing I have said so far implies that one couldn't use the subjunctive conditional even when the antecedent is compatible with the common ground. Interestingly, there are some cases where this systematically occurs; see Karttunen & Peters ( 1 979) and especially Stalnaker (1975) for examples. But it is not an option that is always freely available, and to capture this we must impose an additional felicity condition on rhe choice of the counterfactual. A rough proposal, inspired by Stalnaker {197 5), is that if� would tJ! is felicitous in a context c only if there is at least one world w E c such that Simw(rev16(c) + �) is nor a subset of c + ¢. (A rationale for this might be that the counterfactual is rhe marked choice and rhus pre-empted by the indicative conditional when one might as well have used the latter.) 42 Proof: suppose the CCP of� is defined for exactly those contexts which entail p. The definition in (6 1 ) thus amounts to rev;(c) - u (X: c � X � pJ. We need to show-that rev;(c) entails p iff c does. First, assume that c does not entail p. Then no superset of c does, so (X: c � X � p} - 0 and its union is W and doesn't either. Second, assume that c does entail p. Then u (X: c � X � p} - p. which of course entails p. 43 C£ n. 5·
Irene Heim 2 1 9
-
5 I One reason for my scepticism i s that I don't see off-hand how this approach throws light on the appropriateness of also in the following minimal variation of (7 I): imagine John and Mary competed for one job, and everybody, including the parents, knew this. (i) John: I1 got the job. Mary: My parents think that IF also1 got it. Why isn't also;get thejob a description that fits the property ofgetting thejob when it happens that xi gets the job? We might amend the proposal so that a properry only falls under the description also; � if it is true of xi and at least one other individ ual. But this is not quite what we need here, since the intuitive reason why (i) is out is not that Mary believes only one per son got the job, but that herparents believe rhis. 52 This has also been argued for by von Stechow (I 984) and it is tacitly taken for granted in Higginbotham ( I 989). 53 It may also make it easier to reconcile the two-way de re!de dicto ambiguity of the standard theory with finer classifications such as the four-way distinction in Fodor (1979: 229). (I owe this reference to Angelika Kratzer.) 54 In a theory like Gazdar's, this could be atrributed to the mere fact that (66) also asserts that John believed there was rain. But we also infer such a belief in an analogous sentence like (i), where it can't have come as an entailment of the assertion. (That way, we'd only get that John wants there to have been rain.) (i) John wants it to stop raining soon. So there is evidence independent of our analysis that the presupposition that the subject believes the complement's pre supposition is generally accommodated in addition to the presupposition that it is rrue in fact. 5 5 See, e.g., Soames ( 1 989: 567). 56 It is not quite complete for the reason given in IL 1 8.
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It is rrue that we conclude that the speaker has a camera and that it is suitable for black and-white photography. But, as Berman ( 1 989) points out, we spontaneously conclude even more, namely that the speaker's camera is suitable for color, which is not a pre supposition but the content of the comple ment clause. In other words, tell seems to be read factively in this example. But once a predicate is factive, then its being also a hole presents no additional mystery. Consider, for instance, the following meaning rule for the factive verb know, which implements the common idea that factives presuppose their complements. (ii) c + John knows that rp is undefined unless c - c + rp. Where defined, c + John knows that ¢ - (w e c: Dox1(w) + ¢ same). This requires, among other things, that c + ¢ be defined, rhus that c satisfy any presupposi tions of ¢. This is not a story, however, that could be extended to account for all cases where attitude verbs act like holes. If we control for factivity, as in (iii) below, there is still a spontaneous interference that the speaker has a camera and it's suitable for black-and-white. (iii) (This salesman told me a lot of lies, but at least) he didn't tell me that my camera was suitable for color too. 48 See Quine (1956), Kaplan (1 969), Lewis (1979), and others. I leave open here how de re construals are represented at LF; something along the lines of Creswell & Stechow (I 982) should suit my purposes. Of course, transposing their proposal into the present framework would first require an account of variables and quantification in a context change frame work. This also goes beyond the scope of the present article, bur see Heim (I983, I 988). 49 See von Stechow ( I 98 I ) for an explicitly descriptional analysis of factives, for instance. 50 As Rob van der Sandt pointed out to me, examples of this sore are discussed in Fauconnier ( 1 984); see also Zeevat (I 99 1 ).
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Journal ojSemantia 9: UJ-250
© N.I.S. Found arion ( 1992)
Default Logic: Towards a Common Logical Semantics for Presuppositions and Entailments R O BE R T E. MERCER
University of Western Ontario
Abstract
I
I NT RO D U C T I O N
Many ways have been suggested ro address the inadequacies of classical logic to deal properly with the concept of natural language presuppositions. The main � contenders are the cancellation methods exemplified most recently by Gazdar (1 979) and Soames (1982), the discourse view proposed independently by Heim ( 1 983) and van der Sandt (1988), the multiple negation approach resurrected by Seuren (1985), and the computational approach ofGunji (1982). Here, we focus on the cancellation paradigm. By ignoring the other views, we do not suggest that there are no interesting comparison� to be made. However, since they are significantly different, any discussion is inappropriate here. The cancellation paradigm can be divided into subparadigms. The earliest and most basic case is the projection method proposed in various forms in Karttunen ( I 97 3, 1 974) and Karttunen & Peters ( I 979). Here, projection rules are used to cancel 'presuppositions'1 so that the sentence does not inherit unwanted 'presuppositions' from its subparts. Gazdar ( 1979) proposes a cancellation method based solely on consistency. The actual details of this method are not important for this discussion. Although not usually conceived as such, it can be viewed as being a projection method in the sense that the
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Presuppositions and entailments play an important role in determining the meaning of a natural language utterance. Considered as inferences, presuppositions and entailments can be derived from appropriate logical representations of the uttered sentence, the background real world knowledge, and knowledge concerning conversational principles. Presuppositions are conjectural or defeasible in nature, and entailments are deductive. In this paper we describe the application of Default Logic proof theory (which includes First Order Logic proof theory) to the generation of presuppositions and entailments. Classical logic, which can generate the entailments, is enhanced with default rules which capture the linguistic knowledge required to produce the presuppositions. The similarities and differences between presuppositions and entailments when considered as inferences are discussed. We also show that the Default Logic paradigm, in addition to generating the appropriate presuppositions and entailments, has explanatory power
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Towards a Common Logical Semantics for Presuppositions and Entailments
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method uses one trivial projection rule which projects, unchanged, all the 'presuppositions' from the subparts. So, Gazdar's method first projects, then cancels inconsistent 'presuppositions'. Soames (1 982) reverses this order. His method first cancels inconsistent 'presuppositions', then uses a superset of the Kartunnen & Peters projection rules to cancel any remaining unwanted 'presuppositions'. Rather than proceeding in this manner, we instead wish to view the concept of presupposition with a slightly different focus. We want to investigate the view that a presupposition is a type ofinference2 that can be generated from an utterance.3 By doing so, our attention is shifted to studying the properties of the more abstract inference operator. We see many potential gains by doing this. Obviously, the forthcoming method for generating presuppositions of natural language sentences will be less ad hoc than the previous methods. Having a well-principled foundation always provides general procedures for producing the desired end results. Here, the gains are seen in a general proof-theoretic operator to generate the presuppositions from an utterance together with a particular variety of model-theoretic semantics which gives meaning to the presupposition concept. In addition, by forcing the inferential view onto presuppositions, we can better understand the similarities and differences between the entailment relation, captured by the well-studied proof theory and model theory of classical logic, and the presupposition relation which will be discussed later. The logic paradigm has always been well represented in linguistic semantics. Recently, there has been a strong move toward the representation of the syntactic elements of language in logic, also. What we present here would indicate that if we expand our notion of logical inference to include other forms of inference (non-monotonic inference in this case), certain segments of linguistic pragmatics can also be brought under this unified logical view of linguistics.4 Although we wish to view these semantic and pragmatic relations as inferences we do not want to divorce the inference view from the projection view. As a matter of fact, the inference view has its roots in the early cancellation methods, Gazdar's in particular. In addition, the inference approach can be viewed as a projecti�n method which (trivially) projects all of its presuppositional objects. Where it differs from the other projection methods is in the kind of object projected: rather than a precomputed (extensional) object, which is referred to above as a 'presupposition', the objects are uncomputed functional (intensional) objects. Another way to view the difference between the projection methods and the inference approach is that the former are attempts to implement the latter. Understanding why they have failed is an important consequence of studying the inference approach. Some views along this line can be seen in Mercer (1 987). However, the connection
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2.
2.1
S O ME P RE L I M I N A R I E S
Entailments and presuppositions
Entailments of a natural language utterance are those inferences derivable from the utterance which are true whenever the sentence is true. Presuppositions are those inferences, generated from a number of linguistic contexts, which pass a negation test, that is, being implied by the context and the preferred (or natural) interpretation ofits simple negation. Those contexts, lexical and syntactic, which pass the negation test can be called presuppositional triggers . Although entailments occur in situations other than presuppositional triggers, all of the examples of entailments discussed here will be in connection with presuppositional triggers.
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should not be lost viewing the two inferences, entailment and presupposition, as the-inheritance of the meaning of subparts of a sentence by the sentence as a whole, so long as the inheritance stays true to the inference operator, can be a valid and oftentimes more appropriate way to implement the more general inference operator. We have a number of motivations for approaching the study of entailments and presuppositions in the manner that we are about to discuss. Our motivation is to tie the notion of presupposi�on to the classical negation operator. Part of this motivation arises from wanting to deal with the problem of negation by handling the classical negation in a different manner rather than dealing with this problem by trying to fix the negation operator in a more direct fashion. Another part of the motivation arises because this research arose in the knowledge representation area of Artificial Intelligence and the tools that we have require classical languages. Tying presuppositions to classical negation has been accomplished. We are also motivated by the desire to have a common (logical) semantic framework for the two relations. We have been partially successful. The major problem lies with our having to extend Default Logic to deal with (linguistic) disjunction properly. Although there are reasonable model theoretic semantics for Default Logic, there are none for this extended version. So, we indicate what properties a semantics for an extended Default Logic would need to provide the appropriate semantics for presuppositions and entailments. A more ambitious and longer-term goal is a compositional semantics for both inferences. Before turning to the discussion of the technical aspects of a Default Logic approach to solving the problem of correctly deriving the presuppositions of sentences, focussing mainly on the complications created by 'or' and 'if. . then ', a brief discussion of some background issues is required: a short discussion of entailment and presupposition, the two phenomena of interest; the representa tion of the utterance, focussing in the representation of negation, in particular.
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Sentences ( 1)-(4) demonstrate some prototypical examples of presuppositions produced by the following presuppositional triggers, respectively: noun phrases, factive verbs, aspectuals, and definitions of words. In each of these examples the truth of the affirmative a-sentence implies the truth of the c-sentence, that is, the c-sencence is an entailment of (is entailed by) the a-sentence. The truth of the negative b-sentence normally implies (the truth of the preferred interpretation of the b-sentence always implies} the truth of the c-sentence, that is the c-sentence is a presupposition of (is presupposed by) the b-sentence. b. c.
(2) a.
b. c. (3) a. b. c.
(4) a. b. c.
The present king ofBuganda is not bald There exists a present king ofBuganda. Mary regrets that Fred left. Mary does not regret that Fred left. Fred left. (At time t), John stopped beating the rug. (At time t),John did not stop beating the rug. (Prior to time t ), John had oeen beating the rug. My cousin is a bachelor. My cousin is not a bachelor. My cousin is a male adult.
There are natural means to indicate chat a simple negation is not to be interpreted normally. The method used is to make at least one of the normal (presuppositional) inferences inconsistent. There are linguistically natural means, examples of which for each of the sentences ( 1)-(4) are given in (s).
(s) a. The present king ofBuganda is not bald; Buganda is a republic. b. Mary does not regret that Fred left because he didn't leave. c. John did not stop beating the rug because he hadn't started. d. My cousin is not a bachelor. He is only three years old.
In addition, inconsistencies arising from knowledge about the world can override the normal interpretation of negative sentences. The following example provides an instance of a normal (presuppositional) inference being prevented by information contained in the non-linguistic context. Suppose that both Bill and Jim know that Bill's cousin is a-three-year-old. They want to go to a bachelor party tonight but Bill must babysit his cousin. In response to Jim's question, 'What are we going to do with your cousin?', Bill utters (6), in a sense meaning that the cousin wouldn't be able to go to the party. In this case Jim would not make the normal (presuppositional) inference that Bill's cousin was an adult because the non-linguistic context, known to both Bill and Jim, contradicts this inference. ·
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( 1 ) a. The present king ofBuganda is bald.
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(6) My cousin is not a bachelor.
(7) Mary stopped beating the rug or John stopped beating the egg. (8) My cousin is a bachelor or (my cousin is) a spinster. (9) If Fred left, then Mary regrets it (Fred's leaving). How are these seemingly unconnected presuppositional phenomena to be explained? That presuppositions arise from lexical and syntactic contexts is no longer a source of disagreement. However, the projection problem -how does a complex sentence (sentences (5)-(9) are examples) inherit the 'presuppositions' of its parts-has been a major source of disagreement. Most of the debate has centred around the appropriate system for producing the correct presupposi tions for these sentences. The purported solutions have all been structural in nature: Given a tree-like structural description of the sentence and the 'presuppositions' of the leaf nodes, which get recursively inherited by the parent nodes? The three kinds of inheritance (already introduced in the introduction) have been: a set of rules that take the presuppositions of the clauses and remove the undesirable presuppositions as the sentence meaning is being composed (Karttunen 1 973, 1 974), Karttunen & Peters ( 1 979); a set of rules, invoked after all of the leaf-node 'presuppositions' have been inherited, that cancel the inconsistent ones (Gazdar 1979); or a method which is a consistency cancella tion step followed by a set ofinheritance rules (Soames 1 982). The desired result in each case is to retain all and only the presuppositions of the complex sentence. Mercer (1 987) contains a discussion of these systems showing where each fails (many of the works mentioned above have similar discussions). In their place a different approach is presented. One of the major successes of this new approach, viewing presuppositions as inferences (in an appropriate logic) is to give a very simple and uniform explanation for the phenomena described above. This method is discussed below with emphasis on how it relates to the entailment relation.
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Probably the most interesting case is the projection and cancellation found in sentences combined with 'or' and 'if . . . then '. Sometimes, for example (7), these sentences display the presuppositions associated with the presuppositional triggers found in both clauses even though these are disjunctive sentences, not conjunctions. Sometimes cancellation occurs in these sentences because of inconsistencies. However, if the inconsistencies are between 'presuppositions', like in (8), then both of the conflicting presuppositions are cancelled. Finally, sometimes a 'presupposition' can be cancelled even though there is no apparent inconsistency, for example, the 'presupposition' associated with the presupposi tional trigger found in the consequent is not a presupposition of(9).
228 Towards a Common Logical Semantics for Presuppositions and Entailments 2.2
Representation ofthe utterance
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A basic model of communication is the transfer of information from a knowledge base, which we call the speaker and denote KB5, to a knowledge base we call the hearer and denote KBH. Although the model must be quite complex to capture the range of communicative acts possessed by humans, we make some simplifying assumptions for this paper. Firstly, we assume that only declarative sentences are communicated and that they are asserted, that is, the intent of the speaker is to communicate facts. Secondly, only additions to KBH will be considered. So, in this restricted setting the speaker intends that KBH is to be updated with the logical form5 of the sentence just uttered. (For our purposes, the logical form includes Gazdar's clausal quantity implicatures (see the discussion below).) Thirdly, KBH is a set of logical statements (a theory). It contains information 'known' (or believed) by the hearer. We are not trying to model communication or discourse, so the only statement known to exist in KB5 is the one just communicated. Fourthly, the semantic portion of the meaning of the sentence is represented in some semantic representation language (here we use a standard first order language) as a., say. Since the speaker must know6 that a is true, this part of the pragmatic portion of the meaning of the utterance is captured as K5a , where K5 means 'the speaker knows that'? Occasionally, the utterance also indicates that some parts of the utterance, although not entailed by K5a , must be possible, as far as the speaker is concerned, otherwise the speaker would have generated a different utterance. Gazdar ( 1 979) argues that if a speaker were to utter a compound sentence having a constituent which is not itself (or its negation) entailed or potentially presupposed,8 then the speaker would be in breach of Grice's maxim of quantity ifhe knew that sentence to be true or false, but did not indicate to the listener that it was so, since the speaker could have been more informative by producing a compound sentence having the constituent concerned (or its negation) as an entailment or a presupposition. It fqllows that uttering such a compound sentence potentially implicates9 that both the constituent sentence and its negation are compatible with what the speaker knows. They are called clausal quantity implicatures . It follows from this argument (and the formal definition of clausal quantity implicatures (see Gazdar I 979: 6 I )) that the sen tences 'A or B ' and 'IfA then B', where 'A ' and 'B ' are not compound, have the potential clausal quality implicafures P5A , P5 ...,A , P5B , and P5 .....,B . P5 means 'for all the speaker knows it is possible that '. P5 = ....., K5....... If u is the sentence uttered and a is its semantic representation, then I will use the notation G(u) to represent K5a and the clausal quantity implicatures generated from u. Thirdly, a hearer's interpretation of an utterance should include the inferences that can be generated from the sentence uttered, knowledge about the world, and knowledge about language use. So, if the KBH
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contains knowledge about the world and, for our purposes here, default rules representing the hearer's linguistic knowledge about presuppositions, then the inferencing can be captured by taking the logical closure 1 0 of KBn u { G(u)J. If Default Logic proof theory is used as the logical closure method, certain technical problems arise, including generating the complete range of presup positions from disjunctive representations and the inclusion of modal operators in KBn. The method to derive the non-modal cases of KBn is given in section J.J .2. A more complete discussion, including the motivation and justification of this procedure can be found in Mercer ( r987).
Representing natura/ language negation
Classical representation problems are caused by negation. The problems occur because the standard method of negation in the representation language (I am assuming first order logic) does not correspond to the preferred interpretation of negation in natural language. These problems are exemplified in (w). The affirmative sentence (wa) is represented in (wb). The sentence (we) is the negation of the affirmative sentence. Although the negation of ( wb) is given in ( wd), the 'usual meaning' of (we) is more closely represented by (we). On the other hand, (wf) cannot be represented by (roe). (w) a. The present king ofBuganda is bald. b. 3x . King-cif-Buganda (x) 1\ Vy(King-cif-Buganda (y) � x y ) 1\ BALD (x ) c. The present king ofBuganda is not bald d. -.3x . King-ofBuganda (x) 1\ Vy(King-cif-Buganda (y) � x - y) 1\ BALD (x ) e. 3x. King-cif-Buganda (x) 1\ Vy(King-cif-Buganda (y) � x = y ) 1\ -.BALD (x ) ( The present king ofBuganda is not bald because there is no king of Buganda. =
There are two approaches to solving the representational problems caused by negation in natural language. The orthodox view is to say that negation is (syntactically or lexically) ambiguous between two or more representations. What seems to be an insurmountable problem for this view is to provide the means to decide which representation to use in different situations. The heterodoxy is to say that negation is vague , that is, there exists only one representation which is true under more than one set of truth conditions. Proponents of the heterodox view include Kempson ( 1 97 5 ), Wilson ( r 97 5 ), Atlas ( r 977), Gazdar ( 1 979), and Mercer ( r 987). In this view sentence (we) has the single representation given by (rod). The problem for this view is that while the representation allows for multiple interpretations, Grice's Principle
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2.3
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Towards a Common Logical Semantics for Presuppositions and Entailments
3 GE NERAT I N G ENTAILMENTS A N D PRESUPPO S I T I O N S I N DEFAULT L O G I C We consider presuppositions and entailments of a sentence as inferences obtained from the logical (or semantic) representation of the sentence together with other forms of background knowledge. As concerns presuppositions, this view differs with all previous cancellation methodologies (Gazdar 1 979;joshi & Weischedel 1 977; Karttunen 1 973, 1984; Karttunen & Peters 1 979; and Soames 1 982). Although there is no complete agreement concerning entailments, the inference model has broad acceptance and has been well studied. For these reasons the discussion that follows concentrates on the concept of presupposi tion, whereas discussion of entailment is limited to those aspects which lead to the discussion of similarities and differences with presupposition. A standard inferential view of entailment is the following: Given some background knowledge, r, a sentence S' is an entailment of a sentence S when S is presented in the context of the background knowledge if and only if S ' is deducible from r v {S} and not deducible from r. The use of an example
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of Cooperative Conversation (Grice 1 975) commits the speaker to using an utterance that should allow the hearer to generate the correct interpretation, that is, the one corresponding to the interpretation for (we). Choosing the more general (wd) to represent (we) immediately prohibits the use of first order logic to derive the preferred interpretation for the following reason. ( 1oe) is not a logical consequence of (1od) in first order logic and if (1od) were supplemented with a set of axioms that allowed the derivation of (we), an undesirable consequence would be that the presupposition of (we) would be logically valid or they could be derived from the set of axioms (that is, they would be unconnected to the utterance). The other requirement, that the derived interpretation is only preferred and that one of the other possible interpretations is to be chosen if there is sufficiently clear indication to reject the preferred interpretation, also prohibits the use of first order logical techniques to derive the preferred interpretation. Since first order logic is monotonic the preferred interpretation would always be derivable. However, the other interpretations are inconsistent with the preferred interpretation. Given the semantic notion of entailment, we have standard logical methods to generate the appropriate inferences. Given the pragmatic notion of presupposition, since the inference must be conjectural and the rules of inference must be defeasible, non-standard methods are required. Default Logic has been used to capture the required inferencing abilities. The next section discusses these techniques focussing on the problem of generating the correct presuppositions.
Robert E. Mercer 2 3 1
should be sufficient for our purposes. Let us first examine a definition of the property of being a bachelor. 1 1 For our purposes here let us assume that a 'bachelor' is 'an unmarried male adult'. This can be logically represented as ( I I).
( I 1 ) Vx. BACHELOR (x ) MALE (x ) 1\ ADULT(x ) 1\ -.MARRJED (x ) =
In the situation in which 'My cousin is a bachelor. ' has been uttered, and the logical form created maps 'bachelor' into the predicate 'BACHELOR ' and 'my cousin ' onto the constant c 1 , the representation of the sentence would be that given in ( I 2).
( I 2) BACHELOR (c1 )
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If this sentence has been uttered in the context of the background knowledge given in ( 1 1 ), then using standard deductive techniques each of the conjuncts on the right-hand side of universal statement properly instantiated to c1 can be derived as entailments. These inferences correspond to the sentences 'My cousin is male. ', 'My cousin is an adult. ', and 'My cousin is not married. '. Given the knowledge-based and inference-based paradigm that underlies the production of entailments and presuppositions, we are provided with a straightforward notion of the entailments of a sentence in a context. Given that the sentence is uttered in a conversational context which assumes some background informa tion (for example, meanings of words and knowledge about the world), the entailments of the sentence (in this context) are those sentences that can be derived from the set of logical statements representing the union of the sentence uttered and the background assumptions using the normal deduction operator (which is found in Default Logic since Default Logic subsumes First Order Logic). Joshi & Weischedel (I977) and Weischedel (1 979) describe a computational incarnation ofKarttunen's method. Although we present a generalized view of entailments and the procedure to generate them, this view should not be interpreted as a disagreement in prif.1ciple with other methods such as the tree transformation method used in Joshi & Weischedel ( 1977) and Weischedel ( 1 979) for computing the entailments that are discussed therein. Our point here is to indicate that there exists an underlying strategy for explaining the full range of two types of inference. The underlying strategy uses a generalized form of inference for producing these inferences. We are not suggesting that the inference procedures need be implemented as a generalized procedure. There may exist computational 'shortcuts' for subclasses of entailments, exemplified by those discussed in these two papers. The knowledge of these computational shortcuts could be located in the lexicon or with the syntactic rules. However, these issues are better left to those theories whose purpose is much more closely connected to implementation. The negation 'My cousin is not a bachelor. ' has a disjunctive representation.
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None of the entailments of the previous sentence is an entailment of this sentence. A number of truth conditions make this negative sentence true. One of the truth conditions, the preferred interpretation , has special status. What have been called the 'presuppositions', 'My cousin is an adult. ' and 'My cousin is male. ', are true and what has been referred to as 'what is said', 'My cousin is not married. ', is also true. By placing the concept of presupposition in a pragmatic theory we are able to define a context-sensitive method to choose the preferred interpretation of a semantically vague logical representation of a natural language sentence. Semantic theories are insensitive to context and they are incapable of disambiguating semantically vague logical forms. There are a number of ways to cancel a presupposition, but in all cases the reason is related to some property of r u {S}. Firstly, the context provides information that directly contradicts what would be presupposed by the sentence if the context did not contain the contradictory information. For example, ' That person is not a bachelor-he's only five years old. ' is an instance of this form of cancellation. Secondly, given Grice's Maxims for Cooperative Conversation, certain inferences can be generated from the utterance that indicate that some presupposition normally generated by a presupposirional trigger found in the utterance is to be cancelled. For example, 'My cousin is a bachelor or a spinster. ' does not presuppose 'My cousin is male. ' nor is 'Mycousin isfemale. ' presupposed. Grice's maxims indicate that the speaker must be allowing for the possibility of both bachelorhood and spinsterhood for his cousin. If the sentence presupposed that 'My cousin is male. ' then it would be impossible that my cousin could be a spinster: Similarly for female. Thus the sentence does not commit the speaker to either of the inferences that would be licensed if the sentence were 'My cousin is a bachelor. ' or 'My cousin is a spinster. '. This also occurs in sentences like 'IfFred left, then Mary regrets it. '. Here, the antecedent suggests that it is possible that 'Fred didn't leave. ', which is exactly the presupposition that would normally arise from the consequent. Lastly, for technical reasons (such as the uncancellability of entailments by future discourse) entailments are not considered to be presup positions. Our theory addresses this comment directly by proposing default rules as the representational device needed to capture the essence of presuppositions. The default rules are context-sensitive because there are means to block the firing of rules. The logical form of the sentence uttered, in particular, the logical form of sentences of the form 'A or B' or 'ifA then B provides part of the context in which the default rules are appropriately applied. The particular logical form chosen is strongly influenced by Gazdar's theory, in particular the commitment of the speaker to knowing the truth of the sentence uttered and the use of what Gazdar calls clausal implicatures. The clausal implicatures are a result of Gazdar's formal treatment of Grice's conversational principles (Grice 1 975).
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J . I A short introduction
to Default Logic
A normal default rule is a rule of inference denoted a (x) : {J (x) fJ(x) where a (x) and {J(x) are all first order formulae whose free variables are among those ofx = x 1 , , xm . Intuitively, a default rule can be interpreted as: For all individuals x 1 , , xm , if the prerequisite a (x) is believed 1 2 and if {J (:X) is consistent with what is believed, then the consequent {J (x) may be conjectured. For the purposes of this paper, the interpretation of the default rule will be seen to mean: if'a (x)' is possible for the speaker and {J (x) is consistent with the appropriate logical closure of the hearer's knowledge base, KBH, then the hearer can conjecture {J(x). The default rules require some extra information to guard against inappropriate use of the default rules. Since presuppositions arise only from particular lexical and syntactic triggers, the existence of these triggers must somehow be taken into account. One method is to represent this extra information as a conjunct in the prerequisite of the default rule. This conjunct is true only if the syntactic analysis finds the appropriate presuppositional trigger. Except for this technical aspect this extra information plays no role. • • •
• . •
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The sentence uttered by a speaker commits the speaker not only to the truth of the sentence but also to the possibility of its clauses (its parts). So in the case of the speaker uttering 'A or B ' or ' if A then B ', unless there is background knowledge or there are linguistic reasons to prevent it, the speaker is committed to P5A , P5 A , P5B , and P5 -.B . These implicatures will provide the means for translating the modal logical form into a non-modal form for use in the default theory or theories in the case of sentences of the form 'A orB', or 'if A then B'. We prese�t an introduction to our theory ofpresuppositions, the foundario� of which is Default Logic. This theory is partially based upon the ideas of Wilson (1975), Kempson (1975), Atlas ( 1 977), and Gazdar (1 979). It differs from this previous work not only in its including Default Logic as a fundamental notion in the definition of presupposition but also in its generating certain linguistic features as side-effects of the logic rather than including these same features directly in the top-level linguistic theory. The first point indicates the possible importance of nonmonotonic reasoning in the realm of linguistic pragmatics. The second point demonstrates that this synergism of linguistics and nonmonotonic reasoning can provide explanatory power unavailable in the prior linguistic theories. We provide an introduction to this explanatory power by showing a close connection between the definitions of entailment and presuppositions.
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Since it creates long default rules and the examples can be understood without it, I have left it out of all the examples. For further details see Mercer ( 1 987). A default theory , IJ., is composed of a set of first order formulae W, and a set of default rules, D. The defa ult rules can be viewed as extending the first order formulae with the consequents of the default rules. An extension , E, of a closed default theory is a fixed point having the following properties. r. 2.
A normal default theory is a set of first order formulae together with a set of normal defaults. An extension of a normal default theory is the deductive closure of the set comprised of the first order formulae and some maximal set of consequents that are consistent with the extension. Normal default theories alw
IJ. 1
=
I
=
=
I
f
A , -.B , A�· -. C , · D has one extension £1 - Th ({A , -.B , -. C, D}). C D
Example
IJ.2
1
2
I
-.A , · -.B A V B , ·· has two extensions E2•1 - Th ({A , -.B)) and Ez.2 · .....,A -.B 11z ({-.A , B)).
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3-
W�E if E I- a , then a E E (E is logically closed, that is, Th (E) - E , where Th is a fixed point operator defined by 1-) a (x: f3 (x) e D , if a (x ) E E, and -.p(x ) � E ,then f3 (x ) E E for each default, f3(x)
Robert E. Mercer
Example
113
=
l
3
235
i
A : -. C-::;c- , : B has one extenswn . E3 = Tn''- ({A , -.B, -. q). A , A :::> -.B, ---B
The consequent of the default rule,
=; , cannot be in any extension because its
justification -.B is inconsistent with a statement that can be derived with only first-order inference rules (B can be derived from A and A :::> -.B using modus ponens).
3 .2
Representing presupposition using default rules
The discussion that threads itself through the remainder of this paper uses definitions of 'stop ', 'regret', 'bachelor' and 'spinster'. Stopping an event means that the event had been occurring and that the event has ceased, regretting an event means that the event has occurred and the event is regretted, a bachelor is an unmarried male adult, and a spinster is an unmarried female adult. Under normal circumstances it is said that the negation of 'stopping an event ' presupposes that the event had to be happening, the negation of 'regretting an event' presupposes that the event has happened, the negation of the term 'bachelor' presupposes that the individual being referred to is a male adult, and, similarly, the negation of the term 'spinster ' presupposes that the individual being referred to is a female adult. There exist situations in which the presuppositions associated with these triggers do not survive. In the following example e represents an event, and t1 and t2 are time parameters meant to represent times relevant to the event, e . Although the representation of 'stop ' given in ( 1 3) does not capture its complete meaning, I assume here that this definition is sufficient for the present discussion. Paraphrasing ( 1 J), an event stops if and only if there is a time, 11, at which the event was being done and a later time, t2, at which the event was not being done. By a simple wide-scoped negation of(1 3) the definition of'notstop ' given in (14) can be generated. In addition to the usual definition of 'not stop ' given in (14), the default rule ( 1 s) also supplies part of the meaning of 'not stop '. This default rule plays a crucial role in generating the preferred interpretation of'not stop '. The LF predicate is used to prevent the default rule from being used except in those cases in which the predication ofSTOP to the event e arises directly from the linguistic form, that is, the sentence.
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Being a logic, along with the syntax goes a proof theory. For the purposes of this paper all that needs to be known about the proof theory is that if f3 is in some extension then there exists a default proof of f3 .
236 Towards a Common Logical Semantics for Presuppositions and Entailments
( 1 3) STOP(e) = 3t1 3 t2. t1 < t2 1\ DO (e, t1) 1\ -DO(e, t2) ( 1 4) -. STOP(e) = 'r:Jt1Vtz. -. (t1 < tz) V -. DO (e , t1) V DO (e , tz)
( I S ) -. STOP(e) 1\ LF(STOP, e ) : 3t . DO (e , t ) 3t . DO (e , t)
In order to capture the knowledge about factive verbs, such as 'regret ', the axiom ( 16) and the default rule ( 1 7) are used. In these two rules 13 � is any proposition.
�
For purposes of all the following examples, the definition of 'bachelor' is represented by the first order sentence (1 8). Then the negation of 'bachelor' would be represented by ( 1 9). Similarly the definitions of 'spinster', and its negation, are given by (2o) and (2 1 ), respectively.
( 1 8) ( 1 9) (2o) (2 1 )
'r:Jx . BACHELOR (x) = MALE(x) 1\ ADULT(x) 1\ -.MARRJED (x) 'r:Jx. -.BACHELOR (x) = -.MALE(x) V -.ADULT(x) V MARRIED (x) 'r:Jx . SPINSTER (x) = FEMALE (x) 1\ ADULT(x) 1\ -.MARRJED (x) Vx . -.SPINSTER (x) = -.FEMALE(x) V -.ADULT(x) V MARRIED (x)
We add more information about the meaning of the lexical item in question. This extra information concerns the presupposed parts when the lexical item occurs in the scope of a negation. This extra information takes the form of default rules and implicitly adds a new form of inference, as well. So, for example, we add to the representation of' bachelor' the two default rules (22) and (23). Similarly, we have two default rules (24) and (25). (22)
-. BACHELOR (x) 1\ LF(BACHELOR , x) : MALE(x) MALE(x)
(2 ) -. BACHELOR (x) 1\ LF(BACHELOR , x) : ADULT(x) J
(24)
·
ADULT(x)
-. SPINSTER (x) 1\ LF(SPINSTER , x) : FEMALE(x) FEMALE(x)
(2 ) -. SPINSTER (x) 1\ LF(SPINSTER , x ) : ADULT(x) s
ADULT(x)
Using default rules provides a context-sensitive method to generate the appropriate presuppositions. A presupposition of a preferred interpretation of a simple sentence can be viewed as the consequent of a default rule and the
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( 1 6) 'r:Jx . REGRET(x, � ) :J � ( I 7) -.REGRET(x ,�) 1\ LF(REGRET, x,�) :�
Robert E. Mercer
2. 3 7
preferred interpretations of vague linguistic forms are then inferences made . using these assumptions. 3·3
The generation method
3 · 3 · 1 Generating entailments and presuppositions in simple sen-
tences
We split the discussion of the generation method into two parts, simple sentences and complex sentences, only because the discussion of the use of clausal quantity implicatures is better motivated in the complex sentence case. This discussion occurs immediately following the presentation of the simple sentence case below. It is an important feature ofthe Default Logic method that the method for computing entailments and presuppositions in simple sentences is an application of the same rules used for computing these inferences in complex sentences. Suppose that a speaker, S, utters (26). According to the rules of the communication act given in section 3.2, the hearer can interpret this utterance as (27). The resulting default theory, � 1 , shown in Figure I , represents KBH u {(27)] after it has undergone case analysis (see section 3·3-4)· (28) can be derived from � 1 using the ordinary deductive proof theory of First Order Logic.
ll
1
_
l
STOP(BEA TUolm . r1)) STOP(e) = 3t13t2• t1 < t2 1\ DO(e, t1) 1\ �DO(e, t2) �STOP(e) : 3 t . DO (e, t ) 3 t . DO (e , t ) .
Figure
I
A default theory for 'john stopped beating the rug. '
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I assume throughout this paper that the speaker's utterance has undergone the first phase of the interpretation process which generates a semantic representa tion (logical form) of the sentence uttered. This semantic representation will be a well-formed sentence in a first order S4 modal language containing a countably infinite set of predicate symbols, constant symbols, and variable symbols, plus the logical symbols, /\, V, :::), --., K5, and P5. The two modal opera tors are to be interpreted as 'the speaker knows that' and 'for all the speaker knows, it is possible that', respectively. Although there is no general method known to generate this representation, some general rules can be followed. Any sentence with an explicit negation is translated into the widely scoped negation of its affirmative counterpart. Any compound sentence is mapped clause by clause into a logical form, each clause being tteated as a sentence.
238 Towards a Common Logical Semantics for Presuppositions and Entailments
(26) John stopped beating the rug. (27) KsSTOP(BEAT(john , r1 ) ) 1 4 (28) 3t. DO (BEAT(john , r1 ), t)
�2
l
_
�STOP(BEATUolm , r1)) �STOP(e) = ':Jt1':Jt2. �(t1 < t2) V �DO(e, t1) �STOP(e) : 3 t . DO(e,t) 3t.DO (e , t )
V
DO (e, t2)
l
Figure 2 A default theory for 'john did not stop beating the rug. '
(29) (3o) (3 1 ) (3 2)
John did not stop beating the rug. Ks -. STOP(BEATUohn , r1)) 3t. DO (BEATUolm , r1 ), t ) 3t. DO (BEA TUohn , r1 ), t) A Vt' . t < t' :J DO BEATUohn , r1 ), t')
On the other hand, the speaker can use the 'because '-clause in (33) to indicate the extra qualification represented in (3 I ) which is added to �2, to give �2• which is shown in Figure 3· Neither (3 I ) nor (32) can be derived from the theory generated by this utterance, given in �3. Any derivation of (3 I ) must include a successful invocation of the default rule ( I s ). But in the default theory, �3, invocation of this rule is blocked by the sentence (34). 1 5
�3
_
l
�STOP(BEA TUolm , r1)) 1\ ':Jt. � DO (BEA TUohn , r1), t )) ':Je. � STOP(e) = ':Jt1':Jt2. (t1 < t2 1\ DO(e, t1)) => DO (e, t2) �STOP(e):3t.DO(e, t ) 3 t . DO(e, t )
l
Figure 3 A default theory for 'john did not stop beating the rug because h e was never doing it. '
(33) John did not stop beating the rug because he was never doing it. (34) Ks V t . -. DO (BEATUohn , r1), t )
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Suppose that a speaker, S, utters (29). According to the rules of the communica tion act given in section 3.2, the hearer can interpret this utterance as (3o). The resulting default theory, �2, shown in Figure 2 represents KBH u {(3o)} after it has undergone case analysis. Both (3 1 ) and (32) can be derived from �2 using Default Logic Proof Theory. (3 I ) represents the presupposition of (29), (32) represents the preferred interpretation, which can be paraphrased as there is some time at which the event BEAT (John , r1 ) was being done and it continues to be done at all future times.
Robert E. Mercer 239
3.3.2 Choosing the cases for the case analysis
'
T
=
{Ks(A V B ), P5A , P5 -.A , P5B , P5 -.B , a1,
•
•
•
, am, o1,
•
•
•,
on}
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Because presuppositions do arise from the clauses of complex sentences joined by linguistic disjunctions and conditionals, to be considered complete, the method proposed here must be able to make inferences in the presence of logical disjunctions and conditionals. Since Default Logic proof theory does not display any analogue to the law of the excluded middle (the antecedents of the default rules must be provable and there is no equivalent to the deduction theorem), some form of analysis by cases is required. This should not be considered as a weakness of the Default Logic method. Because the linguistic disjunction and conditional cannot be equivalent to the logical disjunction and conditional, respectively (we must be able to distinguish between the linguistic and the logical 'or', otherwise the problem of all presuppositions being logically valid disappears), even those methods for default reasoning which deal directly with logical disjunction and conditional will need the extra representational machinery described below (or something similar). Since a statement is provable in a case analysis only if it is provable in all cases representing the statement, the generation of the cases is critical. As in the case of a first order theory, too few cases would allow incorrect statements to be proved. In addition because of the context-sensitive nature of default logic, having too many cases or having inappropriately defined cases could prevent the desired statements being proved. In general the choice of cases must reflect two principles. Since the case analysis is a proof theoretic analogue of the model theoretic law of the excluded middle, each case must completely determine the truth values of each of the disjuncts found in the statement to which case analysis is being applied. Also, since the case analysis is justified solely on linguistic grounds (see Mercer I 987 for further discussion), the cases must reflect this linguistic situation. To justify a case, the possibility of the statement that distinguishes the case must be provable from KBH v {G {u)}. In addition to the speaker knowing the truth of the utterance, the communication act (according to Gazdar's formal treatment of Grice's conversational principles (Grice 1975)) normally commits the speaker to the possibility of its clauses and their negations. These clausal quantity implicatures are derived directly from the semantic representation of the natural language sentence. For example, in the case of the speaker uttering 'A orB ' or 'if A then B , unless there is background knowledge or there are linguistic reasons to prevent it, the speaker is committed to PsA , Ps -.A , P5B , and Ps -.B . An example should clarify these ideas. Suppose the sentence 'A or B' is uttered. The updated hearer's knowledge base KBH v {G {'A or B ')} would be
240
Towards a Common Logical Semantics for Presuppositions and Entailments
In this example a1, , am represent the appropriate first order statements and 0 1 , . . ., on represent the appropriate default rules representing the hearer's knowledge before the utterance, P5A , P5 -.A , P5B , P5 -.B are the clausal quantity implicatures, and K5 (A V B ) is the pragmatic information about the semantic representation of the uttered sentence. Since A 1\ -.B and -.A A B completely determine (that is, determine the truth values of both ) A and B , and since the statements P5 (A 1\ -.B ) and P5 (-.A 1\ B ) can be derived, A 1\ -.B and ..., A 1\ B distinguish the two cases. Note that although P5A , P5 -.A , P5B , P5 ...:., B are all derivable, none of A , -.A , B , -.B is a candidate for distinguishing a case because, individually, none of them completely determines the truth values of both A and B. Hence the two cases of the original theory, KBH u { G ('A or B ')} , are •
•
{A 1\ -. B ' a t , . . ., am, 01, . . ., On} { A 1\ B ' a t , . . ., am, 01, . . ., on} - -. -
As an example of this situation, the sentence 'My cousin is a bachelor or my teacher is
a spinster. ' would generate a case in which 'my cousin is a bachelor' and 'my teacher is not a spinster' are true and a case in which 'my cousin is not a bachelor' and 'my teacher is a spinster' are true. Both cases would contain first order statements providing the definitions of bachelor and spinster as well as the default rules that generate male and adult for bachelor and female and adult for spinster. The simple negated sentence, an example of which is presented in section J.2, is just a special instance of the case analysis procedure. In the simple negated sentence, -.X (which is represented as K5 ....., X), the possibility of the only case (distinguished by -.X) can be proved using the utterance and the theorem I- K5 ....., X ::::> P 5 ...... X .
3 · 3 · 3 A proof-theoretic definition o f presuppositions 1: Let u be a sentence uttered by a speaker, S, in accordance with Grice's Maxims ofCooperative Conversation. Let KBH be the hearer's knowledge base bifore the utterance, and let the defoult theories lluease t ' . . . , llueasen 1 6 be thefirst order cases ofthe theory KBH u { G (u)}. A sentence a is a presupposition n ofu with respect to KBH ifand only if
Definition
(i) 6uease i I-6 a and a E Th ( CONSEQUENTS{D}), for i = (ii) KBH u { G (u)} If a , (iii) KBH If6 a , (iv) 6ueaser. If6 ....., a , for i = I , . . ., n .
I,
.
. ., n ,
This definition can be loosely paraphrased as: if a is in the logical closure of the default consequents and is provable from the utterance, and all proofs require
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llA or Ilcasel ll A or Ilcase2
•
Robert E. Mercer
24 1
the invocation of a default rule and in the case of multiple extension default
theories, a is in all extensions, then a is a presupposition of the utterance.
3 · 3 ·4 Generating entailments and presuppositions in sentences
combined with logical connectives The discussion in section 2 indicates that section (35) has the conjunction of all
the presuppositions that its two disjunctive clauses would have if uttered in
isolation. The derivation procedure given below indicates the default proof
theory approach to deriving presuppositions in complex sentences.
Mary stopped beating the rug or John stopped beating the egg.
In the same manner that was described in section Figure 4, is the
KBH v {K5u}
3-2, T4, which is displayed in (3 5) being uttered. The
produced as a result of
statements in T4 are the representation of the sentence which includes the
clausal implicatures derived from the disjunctive sentence, the first order definition of STOP from which the definition of -.STOP can be derived, and
the default rule for -.STOP. The two statements described in (36) are derivable
from T4. The two cases ofT4 distinguished by these statements are displayed in Figures 5 and 6. Case analysis is applied to these two default theories.
(36) P5[STOP(BEAT(Mary , r1) ) 1\ -.STOP(BEAT(John , e 1 ) )] P5 [STOP(BEAT(Mary, r1 ) ) 1\ STOP(BEAT(John , e1 ) )]
K5(STOP(BEA T(Mary, r1)) V STOP(BEAT(fohn , e1))) PsSTOP(BEAT(Mary, r1)) P5--. STOP(BEAT(Mary, r1)) PsSTOP(BEAT(John , e1)) P5--. STOP(BEA T(fohn , e1)) Ve . STOP(e) ::::> 3t13t2. t1 < t2 A DO(e, t1) A --.DO(e , t2) --.STOP(e):3t.DO (e , t) 3 t . DO (e , t) Figure 4 A KB8 u ( G (u )) for 'Mary stopped beating the rug orJohn stopped beating the egg. '
ll
•. 1
_
l
STOP(BEA T(Mary, r1)) A --.STOP(BEA T(fohn , e1)) Ve. STOP(e) ::::> 3t13t2. t1 < t2 A DO(e, t1) A --.DO(e, t2) --.STOP(e):3t.DO (e , t) 3t. DO(e , t)
I
Figure 5 One case for 'Mary stopped beating the rug orJohn stopped beating the egg. '
c
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(3 5)
242
Towards a Common Logical Semantics for Presuppositions and Entailments
6,.z
_
\
�STOP(BEAT(Mary, r1)) II STOP(BEAT(John , e1)) lle. STOP(e) ::> 3t13t2. t1 < t2 11 DO(e, t1) II �DO(e , t2) �STOP(e) : 3 t . DO(e , t) 3t.DO(e , t)
I
Figure 6 One case for 'Mary stopped beating the rug orJohn stopped beating the egg. ' We will now detail the derivation as i t proceeds in the two cases. In �•. , (37) can be derived without the use of any default rules. The default rule and default
proof theory are used to generate
The conjunction of(37) and
(3 8)
gives
(39). Note that (39) is derivable using
default proof theory but not using first order methods alone.
(39) 3t.DO (BEAT(Mary, r1), t) A 3t.DO (BEAT(John , e1), t) The derivation o f( 39) proceeds i n a similar manner in case �4.2- Because ( 39) is
derivable in both cases, and because it is not derivable as an entailment it is a presupposition of (3 S ). The sentence (40) is an example of intrasentential cancellation of clausal presuppositions. In terms of the theory presented here cancellation of clausal
presuppositions is a failure to derive the conjunction of those inferences which would be derived if the disjuncts were used separately (in an appropriate context).
(40)
My cousin is a bachelor or a spinster.
The hearer's knowledge base T5, which is generated as a result of (40) being uttered, is displayed in Figure 7· The contents are the representation of the sentence which includes the clausal implicarures derived from the disjunctive sentence, the meaning posrulates and the default rules concerned with the
concepts BACHELOR and SPINSTER , and the fact that males are not females. The two statements described in (4 1 ) are derivable from T5• The two cases of T5 distinguished by these statements are displayed in Figures 8 and 9·
Case analysis can be applied to the default theories distinguished by these two statements.
(4 1 ) P5 [--.BACHELOR (c1) A SPINSTER (c1)) P5 [BACHELOR (c1) 1\ -.SPINSTER ( c 1)) We will now detail how the derivation of either presupposition of the two
clauses is prevented. MALE (c1) and
ADULT(c1)
can be derived in �5•1 using
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(37) 3t.DO (BEA T(Mary, r1), t) (38) 3t.DO (BEAT(John , e1), t)
(38).
Robert E. Mercer
243
Figure 7 A KB8 u { G (u )) for 'My cousin is a bachelor or a spinster. '
�BACHELOR (c1) 1\ SPINSTER (c1) "'x.BACHELOR (x) = MALE(x) 1\ ADULT(x) 1\ �MARRIED (x) "'x. SPINSTER (x) = FEMALE (x) 1\ ADULT(x) 1\ �MARRIED (x) �BACHELOR(x) 1\ LF(BACHELOR , x): MALE(x) MALE(x) �BACHELOR(x) 1\ LF(BACHELOR , x): ADULT(x) ADULT(x) �SPINSTER (x) 1\ LF(SPINSTER , x):FEMALE (x) FEMALE (x) �SPINSTER (x) 1\ LF(SPINSTER , x): ADULT(x) ADULT(x) "'x. MALE(x) :::> �FEMALE(x) Figure 8 One case for 'My cousin is a bachelor or a spinster. ' only standard deductive techniques. FEMALE (c1) can be derived only by resorting to default proof theory. But the default rule chat would be used to derive it is blocked because its justification is not co�istent with a fiXed point which must contain the first order derivable MALE(c 1 ). Intuitively, my cousin cannot be both a male and a female, and my cousin is male racher than female
because it is stated that my cousin is a bachelor (hence male). Because of this statement the interpretation of -.SPINSTER is forced to be one of the unpreferred ones. In ll5•2 FEMALE (c1 ) and ADULT (c 1 ) are derived by standard deductive
techniques. The blocking of the generation of MALE (c1) is done in a manner similar to the blocking of FEMALE (c1) in An
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K5(BACHELOR (c1) V SPINSTER (c1)] P5BACHELOR (c1) P5�BACHELOR (c1) PsSPINSTER (c1) P5� SPINSTER (c1) "'x.BACHELOR (x) = MALE(x) 1\ ADULT(x) 1\ �MARRIED (x) "'x. SPINSTER (x) = FEMALE (x) 1\ ADULT(x) 1\ �MARRIED (x) �BACHELOR(x) 1\ LF(BACHELOR , x): MALE(x) . MALE(x) �BACHELOR (x) 1\ LF(BACHELOR , x):ADULT(x) . ADULT(x) �SPINSTER (x) 1\ LF(SPINSTER , x):FEMALE(x) FEMALE (x) �SPINSTER (x) 1\ LF(SPINSTER , x): ADULT(x) ADULT(x) "'x. MALE(x) :::> �FEMALE(x)
244
Towards a Common Logical Semantics for Presuppositions and Entailments
�S.2 -
Figure 9 One case for 'My cousin is a bachelor or a spinster. '
Since MALE (c1 ) is derivable from b-5•1 and FEMALE (c 1 ) from b-5•2 (42) is derivable in both cases. Since the statement can be deducted from T5 using only standard deductive techniqu_e�, it is an entailment. What is important is that neither of the 'presuppositions' of the clauses is derivable and the reason for this is quite evident. In addition, since ADULT(c 1) is deducible by standard techniques, it too is an entailment
4
T O W A R D S A M O D E L - T H E O RET I C S E M A N T I C S FOR E NTAILMENTS AND PRESUPPO S I T I O NS
The analogy to entailment is obtained as desired: 'f f- a ' has the meaning that a is derivable from r using First Order Logic proof techniques only. Analogously, a presupposition as defined in Definition 1 is an appropriately constrained result of Default Logic proof techniques. Given that entailments and p resuppositions can both be defined as inferences, and that the operator used to generate the presuppositional inferences subsumes the operator used to generate the entailment relation, seeking a common logical semantics for these inferences is an· obvious next step. The semantics gives meaning to the procedure, something which the previous projection methods fail to provide. As well, we see that the objects that we are dealing with include the more normal extensional objects, together with intensional objects whose extension is generated in the correct context. The normal model-theoretic definition for entailment is given in Definition 2. A first step towards a model-theoretic definition for presupposition is given in Definition 3·
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BACHELOR (c1) 1\ -.SPINSTER (c1) ' -.FEMALE (x)
Roben E. Mercer Definition 2: A sentence a is an entailment ofan utterance �' ifand only ifa all models ofKBH v { G (u)J and is not true in all models oJKBH.
245
is true in
Definition 3: A sentence a is a presupposition ofan utterance u, ifand only ifa is true in allpreferred models ofKBH v { G (u)J but is not true in allpreferred models ojKBH and is not true in all models ofKBH v { G (u)J. The most important notion-preferred model-has been left undefined.
However, the set of preferred models ofKBH v { G (u)J is a subset of the models of KBH v {G{u)J. It is the subset of models in which negations are given their preferred meanings (if possible). Presuppositions were introduced in section
2
as the means to choose the preferred interpretation {the preferred models) of a meaning to the presupposition inference will need to formalize this notion of reducing the set of models provided by the semantic theory to a set of preferred models. Early attempts at defining a model theory for Default Logic (Lukaszewicz 1 98 5 and Etherington 1 987) view the role of default rules in the default theory as reducing the set of models of the first order axioms of the default theory. Model reduction semantics seems to be a natural semantics for presuppositions. However, this model theoretic semantics is closely linked to the proof theory. Model reduction semantics corresponds to the models of the extensions of the default theory. Although it could be considered adequate, an independently motivated semantics would be better. In addition, the common semantics that we are attempting to achieve is lost since the entailment relation mentions all models of KBH v {G{u)J. Although the entailments of u are still true in all the preferred models, this is now a much weaker statement than being true in all models. A better semantics would retain all the models of the original first order axioms of the default theory and place an ordering on them to indicate which are the preferred ones, similar to model preference semantics (Shoham 1 988). Not only does this type of semantics give us the common milieu to define both entailments and presuppositions but it also does not depend on the extensions of the default theory as an intermediate device. This latter benefit means that a more direct meaning of a default rule can be made. This has given us some optimism regarding the notion of a compositional semantics for presuppositions, that is, given the meanings for 'A' and
'B ', is it
possible to describe the meaning of'A and B ', 'A or B ', 'not A ', ' ifA then B ', etc.
'B '?
As well, a semantics, independently motivated by linguistic concerns, is much more easily obtained in a compositional setting. Here, we see that the classical set of extensional objects has been incremented with intensional objects for this composition. Although we have not settled on the final logical semantics, we still benefit from viewing presuppositions as inferences together with the related model reduction semantics. What we have gained is explanatory power. solely as a function of the meanings of 'A' and
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semantically vague representation. Any attempt to define the models that give
246 Towards a Common Logical Semantics for Presuppositions and Entailments
The case analysis proof method can be explained model theoretically. Take,
for instance, 'A or B . Take the models of A . Some are models of B, some are models of -.B. For those models in this latter group remove those which do not '
conform to the preferred meaning of -.B. Similarly for the models of B , those models which do not conform to the preferred meaning of -.A are removed.
The disjunction is just the union of the reduced set of models of A and the reduced set of models of B . This is basically what is happening in the case analysis. We can also see why conflicting 'presuppositions' that arise in clauses connected by 'or ' should both be cancelled, for instance, the bachelor-spinster
happened to be all of them. Doing the same for the models ofSPINSTER , none
is a preferred model of -.BACHELOR . Hence the disjunction is empty. The sentence has no BACHELOR-SPINSTER presupposirions. Disjunctive sentences also have another interesting property. Unless there
are reasons to suggest otherwise, 'or' is normally interpreted exclusively. So, 'or' in the sentence 'My cousin is a bachelor or (my cousin is) a spinster. ' is normally interpreted as an exclusive or. T}le _projection method implicitly requires the
'what is said/what is presupposed' dichotomy to represent the required knowledge. The first clause says that my cousin is unmarried and presupposes that my cousin is male and adult. The second clause says that my cousin is
unmarried and presupposes that my cousin is female and adult. Irrespective of the manner in which the presuppositions are handled, 'what is said', according to this analysis, is that my cousin is unmarried (exclusive) or my cousin is
unmarried which is always false. But of course, the sentence can be true. Given this situation, projection methods have difficulty with the normal exclusive
interpretation of'or' (or it must postulate the projection of the 'what is said' part before the assignment of exclusivity to the 'or'-not a reasonable solution). On the other hand, the Default Logic approach results in the logical
statement that can be read as my cousin is male, adult, and unmarried (exclusive) or my cousin is female, adult, and unmarried. The exclusive or
interpretation is treated correctly. It is interesting to note that the 'what is said/ what is presupposed' dichotomy is still maintained since some of the inferences that can be generated from the Default Logic proof are not in the logical closure of the default consequences (the 'what is said' part). The mistake of previous
theories has been to attach the 'what is said/what is presupposed' properties to the presuppositional trigger and to try to project these properties in a
compositional manner. The inference method correctly projects the function that generates these properties from the presuppositional trigger and then
generates them
in the correct context.
Lastly, the dividing line between semantics and pragmatics has eluded
definition. Here, we have investigated two relations: the entailment relation,
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sentence discussed above. For the models of BACHELOR we remove those that do not also model the preferred meaning of -.SPINSTER , which
Roberr E. Mercer
247
which is usually considered a semantic relation, and the presupposition relation, which has been argued is a pragmatic relation. In most definitions context has played an important role in differentiating semantics and pragmatics. However, from a logical point of view the notion of context is very fuzzy. The background knowledge is an unstructured entity. There is no difference between the meaning of words, facts about the world, and the physical and linguistic context in which the utterance is uttered. So, if the definition of'bachelor ' were changed, or if horses had three legs instead of four, the entailments that we would infer would be different. Hence, even semantic inferences are affected by the 'context'. So, with this problem in mind, we
presuppositions, a nonmonotonic one. The context sensitivity emerges narurally in this paradigm. The difference between semantics and pragmatics is, of course, multifaceted. This suggestion regarding the properties of the inference operator is atempting to clarify but one aspect of this difference.
s C O N CL U S I O NS In this paper we describe the applications of Default Logic to the generation of presuppositions and entailments. Two issues of significance are presented. Firstly, presuppositions and entailments are similar in that they can be considered as inferences differing in the type of inferencing procedure used to generate them. Presuppositions are generated by a nonmonotonic operator whereas entailments are produced by more conventional monotonic ones. Secondly, we also show that the Default Logic paradigm, in addition to generating the appropriate presuppositions and entailments, has explanatory power. We discuss this fearure in the context of the treatment of 'or ' and one facet of the semantics/pragmatics dichotomy.
The semantic representation of a narural language sentence can be vague (that is, it can be true under a variety of truth conditions). Because vagueness contravenes Grice's Principle of Cooperative Conversation this anomaly must
be removed. The ambiguity caused by vagueness is resolved according to prag matic rules . Because the pragmatic rules are defeasible and conjecrural in nature, they are caprured as
defoult rules . The position is taken that presupposi
tions are inferences generated from these pragmatic rules. Presuppositions are then used to generate the preferred interpretation of the vague representation. Model reduction semantics for Default Logic can provide an indirect logical semantics for the notion of reducing vagueness to obtain the preferred interpretation.
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instead suggest that it is the context-sensitive properties of the inference operator rather than the context itself that should be the focus of attention. In the case of the entailments we have used a monotonic inference rule, and for
248
Towards a Common Logical Semantics for Presuppositions and Entailments
Acknowledgements
This paper is a modified version of the paper entitled 'Default Logic and presupposition: simple sentences and beyond' presented to the Esprit Working Group 3 3 1 5 Workshop on Presupposition, Lexical Meaning, and Discourse Processes, Nijmegen, The Netherlands. Most of the modifications, including the tide, arose from ideas presented in a paper entitled 'Toward a common logical semantics of presuppositions and entailments', Proceedings ofthe International Workshop on Inheritance in Natural Language Processing, Tilburg, The Netherlands. This research was partially supported by Natural Sciences and Engineering Research Council of Canada grant oo368s3 and the Institute of Robotics and Intelligent Systems.
N O TE S
1 Scare quotes are used because one o f the main features of the Default Logic proposal is that subparts of sentences do not have presuppositions. The presuppo sition phenomenon occurs only at the sentential level. 2 Throughout this paper inference is used in a sense which includes both the more classical deductive inferences as well as difcwlt inferences. 3 Throughout this paper utterance is used to mean the sentence uttered together with the background information, such as meanings of words, knowledge about the world, and the immediate linguistic and physical context. 4 Various papers at the First International Workshop on Inheritance in Natural Language Processing (Daelemans & Gazdar 1 990) indicate that aspects of morphology and phonology may also fall imo this unified view. 5 All of the terms logical form , semantics, and semantic representation have loaded meanings in linguistics. For us, logical form means the semantic representation plus some additional pragmatic informa tion. Although we are intentionally
6
vague on what is meant by the additional pragmatic information, for our purposes here we include only the quality implica ture and the clausal quantity implica tures of the sentence as formalized in Gazdar (1 979). The semantic representa tion of a natural language sentence is just the representation of propositional con tent of that sentence in a logical language. The purpose of the semantic representation is to capture the semantic meaning of the sentence, that is the part of the meaning inherent to the sentence and unchanging in different contexts. Our enterprise assumes the existence of a method to transform natural language senrences into a sentence of some logical language which can be interpreted model-theoretically. The semantics of the sentence is then given by those models in which the symbols of the logical language have been given the inrerpretation which corresponds to the normal interpretation given co the natural language symbols to which they correspond. Some may disagree that a speaker can (cooperatively) communicate only those
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ROBERT E. MERCER Department ofComputer Science Middlesex College University of Western Ontario Landon, Ontario N6A 5B7 Canada
Robert E. Mercer 249 Default Logic method). A detailed account of a modification to Gazdar's clausal quantity implicatures which over comes this problem can be found in Mercer ( I990). They are sufficient for all of the examples presented in this paper. I O We use this term as an analogue to deduc tive closure oj r that is, the set of sentences containing r closed under the normal deduction operator, f-. Here, logical closure refers specifically co the Default Logic proof theoretic operator, r-A• although there is no intent to disallow others as well. I I We need the definition of spinster later. By exchanging 'female' for 'male' in the definition we obtain the definition for spinster. I 2 The verb believe should be taken co mean first order derivable or conjectured. I 3 These representations should be con sidered as abbreviations for an event based representation. For example, 'john does not regret that Mary came to the party' represented as .
�REGRET(folm , COME(Mary, p1)) should be considered as being actually represented as COME) I 3e. EVENT(e) A 1YPE(e , SUBJ(e , Mary) A OBJ(e , p1) A �REGRET(John , e) 1 4 STOP(BEAT(jolm , r1)) should be inter preted as a succinct notation for the First Order representation: 3e. EVENT(e) A 1YPE (e , BEA T) A SUBJ(e ,jolm ) A OBJ (e, r1) A STOP(e). and -.STOP(BEA T(jolm , r1)) for: 3e. EVENT(e) A 1YPE(e, BEAT) A SUB](e ,jolm ) A OBJ(e, r1) A �STOP(e).
1 s The because ' clause ( 33) together with the definition ( I 4) can be used to derive '
-
-.STOP(BEA T(John , r1}) which paraphrases as 'john did not stop beating the rug. ' Although the ability to
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propositions that he knows to be true. This part of the cooperative communica tion act has been presented exactly as stated in Gazdar { I 979)- Gazdar takes a stron)/ view of cooperative communica tion, that is, the speaker cannot com municate falsehoods. So, the strong vie� would require that if the speaker is only communicating beliefs, then the sentence uttered should be 'I believe that a .' rather than ' a .'. For those who take a weak view of cooperative conversation, that is, the speaker cannot knowingly communicate falsehoods, then beliefs can be communi cated without the requirement that they be prepended with 'I believe that . . .'. Whether the strong or weak view of cooperative conversation is adopted, the logical machinery is basically unchanged. Instead of interpreting Ks in its strong sense, it can be interpreted weakly as 'the speaker knows that he believes that'. It is noteworthy that this interpretation is similar to but not exactly like 'explicit belief' (Lakemeyer I987). That only explicit beliefs can be intentionally com municated seems a reasonable assump tion. So, the only difference between the strong and the weak view of cooperative conversation from a logical/truth per spective is that the strong view requires a to be true in the world whereas the weak view requires a to be true in the speaker's explicit belief space. 7 Gazdar's terminology is being used here because his definition · is given in these terms. In the Default Logic setting there are no potential presuppositions. Instead the implicatures are used to provide the contexts in which the presuppositions are computed. 8. In Gazdar's theory these potential impli catures become implicatures if they are not cancelled by the context in which they are generated. 9 That these clausal quantity implicatures, as described above, are not sufficient has been previously noticed (Soames 1 982 for Gazdar's system; Mercer I 987 for the
250 Towards a Common Logical Semantics for Presuppositions and Entailments derive the main clause of the sentence may have significance, say for an analysis of relevance or causation, I am not interested in it here. 1 6 For purposes of this definition, the only
defaults in KBH are the presupposition generating defaults. 1-� is default deriva tion, and Th (CONSEQUENTS(D)) is the deductive closure of the default consequenrs in KBH.
R E F E RE N C E S
Lukaszewicz, W. ( 1 98 5), 'Two results on Default Logic', Proceedings of the Ninth International Joint Conference on Artificial Intelligence : 45� 1 . Mercer, R. E. ( 1 987), 'A Default Logic approach to the derivation of natural lan guage presuppositions', Ph.D. thesis, Dept. of Computer Science, University ofBrirish Columbia, available as TR 87-35. Mercer, R. E. ( 1 990), 'Deriving natural lan guage presuppositions from complex conditionals', Proceedings ofthe Eigbth Bien nial Conference of the CSCSI!SCEIO : 1 1 420. Mercer, R. E. & R. Reiter ( 1 982), 'The representation of presuppositions using defaults', Proceedings of the Fourth Biennial Conference ofthe CSCSI!SCEIO: 103-7. Reiter, R. ( 1 9llo), 'A logic for default reason ing', Artificial Intelligence, IJ: 8 1 - 1 32. Sandt, R. van der ( 1 9ll8), Context and l:Jresup positions , Croom Helm, London. Seuren, P. A. M. ( 1 98 5). Discourse Semantics , Basil Blackwell, London. Shoham, Y. ( 1 988), Reasoning About Change , MIT Press, Cambridge, MA. Soames, .s. ( 1 979), 'A projection problem for speaker presuppositions', Linguistic Inquiry , 10: 623-66. Soames, S. ( 1 982), 'How presuppositions are inherited: a solution to the projection problem', Linguistic lnquiry, 13: 1 8 3-545. Weischedel, R. M ( 1 979), 'A new semantic computation while parsing: presupposi tion and enrailmenr', in C. K. Oh & D. A. Dineen (eds), Syntax and Semantics, vol. 1 1 , Presupposition , Academic Press, New York: I 5 S-82. Wilson, D. ( 1 975), Presuppositions and Non Truth Conditional Semantics , Academic Press, New York.
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Atlas,J. D. ( 1 977), 'Negation, ambiguity, and presupposition', Linguistics and Philosopl1y, I: 3 2 1 -36. Etherington, D. W. ( 1 9ll7), Reasoning with Incomplete Information , Pitman. Gazdar, G. J. M. ( 1 979), Pragmatics: Implicature, Presupposition, and Logical Form , Academic Press, London. Grice, H. P. ( 1 975), 'Logic and conversation', in P. Cole & J. L. Morgan (eds), Syntax and Semantics, Vol. J, Speech Acts , Academic Press, New York: 4 1 -5ll. Gunji, T . (1982); Toward a Computational Theory of Pragmatics: Discourse, Presupposition, and Implicature , Indiana University Linguistics Club. Heim, I. (1 983), 'On the projection problem for presuppositions', West Coast Conference on Formal Linguistics , 2: 1 1 4-26. Joshi, A. K. & R. M. Weischedel { 1 977), 'Computation of a subclass of inferences: presupposition and enrailment', American Journal ofComputational Linguistics, micro fiche 63. Karttunen, L. ( 1 973), 'Presuppositions of compound sentences', Linguistic Inquiry, 4: 1 69-93· Karttunen, L. ( 1 974), 'Presupposition and linguistic context', Theoretical Linguistics , I: l ll l-94· Karttunen, L. & S. Peters ( 1 979), 'Con ventional implicarure', in C.-K. Oh & D. A. Dineen (eds), Syntax and Semantics, Vol. 1 1, Presuppositions, Academic Press, New York: 1 -56. Kempson, R. M. (197 5), Presupposition and the Delimitation ofSemantics , Cambridge Uni versity Press, Cambridge. Lakemeyer, G. ( 1 9ll7), 'Tractable meta reasoning in propositional logics of belief', Proceedings of the Tenth International Joint Conforence on Artificial Intelligence: 402-ll.
journal ofSemantics 9: 2 5 1 -286
© N.I.S. Foundation
(1992)
Presuppositions and WH-clauses ALLAN RAMSAY
University College Dublin
Abstract
I
B A C K G RO U N D
The main aim of this paper is to consider the contribution the WH-clause what I want makes to: (I) I know what I want . (2) What I want is a cold drink . In particular we are interested in the fact that both (I} and (2) seem to PRESUPPOSE the proposition that I want something. We intend to argue that in both cases the clause what I want is functioning syntactically just as though it were an ordinary NP, so that (I) is a perfectly ordinary transitive sentence and (2) is a perfectly ordinary copula sentence. The presuppositional properties of these two sentences arise entirely from the WH-clause, and they arise in exactly the same way. If we can maintain this argument then there seeins to be no need to appeal to a special syntactic construction called PSEUDO-CLEFTING or WH CLEFTING in order to describe the syntactic structure of(2). Furthermore, exactly the same analysis will deal with
(3) What you see is what you get . which is neither a classical WH-cleft nor a classical reverse WH-cleft, but is somehow a combination of both. The argument will require us to show that the syntactic and semantic properties of the two WH-clauses are identical, and that the presuppositions of (I} and (2) can be shown to follow from these clauses and not from some other source. We will not go into a great deal of detail about the syntactic properties,
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We develop a formal framework for discussing presuppositions, based on the notion that meaning should be seen as a relation between information states. We then provide treatments of some specific presuppositional constructions within this framework in an attempt to show that these constructions can be described using rather simpler syntactic rules than are usually employed
252 Presuppositions and WH-clauses simply remarking that almost anywhere you can have an ordinary NP you can have a WH-clause, so that a single syntactic rule like (R1 )
NP- WH-clause
may be used to derive all of the following from the more normal constructions involving NPs: (4)
I know what I want. (I knowJohn.)
(s) I eat what I'm given. (I eat peaches)
We have ofcourse been somewhat disingenuous in claiming that our very simple rule will deal with all of these. Some forms ofWH-clause are unacceptable in
some ofthe situations where you find NPs but not others (e.g. you can say I know
which I want and I know which one I want but not A little ofwhich you like will do you good or A little ofwhich oneyou like willdoyougood). Other forms can ONLY occur in such situations-whateveryou do cannot be used as a relative clause or as a question or as anything except an NP. This parallels the situation where some WH-clauses
can be used as relative clauses but not as questions (e.g. which chased him ), some can be used as questions but not as relative clauses (which one chased him ,
him ) and
what chased
some as both. A complete description of the way WH-clauses work
clearly requires a great deal of detail on this issue, and it may be that interesting generalizations may arise from a detailed study of these constraints. This is not what concerns us here, however. We will therefore simply assume that there is some rule like (R1 ) but with a great deal more detail concerning the form of the initial WH-marker, and will investigate the way it converts the semantics ofthe WH-clause (which is presumably some sort of abstraction, and which does not seem to be inherently presuppositional) into an NP-like semantics which is presupposition-ind�cing.
2
R E L AT I O N AL S E M A N T I C S
We are concerned then with the semantics of WH-clauses and with presuppositions. In order to argue about such things we clearly need to present a general semantic framework and explain how we will treat presuppositions within that framework. The general framework is similar to situation semantics (Barwise & Perry
1 9 8 3), and various other recent semantic theories (Kamp 1 984; Heim 1 9 8 3), in that we assume that the meaning of a sentence
S
is a
MAPPING
between
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(6) A little ofwhat you like will do you good. (A little ofthis medicine will do you good.) (7) What we needed at that point was a technical breakthrough. (The invention ofthejet engine was a technical breakthrough.) (8) Whatever you will do will upset him. (Your departure will upset him.)
Allan Ramsay
253
We find the arguments that have already been put forward on behalf of these theories convincing, but we have no new ones. We will therefore just assume that the general approach is reasonable, and will concentrate on developing a formal treatment which will support our argument. The first point is that we want to use information states rather than states of the world as our building blocks. Information states are generally incomplete given an arbitrary individual I and an arbitrary predicate P it is quite possible for an information state to fail to specify either that P holds of I or that it doesn't. It is also possible for an information state to be inconsistent. It is, of course, undesirable, since the usual rules of inference are extremely unreliable for inconsistent information states. None the less, it cannot be ruled out as a possibility. Information states are intended to have something in common with belief sets, which we know very well are always partial and may easily be inconsistent. Any formal description of such things will inevitably be an idealization, but there is a difference between idealizing an object and ignoring all its basic properties. Strategies which involve treating belief in a modal framework (Hintikka 1 962; Moore 1 984), and particularly ones whch interpret this modal framework via possible world semantics, are forced to assume that belief sets are consistent and logically closed. These assumptions are so directly opposed to the obvious properties of belief sets that we find them unacceptable, preferring to characterize information states in a way that makes it easy for them to be incomplete and inconsistent. The development of a semantics involving information states proceeds in several stages. We start by developing a language for describing ways the world might be. This language will enable us to say various things about PROPOSITIONS, which we assume are objects which have truth values. We will avoid committing ourselves to any very dogmatic assertions about what propositions really are. All that matters to us here is that their attributes include the property of having truth values, and that things that have truth values can be used for describing ways the world might be. Once we have a language for talking about propositions we can then develop a treatment of information states in terms of the acceptance or rejection of specific propositions. This view of information states allows us to be fairly cavalier. In particular, we do not need to assume that an information state that includes, for instance, the propositions corresponding to the formulae P and P -+ Q also includes (the proposition corresponding to the formula) Q , nor do we need to assume that an information state cannot include both P and -. p . This latter state is clearly undesirable, but it is certainly not impossible. The language we use for describing propositions is based on Turner's ( 1 987) PROPERTY THEORY. We start with a standard first-order language L1, which contains countably infinite sets of variables, constants and predicate letters, the INFORMATION STATES.
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254
Presuppositions and WH-clauses
usual truth functional connectives A, V, -, -. and the quantifiers V and 3. L1 also
(3x : A )B defined 3x(A A Vy{y f= x -.A11x)) (so long as y for x in A ) , and {Vx : A )B defined to be
contains restricted versions of the standard quantifiers, with
to be 3x(A A B ),
3!xA
defined to be
can be appropriately substituted
--+
Vx (A --+ B ). These restricted versions are a standard notational convenience. L1 is given an orthodox classical semantics in terms of MODELS, as follows. A model is defined to be a 3-tuple ( U, u , F) such that:
UM to
U, the DOMAIN of the model, is a set of individuals. We write denote the domain of the model M.
{PM-ii)
U , the INTERPRETATION FUNCTION of the model, is a mapping from constants and variables of L1 to members of U. uM is the interpretation
funcrion of M. {PM-iii) F is a mapping from predicate letters of L1 to N-tuples of members of
U. F (P ) denotes
the set of N-tuples of elelJlents of U whch satisfy
P
according to this information state. We define a relation I= between sentences of L1 and models as follows {M I= should be read as M models A ', or as 'A is true in M'):
A
'
Let M be ( U, u , F). Then
{1=-i) {1=-ii) {1=-iii) {1=-iv) {1=-v) (t=vi) (t= vii)
P(t1, , tn ) iff( u (t1), , u (tn)) is a member of F(P). A A B iff M I= A and M I= B . M I= A V B iff M I= A or M I= B . B iff M I= -.A o r M I= B. M I= A M l= 3xA iff M' I= A for some model M' which differs from M only in the value its interpretation function assigns to x. Ml= VxA iff Ml= A and M' I= A for every model M' which differs from M only in the value its interpretation function assigns to x. M t= -.A iff M � A . M l=
• • •
•
•
•
M I=
--+
The definition of t= provides a semantics for
L1 as a standard first-order logic.
Unfortunately this language lacks the expressive power requi.red for character the semantics of natural language sentences, since we also need intensional operators for dealing with abstraction and with propositional ·
izing
operators. We would need these operators even if we were not considering presuppositions at all. We need intensional operators in order to deal with everyday verbs of propositional attitudes such as
know, want , and say . We need
abstraction simply to develop a compositional semantics of any kind
whatsoever. We choose to extend L1 to an intensional language LPT by adding operators from Turner's ( I 987) PROPERTY THEORY. LPT plays the same role in our
treatment of presuppositions that, for instance, admissible set theory with ur elements plays
in
situation semantics, or that intensional logic plays
in
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{PM-i)
Allan Ramsay 2 5 5
(RBS-i) M0 is obtained from M by ensuring that pMo( TRUE ) and fMO(e) are empty. (RBS-ii) Mi+t is obtained from M; by setting pMi+t ( TRUE) to {o[P ) : M; t= P). In other words, the denotation of TRUE at stage i + I is the set of terms corresponding to formulae which were true at stage i . Similarly pMi +t (e) is set to {( t o[x, P) ): M; t= Pt/xl· (RBS-iii) If A. is a limit ordinal then o[P) will be a member of F"A.( TRUE) iff there is some i less than A. such that o[P) is a member of F"i( TRUE) for all j between i and A. , and similarly for REJECT, e and 3. ,
We then introduce the notion of STABLE TRUTH, saying that a formula P is stably true in the sequence M; if there is some j such that M; t= P for all i greater than j. From now on we write M t= A to say that A is stably accepted in the sequence starting with M. It turns out that for pathological cases corresponding
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Montague grammar. I t provides a consistent formal underpinning, without which we cannot be sure that what we are saying makes any sense. We choose property theory from the numerous competing formalisms because (i) it enables us to distinguish between different propositions with the same truth conditions, which we believe is essential if we are to provide a sensible treatment of verbs of propositional attitude such as know , believe, and want; (ii) the treatment of propositions as first-class objects makes it easy to describe relationships between propositions and temporal objects such as instants and intervals, without trying to develop a fully fledged logic of time; and (iii) property theory is, at least technically, a first-order language, so that it may be easier to develop automated inference systems for dealing with it. We write o[P) to stand for a TERM of LPT which corresponds to the FORMULA P. We add a predicate TRUE whose intended interpretation is obvious, namely that M t= P should hold iff M t= TRUE (o [P]) does. o[P) should be read as something like that P, so that it will serve as the kind of thing required for dealing with sentences like I know that Mary dislikes John and She said that he never helped her with her homework . We also use terms like o [x, P) in order to denote abstractions, with a relation e whose intended interpretation is that M t= (t e [x, P]) should hold iff M t= T11x does. t E A is read as t INSTANTIATES A . It is well known tha.t great care is required in the provision of semantics for languages which include predicates like TRUE and relations like e. It is very easy to state paradoxes such as the Liar paradox and Russell's paradox in such languages, and once you have stated them you have to make some judgement about what they mean. We follow Turner (I 987) (who in turn follows Gupta (1 982) and Herzberger ( 1 982) ) in developing a REVISION-BASED semantics for P1 in order to avoid these problems. Given a model M we define a sequence of models M; as follows:
256 Presuppositions and WH-clauses
(1 1- -i) (A , R ) 11- P( t 1 , , tn) iff P ( t 1 , , tn) is a member of A . Qt--ii) (A , R ) 11- P A Q iff (A , R ) 11- P and (A , R ) It- Q . 01--iii) (A , R ) It- P V Q iff (A , R ) 11- P o r (A , R ) It- Q or P V Q is a member of A . (11--iv) (A , R ) 1 1- P -+ Q iff (A , R ) 1 1- --. p or (A , R ) I t- (P A Q). Qt--v) (A , R ) 11- 'VxP iff (A , R ) 11- P11..- for all constants c . (1 1- -vi) (A , R ) 11- 3xP iff (A , R ) 11- P11..- for some constant c . Qt--vii) (A , R ) II- --.p iff(A , R ) -II P . •
•
•
• • •
(-I I -i) (A , R ) --11 P( t 1 , , tn) iff P( t 1 , , tn) is a member of R . (-! I -ii) (A , R ) --11 P A Q iff (A , R ) --11 P or (A , R ) --11 Q or P 1\ Q is a member of R . (--ll -iii) (A , R ) --11 P V Q iff and (A , R) --11 P and (A , R ) --11 Q. (--ll -iv) (A , R) --11 P -+ Q iff (A , R ) 11- --. p and (A , R) 1- 1 Q . {--ll -v) (A , R ) --11 'VxP iff (A , R ) --11 P11..- for some constant c . (--11-vi) (A , R ) --ll 3xP iff (A , R ) --1 1 PcJx for all constants c . H-vii) (A , R ) --11--.P iff (A , R ) II- P. •
•
•
• • •
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to the paradoxes the equivalences M F= TRUE(o[A ] ) iff M F= A and M F= t E o[x, A ] iff M F= A11... no longer hold, but that they are valid for most ordinary cases (in particular for formulae which do not involve the intensional operators at all). Turner (1990) discusses a large number of similar logics. For now we simply take it that F= provides a reasonable semantics for LPT and move on to the next stage of our relational semantics. LPT provides us with a language for talking about propositions. We assume that there is a mapping between sentences of LPT and propositions, so that we can use sentences of Lpy as NAMES of propositions, and we use the relation F= to characterize the TRUTH CONDITIONS of a proposition. We do not equate propositions with their truth conditions (or, equivalently, with the sets of possible worlds in which they are true). Two propositions may have exactly the same truth conditions without being identical-the propositions 2 + 2 = 4 and -.3NVP(prime(P ) -+ P < N), for instance, have the same truth conditions but are clearly distinct propositions. The truth conditions of a proposition will certainly be of interest to anyone trying to see what can be done with it, but that does not mean there is no more to a proposition than its truth condition. Given this rather detached view of the nature of propositions, it is now easy to say what an information state is: an information state consists of a pair (ACCEPTED , REJECTED ) of finite sets of propositions. The intention is that these correspond to propositions which are forced to be true or false by the information state. We now define two relations I t- and --11 between information states and propositions, where I 11- A is to be read as 'the information state I supports the proposition named by the formula A ' and I --11 A as 'the information state I rejects the proposition named by the formula A ':
Allan Ramsay 257
PROPOSITION TYPE is a set of propositions. A formula A of LPT which contains a free variable x names a proposition type, namely the set of propositions named by Ac1x for all constants c of LPT. We say that an information state I INDUCES a substitution c Ix from the proposition type named by A if A,1x is the only member of A that I accepts, and that a substitution c Ix can be used to SELECT the proposition A,1x from the proposition type A . The relation between propositions and proposition types is very similar to the relation between situations and situation types in situation theory, with substitutions playing much the same role as anchors (Barwise & Perry 1 98 3). (CP-ii) A CONSTRAINED PROPOSITION consists of a proposition type plus a set of constraints, where constraints are themselves proposition types.
(CP-i)
A
The intention is that an information state will induce a series of substitutions from the elements of the constraint, and chat these substitutions will then be used to select a single member of the proposition type. This proposition will then be added to the information state. In other words, a constrained
D
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The definitions oflf- and -!I look very like the semantics for a three-valued logic with strong negation such as the one proposed by Kleene ( 1 952). The crucial difference is that If- and --11 are relations between information states, which are pairs of sets of propositions, and propositions, rather than between inter pretations of a language and formulae. We reiterate that where sentences of Lpy appear in the definitions of If- and --11 they are to be read as the names of propositions. If- and --11 are relations between information states and proposi tions, not between information states and formulae of Lpy. Most of the individual cases in these definitions are fairly straighrforward. We note that the definition of (A , R ) If- P - Q differs from the usual definition of material implication, since we do not have (A , R ) If- P - Q as a consequence of (A , R ) If- Q . This has some intuitive appeal. In particular the equivalence of (P A Q) - R and (P - R ) V (Q - R ) which Gazdar ( 1 979) remarks on no longer holds under this analysis. For I If- (P A Q ) - R now holds if I If- --.(P A Q) or I If- P A Q A R does, whereas I If- (P -+ R ) V (Q -+ R ) holds if one out of I If- --.P, I If- --. Q , I If- P A R and I If- Q A R does. We are not suggesting that this analysis of -+ is a solution to all the paradoxes of implication, merely that it will give us some extra expressive power which we can exploit when we provide formal paraphrases of natural language utterances. We now have a definition of an information state as a pair of sets of propositions, and two relations If- and --11 between information states and propositions. We want to develop a framework for natural language sentences which says that the meaning of a sentence is a mapping between information states. To this end we introduce two new notions.
258 Presuppositions and WH-clauses
proposition can be used to increment different information states in different ways, depending on the substitutions induced from the constraints. We formalize this intuitive notion as follows: If I is the information state (A , R ), then the effect of applying [ ( C, P) ], the of the constrained proposition (C, P), to it is defined as follows. Let a be the collection of all substitutions induced by I from the members of C. If (i) I does induce a substitution for each member of C, (ii) no two members of a assign different values to the same variable, and (iii) a selects a member of P, then [ ( C, P)](t) is I u {a(P)). If any of (i), (ii) or (iii) fails then [ ( C, P)](t) is undefined. RELATIONAL SEMANTICS
3
S I MPLE E N G L I S H S E N TE N CES
We want to consider the semantics ofEnglish WH-clauses, to see how the same expression can be used as a relative clause, as a question and as a presupposition inducing NP. Before we can get as far as WH-clauses, however, we have to consider simple NPs, VPs and sentences. The first move is to decide on an ontology. We assume the existence of a series of predicates which can be used for classifying individuals. Among these predicates we include ones that apply to ordinary physical individuals (e.g. human , animal, table , red), ones that apply to events, actions and states (erupt , eat , sleep ) and ones that apply to locations (corner , morning). Thus 3x human (x) says that there is a human, (Vx: human (x))animal (x) says that all humans are animals, (Vx: human (x ))3y event(y, die) says that for any human there is an event of type dying. Note that this last formula does not say anything about the connection between the human and the dying. We further assume a series of relations between sets of individuals and events, actions and states, corresponding to thematic role relations, and between events, such as states and actions, and temporal entities such as instants and times. Thus we propose the formula
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(i) ensures that the information state supports a unique proposition for each constraint, (ii) ensures that the constraints are coherent, and (iii) ensures that they provide enough information to select a unique proposition from the proposition class. We claim that this relational semantics for the language Lep of constrained propositions provides a framework for developing a formal semantics of natural language. The next task is to show that we can indeed characterize the semantics of the fragment ofnatural language we are interested in using this language as a medium for describing semantic contents.
Allan Ramsay
259
'v'A :{subset(A , •[B , person (B)]) 1\ lA I - I } 3 C : {subset (C, •[D , person (D)]) 1\ ICI = I } 3E state(E , love) 1\ agent (E , A ) 1\ object(E , C) 1\ 3F :[interval(F)}(contains (F, now) 1\ during (F, E)) as a good first approximation to a formal paraphrase of the sentence: (9) Every body loves some body .
( I o) Four men carriedfive pianos . as 3A : {subset(A , •[B , man (B)]) 1\ IA I = 4} 3 C : [subset (C, •[D , piano (D)]) 1\ ICI = 5} 3E action (E , carry) 1\ agent (E , A ) 1\ object (E , C) 1\ 3F : [interval (F)} 3G:{instant(G)Jb40re(G, now) 1\ contains(F, G) 1\ during(F,E) seems to carry much the same information as ( I o) itself The treatment of temporal relations in these examples is fairly primitive, and would certainly benefit from the kind of considerations discussed by Moens & Steedman ( I 98 8). However, since very little in the present discussion depends on our analysis of tense and aspect we will simply leave them as an indication of where and how we would incorporate a better treatment. These interpretations were constructed on the basis of paraphrases of the constituents of (9) and ( 1 0) using the standard technique of Montague grammar. We translate loves some body as
•[E, 3A : [subset (A , •[B, person (B)]) 1\ lA I = I } 3Cstate(C, love) 1\ •[D, agent(C, D)] E E 1\ object(C, A) 1\ 3F: [interval(F)}contains(F, now) 1\ during(F, C)] and every body as:
•[C, 'v'A : {subset(A , • [B, person(B)]) 1\ IAI - I }(•[Q, A e Q] E C)]
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This formula says that given any singleton act of entities which are persons there is another singleton set, also of entities which are persons, such that there is a state of loving whose agents are the members of the first set and whose objects are the members of the second, and that this state persists over an interval which includes now. The notation • [B , person (B)] simply denotes the property ofbeing a person, so that subset (A , • [B , person (B)]) says that A is a set of people. The decision to treat thematic roles as relations between sets of individuals and events, rather than between individuals and events, makes the treatment of plurals rather more uniform, without losing any expressive power. In particular, the translation of
260 Presuppositions and WH-clauses
If we instantiate the formula corresponding to every body with the one corresponding to loves some body and repeatedly use the equivalence Ptlx = (t E o [x, P]) we obtain the formal paraphrase of(9) given above. The only unusual thing about our analysis is the presence of the extra level of abstraction in the analysis of NP semantics-the fact that we represent the meaning of every human as o [C, \fA : (subset(A, o [B, human (B)]) 1\ !A I = I } (o [ Q , A E Q ] E C)] rather thanjust o[C , \fA: (subset(A, o[B, human(B)]) 1\ lA I = I } (A E C)]. Our analysis enables us to give e [A , subset(A, o[Z, mouse(Z)])]) as the representation of the bare-plural NP mice in: ( I I) All cats chase mice.
as the formal paraphrase of ( I I). This paraphrase can be glossed as saying that for any cat there is a chasing event all of whose objects are mice. This may not capture exactly the entailments of ( I I ), but it comes closer than most other treatments (e.g. Chierchia & Turner I987; Carlson I 989) without appealing to special purpose quantifiers or suggesting that ( I I ) expresses a relation between the objects in the set of cats and the property of being a mouse. (I I ) can be dealt with without any reference to constraints. If I've just told you that my cat doesn't chase mice then uttering ( I I ) will reveal me to be, at best, somewhat confused since every view of the world that can be constructed on the basis of what I have said will be incoherent. Nonetheless, the utterance is meaningful in this situation. This contrasts with: ( 1 2) The man ate a peach . This sentence will only be interpretable in situations where there is exactly one man under consideration. In any other situation it is uninterpretable. In order to capture this we paraphrase it with a constrained proposition (in the formal paraphrases of English sentences we refer to the constraint part as the PRESUPPOSITIONS. We follow common practice in taking the presuppositions to be exactly those items which are unchanged by negation of the sentence as a whole): CONTENT:
3C: (subset(C, o[D, peach(D)]) 1\ ICI = I} 3E action(E, eat) 1\ agent(E, A) 1\ object(E, C) 1\ 3F : (interval(F)) 3 G : (instant(G))b1Qre(G , now) 1\ contains(F, G) 1\ during(F, E)
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This leads to \fA :(subset(A , o [B , cat(B)]) 1\ !AI - I } 3 C action( C, chase) 1\ agent(C, A) 1\ subset(a[D, object(C. D)] , o [E, mouse(E)]) 1\ 3F: ( interval(F))contains(F, now) 1\ during(F, C)
Allan Ramsay 261 PRESUPPOSITIONS:
subset(A , •[B, man(B)]) 1\ !AI = I An
(R2) Simple Nominal Group: fd(syntax((NOMINAL GROUP)), semantics(presuppositions(0), prtjlx(•[I, I]), matrix(PROPERTY))) fd(syntax((NOUN)), semantics(presuppositions(0), prtjlx(0), matrix(PROPERTY)))
(R2) says that a nominal group may consist of a single noun, in which case the
matrix of its semantic description is simply the property of being a member of the class denoted by the noun. The prtjlx is the null quantifier •[ I, I] and the presuppositions are empty. Thus the formal paraphrase of the simple nominal group peach is semantics(presuppositions(0), prtjlx(•[I, I]), matrix(•[A, peach(A)]))
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information state in which there is exactly one singleton set of men will induce a substitution for A from the presupposition. This substitution can then be used to select a proposition from the proposition type corresponding to the content. In other words, in a situation in which there is exactly one man ( 1 2) provides the information that this individual ate a peach. In situations where there are no men, or where there are several, ( I 2) is uninterpretable. In order to obtain the given paraphrase of ( 1 2) we need to split the semantic component of the description of a linguistic structure into three parts. The first one constructs the PRESUPPOSITIONS, and the others construct the content. The first part of the content is a stack of quantifier-like expressions, which we refer to as the PREFIX, and the second is a quantifier-free formula which we call the MATRIX. The main reason for separating out the prefix and the matrix is to support a mechanism like 'Cooper-storage' (Cooper I 98 3; Keller I 987; Vestre I 99 I) for dealing with quantifier scope ambiguity. The elements of the prefix are formulae which will add a quantifier to a formula. A typical example would be something like •[I, 3X I]. If this were instantiated with, say, the formula p(X) the result would be the sentence 3Xp(X). The identity prefix •[I, I] simply produces the formula it is instantiated with. The following rules suffice for the analysis of ( I 2):
262 Presuppositions and WH-clauses
We have omitted virtually all syntactic detail from (R2), as we will do throughout this paper. Detailed discussion of the syntactic aspects of all the rules in the current paper is given in Ramsay ( 1 990a), where a computationally tractable grammar for a substantial fragment of English is given. The current paper is primarily concerned with semantic issues, and we make no further apology for omitting syntactic details. (R3) Simple Noun Phrases:
-
jd(syntax((DETERMINER)), semantics(presuppositions(PREJ,1), prefix(QUANTder), matrix(CONTder))), fd(syntax((NOMINAL GROUP)), semantics(presuppositions(PRE nn ), prefix(QUANTnn), matrix(CONTnn))) (R3) then says that an NP may consist of a determiner and a nominal group. The semantic description of the NP is obtained via very simple combinations of the semantic descriptions of the determiner and the nominal group. The pre suppositions of the NP are obtained by taking the union of the presuppositions of the nominal group and the result of instantiating the presuppositions of the determiner with the matrix of the nominal group. The prefix of the NP is obtained by sequencing the prefix of the nominal group and the result of instantiating the prefix of the determiner with the content of the nominal group. We have already seen what the semantic description of at least a simple nominal group looks like. The semantic descriptions of determiners can be fairly complex. The description of a is:
semantics(presuppositions(•[DUMMY, 0]), preflx(•[PROP, • [A , (3X: (subset(X, PROP) 1\ lXI - 1))A]]), matrix(•[ Q, X E Q])) The presuppositions will produce an empty set no matter what nominal group the determiner is combined with. The prefix constructs an existential quantifier, restricted by the property supplied by the nominal group, and leaves it waiting for a matrix to quantify. The matrix provides the property of being
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jd(syntax((NOUN PHRASE)), semantics(presuppositions(PRE nn u (CONTnn E PREJ,1)), prejix(QUANTnn + (CONTnn E QUANTJ,,)), matrix(CONTnn E CONTde,)))
Allan Ramsay 26 3
some property that holds of the quantified variable X. Combining this with the description of the nominal group peach according to (R2) leads to:
semantics(presuppositions(0), prpx(•[A, (3X : (subset(X, • [ Y, peach( Y)]) 1\ lXI = 1 ))A]), matrix(•[Q, X E Q]))
The description of singular the, on the other hand, is:
semantics(presuppositions(•(PROP, (subset(X, PROP) 1\ lXI = 1 )]), prpx(•[DUMMY, • [I, I]]), matrix(• [Q, X E Q])) semantics(presuppositions(subset(X, •[Y, man (Y)]) 1\ lXI = 1 ), prif!x(• [I, I]), matrix(•[Q, X E Q])) for the NP the man . In other words, (R3) says that the property denoted by the nominal group may be absorbed either into the presuppositions or into the prif!x. The particular descriptions of different determiners specify which way this property will actually be used-a says that it should be absorbed into the prefix and ignored in the presuppositions, and the says the opposite. Most other determiners can be dealt with in much the same way, though ones like most presumably require us to call on some extension of Lpr which includes DEFAULTS. Given the current lack of agreement about the best way to deal with defaults (Ginsberg 1 987), we decline to specify just what sort ofextension of LPT would be required, but we recognize that eventually we will need to incorporate some such theory into our representation scheme. It is worth noting in particular the effects of the determiners six and the in the analysis of
( 1 3 ) John ate six ofthe peaches. as: CONTENT:
3£ : {subset(£, C) 1\ lEI - 6) 3F action (F, eat) 1\ agent(F, A ) 1\ object(F, E ) 1\ 3G : {interval( G)) 3H: {instant(H)}bifore(H, now) 1\ contains( G. H) 1\ during(G, F) PRESUPPOSITIONS:
subset(A , • [B, name(B,john)]) 1\ !AI - 1 , subset(C, • [D, peach(D)]) 1\ I CI > I The definite NP the peaches presupposes the existence of a set of peaches with more than one member. The determiner six then picks out a subset of these
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Combining this with the description of man produces
264 Presupposirions and WH-clauses
(R4) Transitive Verb Phrase:
fd(syntax((VERB PHRASE )), semantics(presuppositions(PREobj), preflx(QUANTobj), matrix(CONTobj E CONTvp))) fd(syntax((TRANSITIVE VERB )), semantics(presuppositions(0), prefix(0), matrix(CO NTvp))), fd(syntax((NOUN PHRASE )), semantics (presuppositions (PREobj), preflx(QUANTobj), matrix(CONTobj))) (R s ) Simple Declarative Sentence:
fd(syntax((SENTENCE)), semantics (presuppositions(PREsubj v PREvp), prefix(QUANTsubj + QUANTvp), matrix(CONTvp E CONTsub))) fd(syntax((NOUN PHRASE)), semantics(presuppositions(PRE,ubj), prefix(QUANTsubj), matrix(CONTsubj))), fd(syntax((VERB PHRASE)), semantics(presuppositions(PRE vp), prefix(QUANTvp), matrix(CONTvp)))
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with exactly six members. Thus the single complex NP six ofthepeaches makes a contribution to the presuppositions and also adds a complex quantifier to the content (see Pulman ( 1 99 1 ) for a similar treatment of complex determiners of this kind). The presentation of the semantic analysis of complete sentences as a content and a set of presuppositions assumes that the prefix of the sentence has been combined with its matrix to provide a single well-formed formula. Other sources of definite reference such as PROPER NAMES and PRONOUNS are treated very similarly. Thus, in ( 1 3 ) the proper name John is taken to be something like a definite NP of the form the person named John. Similarly a referring pronoun such as he is taken to be something like a definite NP of the form the male individual. I and you are treated similarly.
Allan Ramsay 265
(14) and (R s) are very straightforward rules for describing the structure ofVPs and sentences, and require no further discussion.
4 RELAT I V E C L A U SE S A N D Q U E ST I O N S
( 1 4) I met a man who likedfig urative art. ( I s) The man who you accusedflew to Paris yesterday afternoon . In both cases the WH-clause provides information which is combined with the basic property provided by the relevant noun to produce a more specific prop erty. In ( I 4) an individual satisfying this complex property is introduced into the information state, and in ( 1 s) the existence of some such individual is pre supposed. In both cases, however, the WH-clause produces an abstraction which is combined with a property to construct a more specific property. Appropriate formal paraphrases of such WH-clauses are obtained by allowing the WH-marker to mark the sentence as a whole as an abstraction, with the abstracted individual taken up by the relevant thematic role. We thus propose to paraphrase
(I6) who ate it as
semantics(presuppositions(subset(B, • [ C, neuter( C, (C)]) 1\ IBI = I), prtftx(• [I, I]), matrix(• [D,
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The discussion above sketched a framework for constructing formal paraph rases of simple English sentences. A number of terms were introduced but not fully specified. In particular the properties of thematic roles such as agent and object and of temporal relations such as bifore and during deserve further discus sion, but will not receive it in this paper. Numerous attempts have been made to spell out the significance of propositions such as agent(e, j) or during(i, e) (Dowry I 989; McDermott I 982, Allen I 984). We assume that ANY semantic theory will have to use notions like these, and that existing work provides at least some clues about their correct explication. For the remainder of the pres ent paper we will use these terms without further discussion. Our purpose is to see what we could do if we did have proper descriptions of them, not to provide those descriptions. The main argument below will describe the presuppositional effects ofWH clauses when they are treated as NPs. The principal uses ofWH-clauses, how ever, are as relative clauses of various kinds and as questions. We therefore start by considering their contributions in these more common contexts. Consider the WH-clauses in:
266 Presuppositions and WH-clauses
3E action(E, eat) 1\ agent(E, D) 1\ object(E, B) 1\ 3F: (interval(F)) 3G: ( instant( G))bifore( G, now) 1\ contains(F. G) 1\ during(F, E)])) and
( I 7) which he ate
The presupposition that there is some individual which is neither male nor female in the formal paraphrase of ( i 6) arises form the pronoun it ' and similarly for the presupposition in the paraphrase of( 1 7). In both cases the WH-word is paraphrased via an abstraction of the from •[P, X E P], with the sentence as a whole being treated as an abstraction with respect to X. We deal with WH-clauses which are being used as RESTRICTIVE RELATIVE CLAUSES, as in ( I 6) and ( 1 7), by combining the abstraction corresponding to the WH-clause with the property delineated by the nominal group at the heart of the NP. To do this we propose the following rule: (R6) Restrictive Relative Clause
fd(syntax((NOMINAL GROUP)), sernantics(presuppositions(PRE,, U PRErclause), prefix( QUANTS,,), matrix(• [X, (X ECONT,,) 1\ ((X E CONT,ctause) E QUANTSrclause]))),
-
fd(syntax((NOMINAL GROUP)), semantics(presuppositions(PRE,,), prefix( QUANTS,,), matrix( CONT,,))), fd(syntax((RELATIVE CLAUSE)), sernantics(presuppositions(PRE,ctause), prefix( QUANTSrclause), matrix( CONT,ctause)),
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as semantics(presuppositions(subset(A, •[B, male(B)]) 1\ lA I = I ), prefix•[!, I]), matrix(• [ C, 3D action (D, eat) 1\ agent(D, A), 1\ object(D, C) 1\ 3E : (interval(E)J 3F : (instant(F)) before(F, now) 1\ contains(£, F) 1\ during(E, D)]))
Allan Ramsay 267 As usual we are not particularly interested in the details of the syntactic compo
nents of this rule, and we simply assume that they could be spelled out in detail if required (or see Ramsay 1 990a). The matrix of the complex nominal group is obtained by combining the property denoted by the matrix of the constituent nominal and the property obtained by attaching the prefix of the relative clause to its matrix. The presupposition is obtained simply by taking the union of the two presuppositions of the constituents. (R6) would combine the description which we derived earlier for the semantics of the nominal group peach with the description given above for (r6) to produce
as the formal paraphrase of:
( I 8) peach which he ate This is of exactly the same type as the original paraphrase of the simple nominal group peach -its matrix is a formula containing free variables, its prefix is a mapping from propositions to propositions, and its presuppositions is a set of presuppositions. It is therefore the right kind of thing to be used in the kind of context where the simple nominal group could have been used. In particular it is the kind of thing that can be combined with a description ofthe meaning of a determiner to produce a description of the meaning of an NP. Using the descriptions of a and the give above we can paraphrase
( I 9) a peach which he ate as:
semantics(presuppositions(subset(A , • [ B, male(B)]) 1\ lA I = I ) , priftx(•[I, 3 C : (subset( C, • [D, peach(D) 1\ 3E action (E, eat) 1\ agent(E, A) 1\ object(E, D) 1\ 3F : (interval(F)) 3 G : (instant(G)J before( G. now) 1\ contains(F. G) 1\ during(F, E)]) 1\ ICI = I )I]), matrix(•[H, C E H]))
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semantics(presuppositions(subset(A, • [B, male( B)]) 1\ lA I � I ), priftx(• [I, I)) , matrix(•[ C,peach ( C) 1\ 3D action(D, eat) 1\ agent(D, A) 1\ object( D. C) 1\ 3E : (interval(E)) 3F : {instant(F))before(F, now) 1\ contains(E, F) 1\ during( E. D)]
268 Presuppositions and WH-clauses
The preftx here contains a single quanrifter with a rather complex restriction. This quanrifter introduces a singleton subset C of the set D of things which are peaches and are also items which were eaten by the male individual A intro duced in the presupposition. This is fairly complex, but nothing simpler will do. We can similarly analyse (2o) thepeach which he ate
prqlx(• [I, !] ), matrix(•[H, H - C])) The presuppositions here introduce a singleton set of male individuals for he and a singleton subset C of the set D of things which are peaches and were eaten by the male individual. Complex again, but unavoidably so. WH-clauses can also be used as attributive relative clauses, as in: (2 1 ) I bought a peach, which he ate. (22) Yourfriend, who I metfor thefirst time yesterday, said that she had seen me at the match on Saturday. The WH-clauses in (2 1 ) and (22) are not being used to provide informacion which will help identify the relevant individual. Their function is rather to pro vide new informacion about them. (2 1 ) and (22) are roughly equivalent to: (2 3 ) I bought a peach and he ate it. (24) I met yourfriendfor thefirst timeyesterday and she said she had seen me at the match on Saturday. There are clearly differences between the two pairs of sentences, but we believe that they are largely a matter of emphasis-which we are not attempting to deal with here-and that formal paraphrases of(2 1 ) and (22) which made them look like (23) and (24) would capture a good deal of their semantics. In order to obtain such paraphrases we propose the following rule: (R7) Attributive Relative Clauses:
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as: semantics(presuppositions(subset(A, •[B, male(B )] ) 1\ lA I - I ), subset( C, •[D,peach (D) 1\ 3E action (E, eat) 1\ agent(E, A ) 1\ object(E, D) 1\ 3F : (interval(F)} 3G : { instant( G)} before(G, now) 1\ contains(F. G) 1\ during(F, E)])
Allan Ramsay
269
fd(syntax((NP)), semantics(presuppositions(PRENP u PRE,cfaust), prefix( QUANTSNP + • [J,(((CONT,cfaust E CONTNP) E QUANTSrclause) A J)]), matrix( CONTNP)))
This rule seems to violate one of the conditions for a semantic analysis to be compositional, namely that the meaning of the whole should be some simple function of the meanings of the parts. We have had to construct a fairly complex expression in order to obtain the right combination of the prefixes and matrices of the core NP and the relative clause. This expression does essentially the same job as the TYPE-RAISING operation used in numerous places in categorial grammar (e.g. Moortgat I 987; Dowty I 988). The problem is that you sometimes need to have access to the internal structure of some semantic expression in order to obtain the interpretation you are looking for, but the requirement that the description of the meaning of the whole should be built out of the descriptions of the meanings of the parts seems to preclude this. Type-raising and the expression in (R7) are devices for exploiting assumptions about the meanings of the parts in order to side-step this problem. (R7) leads to the following analysis of (2 I ): CONTENT: 3D : [subset(D, •[E ..peach (E))) 1\ IDI = I } 3F action (F, eat) 1\ agent(F, B) 1\ object(F. D) 1\ 3G : [interval( G)} 3H : {instant(H)Jbifore(H, now) 1\ contains( G. H) 1\ during( G. F) 1\ 31 action (!, buy) 1\ agent(!, A ) 1\ object(!, D) 1\ 3] : [ intervalU)J 3K : ( instant(K)Jbifore(K, now) 1\ containsU, K) 1\ duringU, I) PRESUPPOSITIONS: member(speaker, A ) 1\ lA I = 1 , subset(B . • [C, male( C)]) 1\ IBI = I
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fd(syntax((NP)), semantics(presuppositions(PRENP), prefix( QUANTSNP), matrix( CONTNP))), fd(syntax((RELATIVE CLAUSE)), semantics(presuppositions(PRE,cfause), prefix( QUANTSrclaust), matrix( CONT,claust)))
270 Presuppositions and WH-clauses
This is very similar to the analysis you would expect to obtain for (23), and as such it satisfies our aim of providing an analysis of (2 I ) which makes it look very like (23). WH-clauses can also be used as questions (subject, as always, to various fine constraints on the form ofthe WH-marker): {25) Who ate the peach?
s
WH-CLAUSES AS NPS
W e now have analyses ofWH-clauses which show how these constructions can be used as restrictive and attributive relative clauses, and we have suggested that the same analyses are likely to be appropriate when such a clause is used as a question. We now return to the central question of the paper: can we use exactly this treatment ofWH-clauses when they appear in sentences like I know what I want and What I want is a cold drink? We start by considering a fairly simple instance of this class of sentence: (26) I enjoyed what I ate. We know that enjoy usually occurs as a simple transitive verb requiring an NP as its sole complement. It is very tempting therefore to suggest that what I ate in (26) is also some sort of NP, so that we do not need to posit an alternative subcategorization frame for enjoy. What sort of NP might it be? NPs can contain WH-clauses as relative clauses. What I ate is a WH-clause. lt is plausible, then, that the NP we are looking for contains what I ate as a relative clause. Of course neither {R6) nor {R7) can provide descriptions of the syntactic constituents of this NP, since they each require other items to be present. Suppose, however, that you wanted to use (R2) to encode some characteristic property of some item, but that although you knew of some complex property which the item satisfied you did not know what its basic category was. You
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We hesitate to be too dogmatic about the semantics of such questions, given the difficulties that Groenendijk & Stokhof ( 1 984, 1989) found for most of the existing candidates. We simply note that whatever semantics eventually turns out to be most effective will inevitably make use of the property of being someone who ate the peach in question. It does not matter whether such a question should be seen as a request for an individual satisfying the proper� {whatever that means), or for an alternative property which the speaker believes is true of the person who ate the peach and which they believe the hearer is not aware of, or . . . Whatever is eventually used will have to refer to the relevant property, which will be provided by the analyses we have been using for relative clauses.
Allan Ramsay 2 7 1
could perhaps use some fairly neutral term such as thing or item . This would lead you to say something like one of the following: (27) (28) (29) (3o) (3 1 ) (32)
I enjoyed the thing which I ate. I enjoyed the things which I ate. I ate something and I enjoyed it. I enjoyed some thing which I ate. I enjoyed some things which I ate. I enjoyed every thing which I ate.
(R8) Headless Relative Clauses
jd(syntax((NP)), semantics(presuppositions(???), prefix(???), matrix(???))) jd (syntax ((RELATIVE CLAUSE)), semantics(presuppositions(PRE,,�allSt), prefix( QUANTS,c/ause), matrix( CONTrclaust))) This says that a WH-clause can always be seen as an NP. This lacks detail, since not every WH-clause can occur in the contexts where you find NPs. In particular, the WH-clause must not be constructed by extraposing a constituent of an AUX-inverted question and in certain contents the WH marker must not be which or which one. This detail is fairly easy to specifY, however. The hard task is to describe the semantics of the resulting NP. Are any of(27)-(32) sensible paraphrases of(26)? If(26) were the only case we had to explain then almost any of them would be acceptable, so that the thing which I ate, . . . , everything which I ate are all candidate replacements for what I ate. To choose between them it is revealing to consider: (33) John does not believe I enjoyed what I ate.
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The word thing adds very little to these. They would be just informative without it. We could omit it if we simply dropped the initial nominal constituent from (R6). This is not quite what we need, since this would leave us with a nominal group rather than an NP. We therefore need to assume that we can leap straight from this nominal group to a full NP, in much the same way as we can for generic nominal groups such as chocolate cake or ripe peaches (I like chocolate cake and I like ripe peaches both involve perfectly ordinary transitive uses of like). This leads us to the following rule:
272 Presuppositions and WH-clauses
It seems that (33) carries the implication that I ate something in much the same way that (26) does. If we embed each of the paraphrases (27)-(32) within the context John does not believe . . . we see that only the first two continue to carry the right message: (34) John does not believe that I enjoyed the thing which I ate. (3 5) John does not believe that I enjoyed the things which I ate. (36) John does not believe that I ate something and I enjoyed it. (37) John does not believe that I enjoyed some thing which I ate. (38) John does not believe that I enjoyed some things which I ate. (39) John does not believe that I enjoyed every thing which I ate.
(R8') Headless Relative Clauses
fd(syntax((NP)), semantics(presuppositions(PRE,clayusr v {X E CONTrclausrj) prefix( QUANTSrclause), matrix(•[P, X E P]))), -
fil (syntax((RELATIVE CLAUSE)), semantics(presuppositions(PRE,clause), prefix ( QUANTSrclause), matrix( CONT,ctause))) With this treatment of headless relative clauses we will find that the formal paraphrases of (26) and (33) are CONTENT:
. 3 G action(G, enjoy) 1\ agent(G, A) 1\ object( G. D) 1\ 3H : {interval(H)J 31 : {instant(I)Jbifore(I, now) 1\ contain(H, I ) 1\ during(H, G) PRESUPPOSITIONS:
member(speaker, A) 1\ !AI = I , member(speaker, B ) 1\ IBI - I , 3 C action (C, eat) 1\ agent(C, B ) 1\ object( C. D) 1\ 3E : {interval(E)} 3F : {instant(F)}before(F, now) 1\ contains(E, F) 1\ during(E, C)
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Out of these only (34) and (35) seem to carry the correct message. It is very difficult to tell which of (34) and (3 5) is closer to (3 3), and it is hard to see what evidence might distinguish between them. The only difference between them is that (34) implies that I only ate one object, and (3 5) implies that I ate several. We suggest that the correct semantics for (R8) is given in the following rule, which simply says nothing about the cardinality of the set of items in question:
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and: CONTENT:
PRESUPPOSITIONS:
subset(A , •[B, name(B,john)]) 1\ IAI = I , member(speaker, C) 1\ ICI = I , member(speaker, D) 1\ IDI = I , 3 E action (E, eat) 1\ agent(E, D) 1\ object(E, F) 1\ 3G :{interval( G)} 3H : ( instant(H)}bifore(H, now) 1\ contains( G. H) 1\ during( G. E) In both cases there are various presuppositions arising from the proper name John and the occurrences of the pronoun I. Each occurrence of I gives rise to a separate presupposition, each of which anchors a free occurrence of a variable. The fact that the presuppositions are identical in form does not mean that one of them is redundant, since they are serving different functions. Of course any inference mechanism that verified that the first was acceptable ought to be able to re-use its analysis in order to show that the other one is, but that is not the same as saying that one of them is redundant. The other presupposition in the paraphrases of (26) and (3 3) arises from the WH-clause. This presupposition presupposes the existence of an eating, whose agent is the speaker (this being enforced by one of the presuppositions induced by I), and whose object is some unspecified set of entities (the free variable D in the presupposition of the paraphrase of (26) and the free variable F in the presuppositions of the paraphrase of (3 3)). It thus forces the situation to be one in which the speaker ate some thing or things. The content of (26) then says that the speaker enjoyed the thing or things that he ate, and the content of (33) says that it is not the case that John believes the speaker enjoyed them. This analysis seems to capture a good deal of the significance of the two sentences. In particular it shows how the existence of an eating event emerges even when the sentence as a whole is negated. (R8'), then, provides a description of the use of WH-clauses as headless relative clauses which describes how they induce presuppositions. In particular
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--..3 1 state(!, believe) 1\ agent(!, A) 1\ object(!, •[3] action (!, enjoy) 1\ agent(!, C) 1\ object(!, F) 1\ 3K : (interval(K)} 3L : {instant(L)Jbtfore(L, now) 1\ contains(K, L) 1\ during(K,j)]) 1\ 3M : (interval(M)}contains(M, now) 1\ during(M, I)
- ���
------.
274 Presuppositions and WH-clauses
we can now provide a formal paraphrase of the first of our initial pair of sentences:
( 1 ) Iknow what l want. This is just a transitive sentence where the complement NP is a WH-clause, and its formal paraphrase is exactly parallel to the one we obtained for (26): CONTENT:
3F state(F, know) A agent(F, A ) A object(F, D) A 3 G : {interval(G))contains(G, now) A during( G . F) PRESUPPOSITIONS:
The presuppositions anchor D to some set of items that the speaker wants (this anchoring is unlikely to be unique-( I ) may presuppose the existence of an objecnhanhe speaker wants, but it docs not provide any further information which could be used to pick out the relevant item). The content then says that the speaker 'knows' this object. Just what this means is unclear. There has been a great deal of discussion about what it means to say that an agent knows a proposition, but very little about what it means to say that an agent knows an object. We do not intend to start this discussion now, beyond saying that there is a great deal more to it than having access to a rigid designator for the item in question. For the purposes of the current paper it is sufficient to say that analysis of sentences like (40) I knowJohn's wife. and (4 1 ) Myfriend knows a good plumber. involves some relation between individuals, and that the same relation is required for the correct analysis of ( I ). We now turn to our other target sentence: (2) What I want is a cold drink. Before we consider (2) itself we will look at (42) john is the winner. (43) john is afool.
It is hard to see that (42) can mean anything other than that there is a person called John, there is a winner, and these two are the same thing. The existence of
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member(speaker, A ) A !AI - I , member(speaker, B ) A IBI = I , 3 C state( C, want) A agent( C, B ) A object( C, D) A 3 E : {interval(E)}contains(E, now) A during(E, C)
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a winner and a person called John are presuppositions arising from the two NPs. The only contribution the copula is can be making is that the two items are identical. We therefore have a reading of be which assigns it the following semantics: semantics(presuppositions(0), pr1!x(•[I, I]), matrix(• [T, • [A1, • [A2, 3E(equality(E) 1\ (•[X, arg 1(E, X)] E A1) 1\ (•[Y, arg2(E, X)] E A2) 1\ (E E T))]]])
(44) John would have been the winner. Using the above analysis of be we obtain the following entirely reasonable paraphrase of (42): CONTENT:
3E state(E, equal) 1\ arg I (E, A) 1\ arg2(E, C) 1\ 3F : (interval(F)jcontains(F, now) 1\ during(F. E) PRESUPPOSITIONS:
subset(A , o[B, name(B, john)]) 1\ IA I = subset( C. •[D, winner(D)]) 1\ ICI = I
I,
The paraphrase of(43) that we obtain this way is more contentious: CONTENT:
3 C : {subset(C, • [D,fool(D)]) 1\ ICI - I } 3E state(E, equal) 1\ arg 1 (E, A) 1\ arg2(E, C) 1\ 3F : (interval(F)jcontains(F, now) 1\ during(F, E) PRESUPPOSITIONS:
subset(A , •[B, name(B,john)]) 1\ !A I -
1
Informally it seeiUS as though (43) says thatJohn has all the properties that a fool would have. The formal paraphrase says that there IS some fool, and that John
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T here is waiting for a temporal relation, to be provided by tense markers and/ or auxiliaries. A1 and A2 are waiting for the kind of expression provided by the NPs which will occur as the subject and complement of the verb. The presupposition set of the verb itself is empty-the rules which say how this sort of verb can be combined with a complement and a subject to make up a sentence will combine the presupposition sets of these two NPs to generate the presupposition set of the resulting sentence, just as happened with transitive verbs earlier on. The use of an explicit entity which IS the equality may seem clumsy, but it turns out to be extremely convenient when we come to consider sentences with complex temporal components such as:
276 Presuppositions and WH-clauses
and this fool are identical. At first sight it looks as though there is a difference between these. It is very hard, however, to see any consequences of the informal paraphrase that do not follow from the formal one, or vice versa. If there is some ' individual who is a fool then they must have all the properties which fools have, so ifJohn is this individual then he must have all the required properties. But if John has all the properties that fools have then he must be one, so one does exist and is identical to John. This is not the end of the matter. We will not obtain accurate formal paraphrases of generic copula sentences like (4 5) The elephant is a herbivore.
(46) No one knows why the dinosaur died out. (47) A lion will eat a gazelle ifit can catch it.
We assume that an adequate treatment of the dinosaur, a lion and a gazelle in these examples will also enable us to use our treatment of copula sentences for (45), and leave the discovery of an adequate treatment of all these cases for others. We now return to (2). Given that what I want can be seen as an NP, there seems no reason to suppose that (2) is anything other than a perfectly ordinary copula sentence. The semantics for copula be that were used for (42) and (43 ) lead to the following paraphrase of (2): CONTENT:
3F: [subset(F, G[G, drink( G) 1\ 3H condition(H, cool, 0[!, drink(!)]) 1\ object(H, G)]) A I Fl = I } 3] state(!, equal) 1\ arg i (!, C) 1\ arg2(!, F) 1\ 3K : {interval(K))contains(K, now) 1\ during(K,j) PRESUPPOSITIONS:
member(speaker, A ) 1\ IAI = 1 , 3B state(B, want) 1\ agent(B, A ) 1\ object(B, C) 1\ 3D : (interval(D))contains(D, now) 1\ during(D, B) As with (43 )
the statement that some cold drink exists and is the same entity as the thing I want is problematic. Again, however, it is hard to see that anything undesirable actually follows. (2) does seem to presuppose the existence of a wanting by the speaker, and as such it must further presuppose the existence of some object that the speaker wants. But once the existence of this object has been conceded the argument that we used to support the treatment of (43 ) works again. This thing that I wanted exists and has all the properties that a long
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this way. Generic uses of definite and indefinite NPs are generally problematic, and seem to require some kind of systematic ambiguity:
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(3) What you see is what you get. This is j ust a copula sentence both of whose arguments are headless relatives, with the following formal paraphrase: CONTENT:
3/state(I, equal) 1\ arg i (l, C) 1\ arg 2 (I, G) 1\ 3]: (interval(J))contains(J, now) 1\ during(!, I) PRESUPPOSITIONS:
member(hearer, A ), 3B action (B, see) 1\ agent(B, A ) 1\ object(B, C) 1\ 3D : (interval(D))contains(D, now) 1\ during(D, B), member(hearer, E), 3F action(F, get) 1\ agent(F, E) 1\ object(F, G) 1\ 3H : (interval(H))contains(H, now) 1\ during(H, F) 6 CONCLUSIONS We have presented a formal framework for dealing with the presuppositional ·aspects of simple natural language sentences, and have used it to show how to
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cool drink has: from this it follows immediately that there is something which is a long cool drink. If this analysis of the semantics of (2) is correct, it seems that there is no need for a special syntactic rule for 'WH-clefts' or 'pseudo-clefts'. We have obtained an interpretation of(2) that captures what seem to be its presuppositions simply by analysing it as a copula sentence. The presuppositional element, which we embody as a set of presuppositions, arises from the presence of a WH-clause in a position where an NP is expected. Exactly the same treatment of such headless relatives leads to appropriate presuppositions in other kinds of sentence. If we wanted to propose a different analysis of their contribution in copula sentences we would in fact have to SUPPRESS their usual presuppositional effects, and then recreate them in the semantics of the rule for pseudo-clefts. It is possible to point to infelicities in our treatment of (2), but exactly the same problems arise with our treatment of any copula sentences with indefinite NP complements. We have tried to argue that the formal paraphrases we have given for (43) and for (2) do not lead to any unwanted conclusions, and that they are therefore correct. But even if they are not, the problems arise from the way we have treated indefinite NPs in copula sentences, not from the collapsing of pseudo-clefts into copula sentences involving headless relatives. We end this section by pointing out that we now have a particularly simple treatment of sentences like:
278
Presuppositions and WH-clauses
describe the syntax and semantics of the English sentences usually referred to as WH-clefts or pseudo-clefts. There are numerous things we have not done. We end with some remarks about three particular issues which we have said nothing about so far, namely the relation between clefts and pseudo-clefts, the use of presuppositions for introducing new informacion and the problem of presupposition projection.
6.1
Clefts and pseudo-clefts
(48) It was a cold drink which I wanted.
has two readings. In one it refers to some known object, was is a simple copula, and a cold drink which I wanted introduces an alternative characterization of the referent of it. The main verb here is indeed a copula, but the WH-clause is functioning as a simple restrictive relative clause and the only presuppositions come from the pronouns it and I. On the other reading the pronoun it does not refer to a previously considered entity. The main verb therefore cannot be read as a straightforward copula asserting the identity of its subject and object, since the subject does not refer to anything. In this case the WH-clause does seem to induce a presupposition in the way that WH-clauses generally do when functioning as NPs, so that it seems unlikely that it is merely a relative clause modifying drink, cold drink or a cold drink. In other words, (48) does embody a specific syntactic form which requires its own semantic treatment. There is nothing remarkable about this. There are plenty of special syntactic forms which require individual semantic treatments. As far as the syntactic properties of genuine clefts are concerned it is notable that the range of permitted WH-markers is quite different from the range permitted in headless relatives:
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We have spent a great deal of time in an attempt to argue that pseudo-clefts do not exist. The main argument above was that WH-clauses can occur in most of the places where NPs can occur, and that whenever they do they induce presuppositions. This being so, there is nothing unusual about occurrences of WH-clauses in copula sentences. The syntax of copula sentences says that the subject and complement should both be NPs. WH-clauses can appear in most places that NPs can so it seems reasonable to allow them to appear in copula sentences. But since WH-clauses always induce presuppositions when they behave like NPs, it is now clear why pseudo-clefts induce presuppositions because they have WH-clauses where NPs are expected. We cannot give any such argument to dismiss the existence of clefts themselves. The sentence
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(49) It was what I saw which surprised me. (so) •It was which I saw what surprised me. None the less, even in dialects in which It was a cold drink that I wanted is preferred to (48) it seems likely that the best way to deal with the presuppositional aspects of cleft semantics is by assuming that the second complement is a WH-clause which introduces presuppositions in the usual way. Such WH-clauses may have slightly different syntactic properties from the kinds ofWH-clause that can occur as headless relatives, but their semantics is surely very similar.
Presuppositions and new information
It has been widely noted that presuppositions can be used in contexts where the speaker does not believe that the presupposed information is already known to the hearer. A notable example is Appelt's (I985) suggestion that the sentence (s I ) Use the whee/puller to remove theflywheel . might be used to name some object at the same time as indicating its function (a suggestion that Appelt never really follows up on). Barwise and Perry's ( I 983) examples about conversations at fancy-dress parties (where a speaker points to someone whose identity is known to their hearer and says That's my wife in order to provide a clue about their OWN identity) fit into the same general pattern. Such uses of presuppositions for conveying new information seem to assume that the information is not very new. Consider for instance (52) The driver ofthe bus I came to work on this morning must have been drunk . and: (s 3) The driver ofthe bus I put a monkey on this morning must have been drunk . It would be perfectly acceptable to start a story by saying (52). Even if my hearer did not know how I usually get to work, going by bus is a sufficiently ordinary thing to do that (52)'s presuppositions that I came to work on a bus and it had a driver could easily be ACCOMMODATED. Similarly, if it is absolutely clear which tool the speaker intends the hearer to use for removing the flywheel then ( s I ) could probably be used in the way that Appelt suggests. (s 3), on the other hand, would be a remarkable way to start a story. Putting monkeys on buses is not something which people do very often. (s 3) presupposes that the speaker did perform this rather unusual action, and because the action is so unusual it cannot be accommodated. The cases where new information is provided via a presupposition seem
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6.2
280 Presuppositions and WH-clauses
more puzzling than the ones where this is not acceptable. We have dealt with presupposmons in terms of constrained proposmons, where the presuppositions anchor the content in the initial information state. Therefore if the initial information state fails to induce a substitution from the presuppositions then the incremented information state will be undefined. At least this is what ought to happen. What happens when (52) is used without appropriate preliminaries? We suggest that much the same processes are happening here as when someone asks (54) Can you pass me the salt? Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
in a situation where it is quite clear that their hearer can indeed pass them the salt. The MEANING of (54) is that the speaker wants to know about the hearer's physical ability to perform the relevant action. What the speaker MEANS BY IT is something else entirely. The discrepancy between what something means and what someone means by it has, of course, been studied at great length in the literature on speech acts (Searle 1 969; Allen & Perrault 1 980; Cohen & Perrault 1 979; Cohen et a/. 1 990). Some progress has been made, though there are still serious flaws in a lot of this work (Ramsay 1 99ob). The major point is that indirect use of speech acts like asserting and querying depend crucially on the presence of a fixed direct interpretation. Most work in this area claims that (54) works because the hearer recognizes that the speaker cannot really be intereted in their ability to pass the salt (since this is self-evident) and hence tries to reconstruct some plan for which this ability would be a prerequisite (e.g. persuading the hearer to actually pass it). Any such story must use the literal meaning, even if it eventually gets used in some indirect way. Much the same is true of presuppositions that are not in the common ground of the speaker and hearer. By presupposing A the speaker is asserting that he believes that A is common ground, in just the same way that someone saying (54) is asserting that he does not know what his hearer can do. The speaker is quite entitled to reject these assertions, just as she would if she thought the speaker was lying. None the less, she may want to know WHY the speaker asserted this false proposition. The use of presuppositions for conveying new information, then, is just like the use of YES/NO questions about people's knowledge and physical abilities. The words as uttered have a distinct well.:..defined meaning. Speakers can, however, utter them in contexts where that meaning is inappropriate. By doing so they invite their hearers to see what would have to happen to the context to make the literal meaning appropriate. The inference mechanisms that hearers use for this are clearly well worth studying, but the focus of the current paper is the literal meaning which the hearer is given and invited to manipulate rather than the mechanisms they use for manipulating it.
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6.3
28 r
Presupposition projection
The argument of this paper has been directed entirely at the way the components of a simple English sentence contribute to its presuppositions-in particular at the contributions that headless relative clauses make. A large part of the literature on presuppositions, however, is concerned with what happens to the presuppositions of isolated sentences when they are combined together the PROJECTION problem. We end by looking at two particular cases, in order to see what sort of solutions are available in our framework. The first of these is the well-known 'donkey sentence': The problem here is that the constituent sentence lze beats it clearly presupposes the existence of a male individual and a neuter individual, whereas (s s) as a whole does not seem to presuppose the existence of either. Somehow these presuppositions get masked by the initial clause of ( s s). The following rule achieves the required effect: (R9) If (S 1 ) then (S2)
jd (syntax((SENTENCE)), semantics (presuppositions (PREanuudent U {( CQNTanteudent E QUA NTSanttcedent) --> PR£consequent }), prefix(•[!, I]), matrix(( CONTanteudent E ( CON�onsequent E QUANTSconstquenr))) -
jd (syntax((I F)), semantics (. . .)), jd (syntax((SENTENCE)), semantics (presuppositions (PREantecedtnr ) prefix ( QUANTanteudtnt), matrix( CONTanuudenr)), jd (syntax ((THEN)), semantics (. . .)), jd (syntax((SENTENCE)), semantics (presuppositions (PRE,oruequenr) prefix( QUANTconsequent), matrix( CONT,o,.q.. uenr)), It seems uncontentious that the compound sentence should inherit the presuppositions of its antecedent. The difficulty is to decide what to do about
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(s s) IfPedro owns a donkey then he beats it .
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Presuppositions and WH-clauses
the presuppositions of the consequent. (s s), for instance, was problematic because the consequent had presuppositions which were not presuppositions of the sentence as a whole, namely that there must be a male individual and a neuter individual. We have shown that this can be dealt with by converting the presupposlnon PREconsequent of the consequent to ( COJ\;Tanttcedent E Q UANTSantuedent) -+ PRE,onsequmt before we include it in the presuppositions of the overall sentence. Consider the following analyses of the constituent sentences of (s s): (56) Pedro owns a donkey . CONTENT:
PRESUPPOSITIONS:
subset(A , •[B , name)]) 1\ IAI =
I
(57) He beatsit . CONTENT:
3Eaction (E , beat) 1\ agent(E , A ) A object (E, C) 1\ 3F : {interval (F))contains (F, now) 1\ during (F, E) PRESUPPOSITIONS:
subset(A , • [B , male(B )]) 1\ IA I = 1 subset ( C. • [D , neuter(D)]) 1\ ICI =
I
The content of the first of these entails the presupposition subset(C, • [D , neuter (D)]) 1\ ICI = I o f the second (this is the presupposition that arises from the pronoun it). Hence if we take the presupposition of (s s) to be the claim that the content of the antecedent implies the presupposition of the consequent then this element of the presupposition of the consequent is vacuous. It can be verified by showing that the existence of a donkey entails the existence of a neuter object, which can be done without any reference to the context of the utterance (in other words, without any reference to the initial information state). The other presupposition of he beats it is itself entailed by the presupposition arising from the use of the name Pedro in the antecedent. Thus although this presupposition survives to be a presupposition of (s s), it will always be supported by any information state which supports subset (A , • [B , name (B , pedro)]) 1\ !AI - I and hence cannot cause any problems. (R9) thus shows how the projection problem for compound sentences might be approached. Similar stories could probably be told about sentences like
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3C :{subset (C, •[D, donkey)]) 1\ I CI - I } 3Estate (E , own ) 1\ agent(E, A ) 1\ object(E, C) 1\ 3F : {interval (F))contains (F, now) 1\ during (F, E )
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28 3
(s8) Mary bought a peach and a pear and gave the pear toJohn . and: (59) Pedro beats his donkey ifit disobeys him . This is, however, only half the projection problem. The other half is closely associated with what in other contexts is referred to as the de re!de dicto distinction or as opaque/transparent reference. Consider (6o) The mana�er is Mary's husband. and: (6o) clearly presupposes the existence of a manager. What about (6 I )? We can paraphrase (6 I ) in two ways. The de re reading is something like:
(62) There is a unique individual X who is t!te manager, andJolm believes X is Mary's husband. On this reading (6 I ) clearly inherits the presuppositions that there is a manager. This contrasts with the de dicto reading, which we can paraphrase as: (6 3) John believes that there is a unique individual X w!to is t!te mana,�er and that X is Mary's husband. This time (6 I) would equally clearly not inherit the relevant presupposition. Suppose we introduce an alternative description of the semantics of the as:
semantics(presuppositions(•[DUMMY, 0]), prifix(• [PROP, • [A, (3!X : (subset(X, PROP) 1\ lXI matrix(• [ Q, X e Ql))
=
I ))A]]),
This is extremely similar to the basic description of the semantics of a, apart from the uniqueness requirement. If we use these two descriptions of the in the analysis of a typical definite NP such as the the manager we will obtain the following two interpretations of (6 I ): CONTENT:
31 state(I, think) 1\ agent(!, A) 1\ object(!, • [3] stateU, equal) 1\ arg i U, C) 1\ ar�2U, G) 1\ 3K : (interval(K))contains(K, now) 1\ during(K,J)]) 1\ 3L : {intervai(L ))contains(L, now) 1\ durin�(L , I) PRESUPPOSITIONS:
subset(A , • [B, name(B,john)J) 1\ IA I - I ,
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(6 I ) John believes the mana�er is Mary's husband .
284 Presuppositions and WH-clauses
subset(C, • [D, manager(D)]) A ICI = I , subset(E , • [ F, name(F, mary)]) 1\ lEI = I , subset(F, •[H, husband(H)]) I\ own(E, C) A lGI -
I
and: CONTENT:
PRESUPPOSITIONS:
subset(A , • [B, name(B,jolm)]) 1\ IA I = I , subset(C, • [D, name(D, mary)]) A ICI = I , subset(E, • [F, husband(F)]) 1\ own (C, E ) 1\ lEI =
I
The analysis of Mary's husband in terms of a singleton set of husbands that Mary owns is rather inelegant, though the decision to treat this kind of NP as something which introduces presuppositions is correct. What is of considerably greater interest is the treatment of the manager in the two analyses. The first deals with it as an ordinary definite reference, introducing the presupposition that there is a manager. The second attributes to John the belief that there is a unique individual who is the manager. On the second reading (6 I ) could be true even if there is in fact no manager. Thus the machinery we have developed provides us with the expressive power to investigate various interpretations of definite NPs. Using it we have shown how to provide a formal paraphrase of the NP the manager which does not lead to any presuppositions. There is, however, a great deal more to be said about both donkey-sentences and about uses of definite NPs in opaque contexts. All we have tried to show in this concluding section is that the framework we have developed for dealing with simple uses of definite NPs and with headless relative clauses is rich enough to support investigations of these other phenomena. Arguing for specific treatments of these phenomena within this framework is a task for another day. ALLAN RAMSAY Department ofComputer Science University Collexe Dublin Belfield Dublin 4 Ireland
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3G state( C. think) I\ agent( C, A) I\ object( C . • [3 !H : {subset(H, •[I, manager(!)]) 1\ IHI - I ) 3] stateU, equal) I\ arg i U. H) I\ arg2U, E) 1\ 3K : {interval(K))contains(K, now) 1\ during(K,j)]) I\ 3L : {interval(L))contains(L, now) I\ durin�(L, G)
Allan Ramsay 285
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