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JOURNAL. OF SEMANTICS Volume rs Number
I
CONTE NTS REINHARD BLUTNER AND
Editorial Preface
RoB
VAN DER SANDT
1
KEEs vAN DEEMTER
Ambiguity and Idiosyncratic Interpretation EGG Wh-questions in Underspecified Minimal Recursion Semantics
MARCUS
NICHOLAS AsHER AND ALEX LASCARIDES
Bridging
s
37 83
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Scope of this Journal The JOURNAL OF SEMANTICS publishes articles, notes, discussions, and book reviews in the area of natural language semantics. It is explicitly interdisciplinary, in that it aims at an integration of philosophical, psychological, and linguistic semantics as well as semantic work done in artificial intelligence and anthropology. Contributions must be of good quality {to be judged by at least two referees) and should relate to questions of comprehension and interpretation of sentences or texts in natural language. The editors welcome not only papers that cross traditional discipline boundaries, but also more specialized contributions, provided they are accessible to and interesting for a wider readership. Empirical relevance and formal correcmess are paramount among the criteria of acceptance for publicatioiL
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journal of&manlics
15: 1-3
© Oxford Universiry Press 1998
Editorial Preface
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Underdetermination of meaning has recently become a central issue in computational semantics and formal language processing. Developments in these fields have made clear that spelling out all the information which can be given at some level of representation goes beyond what is needed to arrive at a full interpretation of an utterance. The proliferation of formal structures (and their corresponding interpretations) in actual attempts to·do so is moreover unwanted for reasons of computational complexity and at odds with the fact that natural language users tend to process ambiguous expressions without any effort. Over the last few years several efforts have been made to overcome these limitations by developing semantic theories of underspecification. Such theories are based on representations that are themselves ambiguous. Much of this research has been motivated by computational considerations, the favorite applications having to do with (quantifier) scbpe and ellipsis. This has led to various representational formats all of which underdetermine the actual interpretation of utterances. From a methodological perspective work on underspecification forces us to rethink the traditional way in which the semantics/pragmatics boundary has been drawn. In recent years (and under the influence of the 'dynamic turn') there has been a shift in emphasis from pragmatics to semantics. Many phenomena which had been labeled pragmatic in earlier theories turned out to be amenable to a semantic treatment in dynamic theories ('intonational' focus, 'pragmatic' presupposition, connotations of temporal succession, etc.). Recent work in underspecification seems to push us in the opposite direction. Once we allow 'flat' underspecified representations we shift much of the burden of determining the information that a sentence conveys back to pragmatics again. The point is more than just a matter of terminology and brings us to questions of lexical representation, abduction, defeasible reasoning and the role of contextual accommodation in linguistic processing. Most of the papers in this issue derive from a workshop on 'Structural Grammar' which was organized by the Max-Planck ·Research Group in Berlin. The aim of the workshop was to consider underspecification from the perspective of theoretical linguistics. Recognizing the important role of the lexicon in current theorizing, the workshop devoted special attention to the lexical aspects of semantic underspecification and the inclusion of underspecified lexical entities in the general setup of grammar. A second
2
Editorial Preface
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central topic of the workshop related to the mechanisms which allow us to derive conceptually/contextually enriched interpretations from semantically underdetermined representati
Journal of Semantics
3
·
REINHARD BLUTNER ROB VAN DER SANDT
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Lascarides' formalization is based on a combination of segmented DRT and a 'glue logic' of commonsense entailment known as DICE. Blutner's paper, which-together with Strigin's contribution-is pub lished in vol. 1 s .2, investigates the interaction between the (mental) lexicon and pragmatics. Its aims to give a systematic and explanatory account of pragmatic phenomena connected with the semantic underspecification of lexical items. Special attention is given to the pragmatics of adjectives, systematic polysemy and blocking phenomena. The account is based cin conditions of updating the common ground and explicates such notions as (generalized) conversational implicature and pragmatic anomaly. The basic mechanism is extended· by an abductive reasoning system. This system differs from the one proposed by Hobbs where interpretation is seen as inference to the best explanation. On Blutner's account interpretation is viewed as abductive· inference to coherent (but possibly inconsistent) ·enrichments. Strigin's main topic is the characterization of sense extension as a kind of . regularity in the interpretation of polysemous words. The literature offers two principally different ways to analyze these regularities. On the one hand there is the lexical account which tries to understand them as implicational relationships. On the other there is the pragmatic account which seeks to understand them as sense transfer triggered by conceptual knowledge. Strigin gives a critical discussion of both accounts, develops a variant of the pragmatic approach and· sketches the notion of a transfer function in the context of an abductive theory of lexical interpretation.
journt�l ofSnnaniW 1 s: s-36
© Oxford University Press
1998
Ambiguity and Idio�yncratic Interpretation KEES VAN DEEMTE R
University of Brighton Abstract
1
INTRODUCTION
Natural language is ambiguous at various levels of interpretation. At a low (e.g. speech recognition) level, a signal can be ambiguous between various utterances ; at a higher (semantic) level, a fully recognized utterance can be used to express various different propositions; and at an even higher (pragmatic) level, a proposition may be used for various different purposes. Ambiguity, understood in this broad way, is the main problem that confronts humans or machines when they try to interpret natural language. This paper will focus on ambiguities of the second kind, which are sometimes called semantic ambiguities or also just ambiguities, when there is no likelihood of confusiotL Semantic ambiguity can arise from various different sources. For example, the source of an ambiguity may be lexical (as in cases of lexical homonymy and polysemy), syntactic (when an expression has more than one possible syntactic derivation), or contextual (as in anaphoric ambiguities). Combinations of such different sources occur as well, for example when a word is ambiguous between different parts of speech. It has often been observed that semantic ambiguity is one of the most daunting problems for automatic interpretation of natural language. (See
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This paper discusses logics whose premisses and/or conclusions can contain ambiguous material. Two different kinds of applications are sketched for these logics. first, the paper discusses how logics with ambiguous expressions can shed light on the way in which human hearers or readers understand certain 'paradoxical' logical arguments, in which crucial use is made of ambiguous material. Second, the paper uses practical applications to show how a logic ambiguous expressions can be used to avoid interpretational deadlock in such systems. Here a key role is played by the Principle of Idiosyncratic Interpretation, which states that, in a given context of occurrence, different human interpreters may be unaware of each other's interpretations of an utterance. This principle is shown to have important consequences for the choice between different possible logics. To illustrate how a logic of ambiguous formulas can be used in Natural Language Processing, the case of a Question-Answering system is discussed in some detail.
6
Ambiguity and Idiosyncratic Interpretation
Bar-Hillel 1 960 for an early and very outspoken statement of this claim). It is sometimes suggested that the main problem here is one of combinatorial explosion and it is true that the number of calculations to be performed for some types of ambiguities can 'explode' (see e.g. Ristad & Berwick 1989). But the situation is not the one in which considerations of computational complexity usually come to the forefront, namely where one has to perform a great number of calculations each of which is unproblematic in itsel£ The situation in disambiguation is typically much more complex: the number of interpretations may be small or great, but it is often completely unclear how to decide which ones can be refuted. As a result, disambiguation is deadlocked. For example, consider the following sentences. Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Three boys carried a piano up the stairs. None of the standard disambiguation algorithms can refute interpretations according to which each boy carries a separate piano. To discard this interpretation one would have to represent some highly nontrivial bits of common sense knowledge about
- boys (How much can they carry?) - stairs (What is their size, shape, and structure?) - pianos (What is their shape and weight?) Let us assume that all this information may once be formally represented in some common-sense knowledge base, perhaps of the kind advocated in Guha & Lenat 1990. This knowledge would have to be used in inference, along the following lines (see e.g. Buvac 1996), where cs represents the knowledge presumably shared by all competent speakers of the language. A 'grammatically possible' interpretation is an interpretation that is. logically well formed 1 as well as in accordance with all the linguistic rules governing the sentence as uttered in its linguistic context. Speaker has uttered sentence S; , Pn are the only grammatically possible interpretations of S; cs f= ..., p;; therefore, P1 , . . . p;- 1 , Pi+ 1 , Pn are the only remaining interpretations of S.
p1 ,
•
•
•
•
•
•
More intricate versions of the same pattern of reasoning aimed at 'charitable interpretation' would include knowledge of the speaker that is not a part of cs but, for example, asserted earlier by the same speaker. Note that the inference presented is only valid if several assumptions are made whose truth can be extremely difficult to assess in practice. For example, it must be assumed that cs contains, in principle, sufficient information to refute p; (e.g. Does common-sense knowledge rule out the possibility of a boy carrying a piano? Even if he is aided by advanced
·
Kees van Deemter
7
equipment?) ; it must be assumed that the speaker is not only a competent speaker of the language, but she must also be able to perform the inference cs F •p; 'on line', and she may not be speaking in irony, etc. Clearly, all of this makes it extremely difficult to exploit common-setl.se knowledge for the disambiguation of natural language. So difficult, that it is unlikely that this strategy will allow a natural language interpreting system to get rid of all ambiguity.
2
UNDER S P ECI FIED REPRESENTATIONS
1.
2. 3· 4· 5·
Ax: Ax: Ax: Ax: Ax:
Country(DeparturePlace(x)) USA (for a flight), Country(ArrivalPlace(x)) USA (for a flight), Country(Manufacturer(x)) USA (for an airplane), Country(PlaceOJBirth(x)) USA (for a person), Carrier(x) = American Airlines (for a flight), =
=
=
=
and so on. Let us assume that these five options exhaust the possible interpretations of American. In Phliqa, the word AMERICAN would be mapped on to an ambiguous constant AMERICAN, which is later mapped to one of the unambiguous paraphrases AMERICAN 1, AMERICAN2, etc., each of which had one of the interpretations listed. For example, the query 'How many American flights are operated by Quantas?' would be translated into a formula describing the cardinality of the set
{xt:
flights: AMERICAN (x) &
Operator(x)
=
Quantas},
where Operator(x) stands for 'the carrier operating the Departure of the flight x'. The interpretations corresponding with (3) and (4) above are refuted as a result of type conflicts. (The Predication Operator(x) = Quantas shows that x can neither be a person nor an airplane.) But ( r ), (2), and (s) lead to distinct and respectable interpretations:
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Mainly to avoid the need for separate storage of all possible interpretations, computational semanticists now routin�ly use levels of semantic inter pretation that contain ambiguous representations. An early example is the PHLIQA system (see e.g. Bronnenberg et al. 1979), in which this strategy was applied mainly to cope with lexical ambiguities. An examplez is the ambiguity of the word American, which can mean
8
Ambiguity and Idiosyncratic Interpretation {Xf. flights: Country(DeparturePlace(x ) )
Operator(x)
=
{xf. flights: Country(ArrivalPlace(x ) )
Operator(x)
=
=
USA
&
Quantas}, USA
&
Operator(x)
=
=
Quantas}.
{xf. flights: Operator(x )
=
AA &
Quantas}.
1.
2.
How do people process ambiguous information? What kinds of processing are (logically) possible on the basis of underspecified representations? In particular, how can ambiguous information be represented and how can it enter logical inference?
Processing of ambiguous expressions by humans (r) has always been a major concern of psycholinguists. Psycholinguists, however, have usually focused on 'apparent' ambiguities, which can be resolved by linguistic aspects of the context of occurrence (e.g. MacDonald et al. 1994 ). The widespread use of underspecified semantic representations has triggered questions such as, for example, Under what circumstances is disambiguation necessary (Poesio 1994, 1996 )? What kinds of inferences do people draw from an utterance
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Similar ideas were applied to quantifier scope ambiguity in Schubert & Pelletier 1982. This track of research gained popularity in the late 198os, when linguists at SRI proposed their underspecified 'quasi-logical forms' (see e.g. Alshawi 1990 ). The advantage of using underspecified logical formulas for the representation of linguistic meaning can be considerable: the syntax is not burdened by purely semantic considerations (Fenstad et al. 1987), and the computational load on the system, for storing and processing the meaning of a formula at a stage at which it has not yet been resolved, is reduced considerably. On the other hand, the ambiguous representations are typically not put to real use until a separate module has disambiguated them. In particular, the information in them is not evaluated semantically or used in logical inference. 3 Thus it was impossible for the systems described to exploit the fact that, since Quantas operates only flights whose departure and arrival are in the same country, AMERICAN, and AMERICAN 2 lead to basically the same query. We will see in section 5·3 how such facts may be exploited to improve the system. Since the systems described cannot do much before they have resolved all ambiguities, it is often impossible for them to find an intelligent way of dealing with ambiguities at all, because the information that could, in principle, disambiguate them is unavailable. Underspecified representations by themselves do little to solve the problem of interpretational deadlock, but their use has prompted some important questions:
Kees
van
Deemter
9
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before it is fully disambiguated? (For example, if you shout Watch out! He's trying to shoot you, the addressee might decide to seek hiding even if he is unable to resolve the referent of the pronoun he.) It is intuitively clear that language understanding is not an all-or-nothing affair and one would ultimately want to model the understanding process in a way that reflects this. Many of the relevant issues must be left alone here, but one of them will be discussed in some detail: In section 4, we will illustrate how the logic of underspecified representations can shed light on the difficulry people have in assessing the validiry of a certain rype of paradoxical logical arguments; namely those whose paradoxicaliry hinges on the ambiguiry of some of the expressions making up the argument. The second issue (2), which concerns the kinds of processing for which underspecified representations can be used, will be the main topic of this paper, which will also underlie what we have to say about paradoxical arguments. We will focus on one kind of processing, namely logical inference. Many computational linguists (for references, see section 3) are now trying to move one step beyond merely representing ambiguous information in a natural-language processing system and to wait it out until disambiguating information comes along. This next step, which, to the best of my information, has not been applied in any real system yet, is to use ambiguous sentences as premisses or conclusions of logical reasoning. An important motivation for this work is the idea that if and when a reasoning component is in place that can deal with ambiguous premisses, then complete disambiguation is no longer always a necessiry. To give the flavour of the idea, suppose a user of a question-answering system addresses the system by asking an ambiguous yes-no question, and suppose the system is designed to answer questions by trying to prove their truth or falsiry from premisses stored in a database. Now if, for example, the negation of each interpretation of the question can be proven, then the reasoning component could infer that the answer to the question has to be negative. Consequently, disambiguation of the question is not necessary, and a negative answer can be given. The case of an affirmative answer is analogous, of course. In what follows, we will discuss the various ways in which a logic for underspecified representations (an 'ambiguous logic', for short) can be useful. Usefulness will be taken in a rather broad sense, since we will not only show how ambiguous logics can help us cope with the problems of natural language understanding, but also how they can be used to shed light on some issues in philosophical logic. The aims of this paper, as stated here, differ from those of most other work on underspecification. Most of this work focuses on specific linguistic phenomena such as the ambiguities of quantifier scope. The present paper,
1o
Ambiguity and Idiosyncratic Interpretation
3
LOGI C S FOR UN DER S PECIFIED REPRES EN TATIONS
The basic fact underlying the notion of ambiguity is that some expressions can be used for more than one purpose and that this can cause indeterminacy of interpretation. More precisely, and focusing on sentences, a sentence S is ambiguous between two nonequivalent propositions cp and '1/J if S can be uttered to express cp but also to express '1/J. If cp and '1/J can be expressed unambiguously by sentences s. and S2 respectively, it is also said that S is ambiguous between S1 and S2• When no other information about the speaker's intentions is available, the situation can be summed up conveniently in a formalism often used in natural language generation (e.g. Moore & Paris 1 994): Intend (Speaker, Intend (Speaker,
{MB (Speaker, {MB (Speaker,
Hearer, cp))) V Hearer, '1/J))).
Intend (x,¢) says that x intends to make it true that¢; MB(x, y,¢) says that ¢is mutually believed between x and y. The disjunction reflects that the interpreter of S is uncertain whether cp or '1/J is intended. s In accordance with the tradition· of logical semantics (e.g. Montague 1 973), we will use logic as a mediator between linguistic form and model theoretic meaning. From this perspective, the natural move if one wants to study the ambiguity of natural language is to set up a new logic and to define a mapping in which each sentence of natural language is mapped on to one potentially ambiguous formula of the logic. Logicians have, until recently, never had much use for ambiguous formulas. Surprisingly, this is
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by contrast, will abstract away from what the different interpretations of a given utterance are, how they may be discovered and represented. Having done this, we will ask what role the utterance, or its formal representation, can play in logical inference. We will try to answer this question by looking at specific problems. We will suggest that a general appeal to intuitions about the logical validity of an inference is sometimes ineffective since, in the case of ambiguous logic, the validity of an inference can depend on the setting and purpose of the .inference.4 Section 3 will introduce the main concepts that we will need in our discussion of ambiguous logic. Section 4 will show how these concepts can be used as an instrument for the analysis of philosophical questions. Section 5 will discuss the issue of what are appropriate notions of ambiguous consequence. The concluding section will discuss a number of objections that have been advanced against some of the ideas in the preceding sections.
Kees van Deemter
II
-
Truth, relative to a disambiguation: r.p is trued (falsed) with respect to d(r.p) is true (false} w.r.t. M, Strong truth: r.p is truev (falsev)
·
a model
M {::}
with respect to a model M all paraphrases of r.p are true (false} w.r.t. M,
{::}
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also true for logicians who work on the semantics of natural language. An example is Thomason who wrote, explaining Montague's notion of a 'disambiguated language': 'there is no serious point to constructing an artificial language that is not disambiguated' (Thomason 1974). As a result, there still are few formal tools to study logical consequences as a relation between sentences some of which may be ambiguous. But recently, some tentative efforts in this direction were made, including Reyle ( 1993, 1 995, 1996), van Deemter ( 1 991, 1996 ), van Eijck & Jaspars ( 1 995 ), Fernando ( 1995 ), Alshawi ( 1 990), Poesio ( 1 994, 1 996). So far, there is little unanimity about what is or are acceptable notions of logical consequence in an ambiguous setting (ambiguous consequence, for short). In what follows, we will introduce some basic terminology and, drawing on insights from the literature, we will chart the main avenues for defining truth and ambiguous consequence. A discussion of the relative merits of the different definitions will be postponed until section 5 .2. The logic of underspecified representations has been studied using different underlying representational formalisms (predicate logiC, DRSs, etc.). In addition, ambiguity has bee.n modeled in different ways. In our discussion of proposals in the literature, we will neglect representational differences between them, ·pretending instead that one and the same fragment of predicate logic· underlies all these proposals. In addition, we will-for reasons explained in the previous section-adopt a rather simple, 'syntactic' modeling of ambiguity.6 Consider a fragment of predicate logic L and imagine the addition of a class of ambiguous formulas to L. This may be done, for example, by the addition of new constants, or by a loosening of syntax; (For example, one may allow that cer:tain brackets are omitted.) The resulting language, whose sentences form a superset of L, will be called L'. We will assume, for simplicity, that every reading of every sentence of L' L can be expressed unambiguously by some sentence of L. Let a (syntactic) disambiguation d be a function that maps every unambiguous sentence of L' to itself, and that maps every ambiguous sentence r.p of L' to some sentence d(r.p )a that expresses one of the readings of r.p. In addition, let d also map sets of sentences of L' to sets of unambiguous sentences, in the obvious way: Let E � L' then d(E) = {cpa: :lr.p' t:E{r.p = d( r.p1) )}. Given this setting, several ways of defining truth and falsity are possible, including7
12
Ambiguity and Idiosyncratic Interpretation
Weak truth:
The first version speaks for itsel£ As for the other two, truev can be glossed as irrefutable and true3 as defensible. Each option makes sense in its own way. Note that in the case, where every sentence has exactly one meaning, all three notions of truth/falsity coincide with classical truth/falsity: If
true (false) with respect to M {::} trued (falsed) with respect to M {::} truev (falsev} with respect to M {::} true3 (false3} with respect to a model
M.
There are several ways of defining logical consequence in the new setting, each of which has to be plausible for ambiguous as well as unambiguous expressions. So suppose, furthermore, that
for some relation of (unambiguous) logical consequence I= that is itself plausible. This might be called the Conservativity requirement. This requirement still leaves open some very different approaches to defining ambiguous consequence. One way of guaranteeing Conservativity is to define ambiguous consequence as the relation that preserves truth, where truth may be defined in any of the three ways mentioned above.
Van Eijck &Jaspars (vE &J}:
and if 1/J is
Each of the resulting notions of ambiguous consequence respects the Conservativity requirement in the strong sense that it leads to a purely classical logic for nonambiguous expressions.
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Kees van Deemter
13
But, very different avenues for defining ambiguous consequence can be and have been explored. In particular, one can stick to the idea of quantifying over possible paraphrases, while abandoning the idea that premisses and conclusion must be judged independently of each other. This approach makes it possible to define a notion O=a) of ambiguous consequence based on a notion of nonambiguous logical consequence· (F). Reyle (1993), for example, defined essentially
Reyle '93: cp Fa 1/J {::}D1 For each paraphrase of cp, there is a paraphrase of 1/J that makes the . argument valid in the sense of F·
Quantificational schema I:
Fa 1/J {::}D1 Q�x E A Q1.TJ E B: X F T], where A is the set of paraphrases of cp, B is the set ofparaphrases of 1/J, and F is the underlying notion oflogical consequence. Note that F can be any notion of logical consequence defined on nonambiguous expressions. It seems plausible to exclude 'nonlogical' quantifiers such as most and focus on the logical quantifiers (i.e. some, all, no, not all ). But even then, some remaining instantiations of the scheme are clearly implausible. Conservativity, for example,9 rules out the combinations covered by the following scheme: cp
. Q1 = some or all, and Q1. = no or not all. As a result, the quantificational schema has four remaining logically distinct instantiations. For example, the combination Q1 = no, Q2 = no is equivalent to the second version. I.
Q1 = Q2 = some
4-
QI = all, Q2 = some.
2. Q1 = Q2 = all 3· QI = some, Qz = all
Version (I) says that the argument can be made valid by a properly chosen disambiguation; in other words, the argument is defensible. Version {2) says that the relation cannot be invalidated by such a disambiguation; in other words, the argument is irrefutable. Version (3) says that the premisses can be disambiguated in such a way that the conclusion cannot be disambiguated in such a way that it fails to follow; (4) expresses that no matter how the premisses are disambiguated, a validating disambiguation of the conclusion
·
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This definition is equivalent to what one gets if both the premisses and the conclusion are represented by means of the disjunction of their interpretations.8 It instantiates the schema
14
Ambiguity and Idiosyncratic Interpretation
can be found. Below, (1 ) will be denoted as
(4)
as
FV3·
F33· (2) as l=w, (3) as F3V. and
Variants of the quantificational schema are also possible. In particular, the scope of the quantifiers Q, and Q�, may be reversed to produce the following schema:
Quantificational schema 2:
X
F 1J
For each paraphrase. x of
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where, as before, A is the set of paraphrases of
and 1/J. Assume is ambiguous between p,, p2, and p3 while 'lj; is ambiguous between p, and p2 only. Assume, furthermore, that p,, p2, and p3 are logically unrelated. Then, on the first quantificational schema, F33 is the only of the four relations of ambiguous consequence that validates the inference I=· 1/J. On the second quantificational schema, however (where the quantification over paraphrases of the conclusion takes wide scope), I= 'lj; is also validated by the relation F3V· Finally, one might use Boolean combinations of the clauses featuring in the two schemas.'° For example, combining a clause from the first with one from the second,
Kees van Deemter I 5
·
4
AMBI G UOUS LOGI C A S AN ANALYTI CAL TOOL
In this section, we will briefly sketch how the tools developed in the previous section may be used for analytical purposes. Many ancient logical paradoxes hinge on the ambiguity of one or more premisses in the argument. For example, consider the following argument, where the expression 'The king' refers to different persons (say, the present and the previous king of a given country) in the two premisses:
p: The king= Mr. X; q: The king= Mr. Y; therefore, r: Mr. X = Mr. Y. Let us dub this argument the Fallacy of Description. What makes this a fallacy in the sense of a plausible piece of invalid reasoning'' is the fact that one might get confused by the situation: p has an interpretation that makes it true, q has an interpretation that makes it true. If p and q were unambiguous the reasoning from P. and q to r would have been valid. But it is somewhat unclear what this means for the argument as it stands, that is, with ambiguous premisses. Aristotle distinguished several situations in which ambiguity can lead to paradox: amphiboly if the ambiguiry involved grammatical constructions and ambiguity if the ambiguity (modern usage) involved the meaning of a word. It is not immediately clear which of the two is more appropriate in the case
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out the implications for the other notions of ambiguous consequence, which are mostly straightforward. There is one group of consequenc� relations that is not covered by the survey in this section. These are the relations of ambiguous consequence that take cohe�ence relations {i.e. contextual restrictions on interpretation) into account. For example, different notions of logical consequence result when different occurrences of the same ambiguous constant are required to be interpreted in the same way. The resulting nonmonotonic notions of logical consequence are discussed briefly in section 5.2. At this point, some of the terminology of ambiguous logic has been introduced and some of the main perspectives on truth and ambiguous consequence have been surveyed. Before turning to the question of which notion of ambiguous consequence is most plausible (or even the 'correct' one), we will show how the terminology of ambiguous logic can be used to analyse logical fallacies.
I6
Ambiguity and Idiosyncratic Interpretation
of an anaphoric ambiguity but the latter does not seem inappropriate given current usage of the word 'ambiguity'. If we analyse the Fallacy of Description making use of the logics sketched in the previous section, we find that these induce different answers to the question of whether the premisses or the reasoning itself should be blamed for the paradox. First, we have to generalize the logics in such a way that they cover sets of premisses. This is trivial in all except one case, namely the version by van Eijck & Jaspars, which now goes FvE &] 'If; {:::}Def For all models M, if all cpEf are strongly true with respect to M then 'If; is strongly true with respect to M and if 'If; is strongly false with respect to M then at least one cpEf is strongly false with respect to M. r
(a) p , q (b) p, q (c) p , q (d) p , q (e) p , q
�V3 r �w r F33 r F3V r FvE &] r. The 'reverse. scope' . variants of FV3 and F3V (along the lines of quantificational schema 2) behave just like FV3 and F3V themselves. So much for the soundness of the reasoning. How about the premisses? Here a similar story can be told. One has to conclude that the question of whether the premisses are true has no unique answer. Instead, they are (1) neither truev nor falsev but (2) true3. What does this mean? If (ambiguous) truth can be interpreted in such a way that the premisses are true, and if (ambiguous) logical consequence can be interpreted in such a way that the reasoning comes out valid, then does that mean that there is nothing wrong with the Fallacy of Description? Of course not. There are disambiguations that make the reasoning valid and there are disambiguations that make the premisses true, but there are none that do both. The problem is that received terminology is not very suitable for making this point. Suppose one dubbed an inference good if it is not only logically valid, but if its premisses are true as well: An inference 'p, q therefore r' is good iff it is logically valid and both p and q are true.
In the situation in which premisses may be ambiguous, this definition can take at least four different forms, depending on which notion of ambiguous
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In particular, FV3 and f=w find fault with the reasoning, but F33. F3v. and FvE & 1 do not, as may easily be verified:
Kees van Deemter
17
Truth, relative to a diSambiguation: is trued (falsed) with respect to a model M {::} d ( r.p) is true (false) w.r.t. M, r.p
Logical consequence, relative to a diSambiguation: r Fd 1/1 iff d ( r) f= d ( 1/1) •
. Goodness, relative to a diSambiguation: An argument T p '¢' is goodd w.r.t. a model M iff r Fd '¢ and all the elements of r are trued w.r.t. M. 'Absolute' goodness can then be defined as goodness with respect to at least one disambiguation: An
argument
r
F= '1/J is go�d iff 3d such that r F= '1/J is goodd.
If the relation r Fd '¢ holds between premisses and conclusion, we will also say that the argument is validd. An argument r p '¢ is valid3 in case there is a d such that r Fd '¢. The notion of a sentence being true3 with respect to a model has been defined in the previous section. This terminology allows the following analysis of the paradox: it is validd for some d and its premisses are trued for some d; however, there is no d such that both conditions are met. Consequently, the argument is not good. Any argument that is valid3 and whose premisses are true3, but that is not good is a Fallacy of Ambiguity. The Descriptive Fallacy instantiate this scheme. In van Deemter (1993), it has been shown that some of the most compelling versions of the sorites
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consequence and which notion of ambiguous truth are selected. Suppose, for instance, one selects F3 and true3, then the definition makes our paradoxical argument good, which makes it hard to understand what is wrong with it; on the other hand, if one selects pv and truev, then the argument comes out not good for the double reason that it is not logically valid and its premisses are not true, which makes it hard to see why the argument is at all plausible. One way to look at this situation is the following: modern logic has never made much fuss about the truth of premisses. The notion of truth can simply be paired with that of logical consequence. The two can be. kept separate. On the other hand, as soon as one looks at ambiguous formulas, a . simple pairing of truth and logical consequence obfuscates some important issues: saying that the premisses 'can be true' and that the argument 'can be valid' (i.e. they are true/valid on at least one paraphrase) does not tell you whether the argument can be valid, having true premisses at the same time. Here is a bit of terminology that helps to fill this gap, by introducing 'context-dependent' versions of truth and logical consequence:
r8
Ambiguity and Idiosyncratic Interpretation
argument can be analysed along exactly analogous lines and that this ·leads to a good explanation of why they represent a fallacy.'" This section has demonstrated how the terminology of ambiguous logic can be useful for the analysis of conceptual problems. The following section will highlight a very different question, namely How to choose between the different notions of logical consequence that are available for ambiguous logic.
We now turn to the question of which notions of ambiguous logic are most plausible. First we will make a quick comparison of some of the notions of ambiguous consequence advocated in the literature (section 5.1). Then we will discuss the requirements posed by practical NLP applications on the notion of ambiguous logic (section 5.2). Finally, we will focus on one particular type of application, namely Question-Answering, to see how ambiguous logic can be used to deal with ambiguities that threaten to lead to interpretational deadlock (section 5·3)·
5.1
Initial Comparison of Proposals
We have seen in section 3 that there are different possible ways of defining relations of ambiguous consequence and that different authors have made different choices from among the set of possibilities. Let us briefly contrast three of the main proposals that have been advanced, namely (1 ) the relation FV3. proposed by Reyle (1 993); (2) the relation FvE &]• proposed by van Eijck & Jaspars (1995), and (3), the relation f=vv, which is one of the options discussed by van Deemter (1991, 1996). Some of the most striking properties of each of the three will be listed, but an evaluation will have to wait until the next section. As was noted above, each of the three logics fulfil the requirement of Conservativity, so· if none of the formulas in the premisses and the conclusion are ambiguous then all three are equivalent. Likewise, if only the premisses can be ambiguous, it does not matter how one quantifies over paraphrases of the conclusion. Consequently, f=vv FV3 __:__ FvE &]· Conversely, if only the conclusion is ambiguous, it does not matter how one quantifies over paraphrases of the premisses. Consequently, in that situation, f=vv F3V FvE &]· =
=
=
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5 C H O O S IN G APPROPRIATE N OTI O N S O F AMB I G U O U S C ON SEQ UENCE
Kees
van
Deemter
19
Having noted these areas of overlap, let us briefly discuss the logics one by one, stressing some of the differences between them. Firstly, F'v'3· This relation is monotonic, reflexive, and transitive and this has been taken as an important argument in favour of it (Reyle 1 993). However, it is also inconsistent in the sense that contradictory conclusions can sometimes follow from noncontradictory premisses (van Deemter 1 991, 1 996, Reyle 1995).'3 To see this, we have to allow that an expression can be ambiguous between contradictory paraphrases. Suppose, for example, the predicate F is ambiguous between .AxG(x) and .Ax -.G(x). Then
whenever paraphrases are quantified over existentially. Secondly, FvE & ]· This relation is also monotonic, reflexive, and transitive. In addition, it makes all expressions that are ambiguous between contradictory paraphrases equivalent, because in this case the expression can neither be truev: nor falsev. Thirdly, f=w. It is easy to see that this relation is monotonic as well as transitive, but it is not rejlexive. Stronger even, if a sentence p has (nonequivalent) paraphrases p 1 and p2, then p, � p2 and consequently p �'v"v' p. Thus, we have ·
Let p be ambiguous between nonequivalent paraphrases p, and p2• Then p f=w p {:::} peL, where L, as before, is the nonambiguous subset of L'. Given what has just been observed about the (non)reflexiveness of the relations proposed in the literature, it is good to look at a simple example. Consider the situation in which dates can be written in either the American (m-d-y) or the European style (d-m-y) and consider the sentences p: The meeting took place on 10-04-98. q: The meeting took place on 04- 10-98. In this situation, p is ambiguous between the tenth of April (European style) and the fourth of October (American style). But q is ambiguous between the tenth of April (American style) and the fourth of October (European style) as well! Sentences p and q are ambiguous between the same two paraphrases. None of the notions of ambiguous consequence considered so far distinguishes between different expressions as long as these expressions have the same sets of interpretations. As a result, we have p FV3 P p �w p
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G(a) FV3 F(a) and G(a) FV3 -.F(a). Analogous problems affect the relations F33 and F3'v' and the same is true if the scope of the quantifiers 3 and \:1 is reversed: inconsistency results
20
Ambiguity and Idiosyncratic Interpretation
P FvE &J P· p FV3 q p �w q P FvE &J q.
'P F a '1/J {::}Dif For all models M, if
Let us go back to the example involving dates. Let
is valid for arbitrary '1/J, which seems undesirable.'4 5 .2
A Practical Perspective
We are left with a difficult situation. Different and incompatible proposals have been made for a formalization of ambiguous consequence. Several of these proposals were accompanied by arguments in defence of them involving, for example, the structural properties of the logics concerned. One wonders what this means. Perhaps there does exist an ambiguous logic that combines all the properties featuring in these discussions (i.e. conservativity, monotonicity, reflexivity, transitivity, and consistency) as well as doing justice to what it means for an expression to be ambiguous (section 3). In that case this logic has not been discovered yet. Or else there does not exist such a logic. In the remainder of this paper it will
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In the next section we will see that this invalidates the relation F'
Kees van Deemter
21
p: The meeting took place on 10-04-98. Suppose x intends this in the European sense, meaning that the meeting took place on the tenth of April, unaware of the other interpretation that the sentence may have. Now a second person, y, comes along and asks '(Is it the case that) p?', intending p to mean that the meeting took place on the fourth of October, and unaware of the ambiguity. Now consider FV 3· We have seen that reflexivity is a theorem of FV3 and, more specifically, p FV3 p. Consequently, a Question-Answering system built on FV3 will answer the query in the affirmative and thereby end up misleading y. The same problem affects F33 and FvE & ] • as the reader may verify.' 5 In a picture: p!
User
x
(p)
(fills database)
DB
User y (p)
=====:::}
(queries database)
p?
A variant of the same example can be constructed in a setting where x has not entered an ambiguous expression into the database but, for example, the unambiguous expression The meeting took place on the tenth of April 1998, which we will abbreviate as PEu · The relevant inference is PEu FV3 p. Now suppose the system has inferred that, if the meeting is on the tenth of April it cannot also be on the fourth of October. Abbreviating The meeting took place on the fourth of October 1 998 as PAm • this means that PEu F 'PAm· Therefore, PEu FV3 'PAm· We also have ._,PAm FV3 •p, and then, due to transitivity, PEu FV3 •p. Thus, the premisse PEu has led to contradictory conclusions. In a case like this it is totally unclear how the system should respond to the query p. These examples point at an important principle governing the
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be argued that there does exist a logic that is appropriate for all different kinds of situations but this logic does not have all the properties listed above, and that some situations allow a strengthening of this logic. Apparently, intuitions on ambiguous inference can conflict. We will try to resolve these conflicts by making the inferences more concrete. In particular, we will add some context to them that will make it clear who is the author of the premisses and the conclusion of the argument. Imagine a situation in which the premisses and the conclusion of an inference can be ambiguous, while the premisses of the argument stem from a person that is different from the one interpreting the conclusion. For example, consider a person x producing a database filled with potentially ambiguous discourse. One of the expressions he or she uses, at a given point of the discourse, is the expression p discussed in the previous section:
22
Ambiguity and Idiosyncratic Interpretation
interpretation of ambiguous material. We will call it the Principle of Idiosyncratic Interpretation:
Principle of Idi osyncratic Interpretation (Pn). If an expression
is
ambiguous then different people may assign different preferred interpretations to it, even in one and the same context of occurrence. In such a situation, each of them may be unaware of the existence of legitimate interpretations that differ from their own preferred interpretation. '6
•
•
•
•
•
•
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The Principle stresses that the ambiguity of an utterance is not guaranteed to disappear when all the publicly accessible circumstances of the utterance (i.e., its linguistic and nonlinguistic context) are taken into account. An ambiguity may be unresolvable. Moreover, it may be that neither the speaker nor the hearer of an utterance realizes that the ambiguity is there. This example shows that, in a situation where both the premisses and the conclusion of an argument can be ambiguous, and where unwarranted inferences on the part of the user of the system must be avoided, the PII forces one to use the weakest of the logics discussed, namely FW· This can be seen as follows. Ambiguity arises when there is uncertainty about the intention of a speaker (c£ section I). In situations like this, there is often equal uncertainty about how a hearer will interpret the utterance. There fore, suppose an agent S enters a premiss c.p that is ambiguous between , IPm and an agent H interprets the conclusion '¢ that is paraphrases c.p1 , ambiguous between paraphrases '¢1 , , '1/Jn · In accordance with the PII, let us assume that. each of S and H have their own preferred interpretation of the ambiguous expressions involved. Let a(¢) denote the interpretation of ¢ that is preferred by an agent a. Then the system performing the inference is in the dark about the values of S( c.p) and H( '¢). Therefore, the only way to guarantee that S(c.p ) I= H( '¢) is by guaranteeing that tp l=w '¢. To sum up the argument: unresolvable ambiguity implies indeterminacy of inter pretation and indeterminacy is best modeled by a supervaluational account . (c£ van Fraassen I 969). Natural language understanding applications may be categorized along the following lines: either ( I ) some of the queries they respond to are ambiguous, while the information sources that contain the answer to the query ('the database', for short) are nonambiguous; or (2) some of the information in the database is ambiguous, while the query itself cannot be ambiguous; or (3) both the query and the information in the database can be ambiguous, or (4) neither can be ambiguous. An example of ( I) is the situation of a natural language question-answering system, such as the PHLIQA system discussed in section 2. Note that in such systems, the query may typically contain ambiguous material, whereas the database
Kees van Deemter
23
Ambiguous conclus ions : Nonambiguous conclusions :
Ambiguous
Nonambiguous
premisses :
premi sses :
( 3 ) NL QUESTION-ANSWERING
(1)
( 2 ) DISCOURSE I NTERPRETATION
NL QUESTION-ANSWERING (STANDARD DATABASE)
(NL DATABASE)
(4)
FORMAL DATABASE QUERY ( e . g . SQL)
With this classification in mind, it is easy to generalize what has just been said about fitting logics and applications: if the premisses of a logical argument can be ambiguous, then one has to quantify universally over interpretations of the premisses; if the conclusion can be ambiguous, one has to quantify universally over interpretations of the conclusion. We have so far assumed that the systems under discussion . have to be fault-proof and this is, in a sense, the normal situation. But there are applications where 'faulty' output is not that problematic. One example is that of a cooperative dialogue of the kind where misunderstandings are unlikely as a result of an abundance of common sense information or where politeness is more important than accuracy. Thus, for example, if participant A in a dialogue says The meeting is on thefourth ofAugust 1998 and participant B responds OK, so the meeting is on 04- 1 0-98, then we might count this as a legitimate inference on B's part, even if we have no prior information about whether B uses the American or the European notation for dates. Mter all, it is unlikely that A's initial statement was misunder stood by B and consequently, A has no reason to doubt that the proposition B intends to convey is correct. But in the general case, where no such assumptions can be made (and where the inference can be taken up by another interpreter who has not heard A's original statement), it is unsafe to
·
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contammg the answers does not. These systems-no matter how they operate internally-may be described as deriving ambiguous conclusions from unambiguous premisses. An example of (2) is the situation of a discourse interpreting systeni, such as one that reads . scientific abstracts to summarize them. Such systems may be described as deriving nonambiguous conclusions (i.e. the information derived from the text) from ambiguous data (i.e. the abstracts interpreted). We h��e just discussed an example of the most difficult kind of application (3), wliich occurs when a user types an ambiguous query, which is used by the system to search a body of natural language. This situation may be described as one in which an ambiguous conclusion is derived from ambiguous premisses. An example of (4), finally, is the standard one, in which ambiguity plays no role. To summarize:
24
Ambiguity and Idiosyncratic Interpretation
count B's statement as a valid inference from what A said. In the general case, therefore, we have to use a notion of inference such as f=vv. that does not warrant the inference. Another example is literary translation. Translation may be modeled as a situation in which an expression S in the source language is related to an expression S' in the target language such that s Fa s ' and s' Fa s. Clearly, for this purpose, FW is not a realistic notion of logical consequence to play the role of Fa , since this would cause all ambiguous sentences to become untranslatable. Assuming that translation requires mutual consequence (i.e., both
The meeting took place on 1 0-04-98, q: The meeting took place on 04-10-98, p:
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It would follow that a source text can be translated into a target text if and only if each interpretation of the source text is equivalent to one of the target text and conversely. Text retrieval systems represent another area where f=vv is not strong enough to be useful and where users might be sufficiently forgiving to allow a stronger notion of consequence. The task of a text retrieval system may be modeled as trying to find constructive proofs for existential formulas of the form 3xcp(x), where
Kees van Deemter 25
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where some of the systems discussed had P Fa P P Fa q while others had p �a P p �;, q We are now in a position to see that it is impossible to determine the correct inference pattern unless we take into account the source of the premiss and the conclusion. If the premiss and the conclusion stem from different agents (as when agent I enters the premiss while agent 2 interprets the conclusion), then the second pattern is correct, due to the PII. If, however, the premiss and the conclusion stem from one and the same agent, then it is reasonable to assume that premiss and conclusion are interpreted making use ofone and the same 'system' of interpretation: the American (m-d-y) or the European system (d-m-y). In this case, the intuitively correct pattern of inferences is P Fa P p �a q (and even p Fa •q). By requiring that different occurrences of the same ambiguous material are interpreted in the same way, one can define 'coherent' versions of our relations of logical consequence. The challenge is to define coherence in . such a way that it can be overruled by contextual factors, such as in 'The pitcher drank wine from the pitcher', where the two occurrences of pitcher are forced to have different interpretations. To explain how 'imperfect' coherence may be defined is outside the scope of the present paper and the reader is referred to van Deemter (I 99 I, I 996) for an exploration and to Asher & Fernando (I997) for related work.'7 As was shown in van Deemter (I99 I), even imperfectly 'coherent' relations of logical consequence tend to support reflexivity. For example, consider the example with the calendar dates. The date appears in the same linguistic context in the premisse and the conclusion. Therefore, if both are associated with the same author, coherence ends up rescuing reflexivity, since there are only two possibilities: both occurrences of a date are interpreted in American style or both are interpreted in European style. As a result, we obtain the pattern p Fa p, p �a q, which is appropriate for the situation where no coherence between premisses and conclusion can be taken for granted. Our discussion of how ambiguous logic can be used in practical applications has been sketchy so far. To show in more detail what role ambiguous logic can play, we will focus on Question-Answering systems in the next section. For simplicity, we will continue to abstract away from any coherence requirements. ' 8
26
Ambiguity and Idiosyncratic Interpretation 5·3
Ambiguous Logic for Question-Answering
Query
1 1
Under specif ied represent at i on
CAN AN ANSWER BE GIVEN YF:f?
l YES
Answer
+------
NO
Replace representat i on by a more spec i f i c one
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Question-Answering, as we have seen in section 2, is the type of application that originally motivated the introduction of underspecified representations and it still is the application in which they are most used. It is therefore worthwhile to see how reasoning with underspecified expressions could affect the way in which such a system operates. Let us assume that l=w (that is, the system that quantifies universally over paraphrases of all the ambiguous expressions in a logical argument) has been implemented in a natural language interpreting system and draw some conclusions for the architecture of the system. The. old-fashioned (i.e. pre underspecification) architecture for a Question-Answering system is one in which a query is translated into a set of disambiguated expressions in a formal language. The system tries to discard all but one of these, selecting the remaining one as the chosen interpretation. The now dominating architecture replaces the set of disambiguated representations by one or more underspecified representations, trying to resolve all sources of ambiguity in it. As before, the remaining interpretation is selected if the disambiguation process is successful. If it is unsuccessful, nothing can be done. As an alternative to the traditional and the dominating architecture we propose the following, more flexible architecture, which makes use of ambiguous logic: A query is-as in the dominating approach-translated into an underspecified representation. Also as before, the system tries to disambiguate the representation but it stops as soon as the resulting representation is specific enough to . warrant an answer. This approach allows the system to display behaviour that is helpful as well as, in an important sense, 'correct', even in situations in which disambiguation would be extremely difficult. The sense of correctness intended here derives from the Principle of idiosyncratic interpretation: No matter what legitimate interpretation the user selects as ·the preferred one, the answer provided by the system will be correct with respect to this interpretation.
Kees van Deemter 27
underspecified representation can be replaced by a more specific one through the use of any common disambiguation technique, including, for example, querying the user ('Did you mean . . . or . . . ?'). In the approaches discussed in this paper, an 'answer can be given' if the answer (e.g., the truth or falsity of a statement in the case of a yes/no question) follows logically from the information in the database, using the relation of logical consequence denoted by F'v''v'· To illustrate, let us return to our earlier example of an ambiguous query: 'How many American flights are operated by Quantas?' (section 2). As we have seen, this question can be translated into an underspecified formula of the form An
·
&
Operator(x)
=
Quantas} II ,
which denotes the cardinality of a set, the precise identity of which has yet to be established. Using the single stroke (! I') to list alternative paraphrases of an ambiguous constant, this formula may also be written as
II {xiflights: AMERICAN, IAMERICAN21AMERICAN5 (x) Operator(x) = Quantas} II
&
since the remaining two interpretations, AMERICAN3 and AMERICAN4, do not correspond to contextually viable interpretations of AMERICAN. Let us assume that not all of the three viable interpretations lead to the same answer. This is extremely plausible, since {xifl,ghts: AMERICAN 5 (x) & Operator(x) = Quantas} must always be the empty set. No flight can be operated by Quantas and American Airlines at the same time, so under this interpretation, the query contains an inconsistency. Let us assume that the interpretation of the query resulting from the interpretation AMERICANs can be refuted on the basis of this inconsistency. (See e.g. Buvac 1996.) The result of this disambiguation step is a second, more specific representation. l l {xiflights: AMERICAN1 1AMERICAN2 (x)
&
Operator(x)
=
Quantas} ll ,
This representation happens to be specific enough to warrant an answer. Intuitively, this is because both remaining interpretations of the query lead to the same answer. This intuition is captured by the inference relation f=w. which allows us to prove that the cardinality of the set described by the underspecified formula does not depend on how AMERICAN is resolved. More specifically, the system may prove, for a certain number n, that II { XEjl,ghts: AMERICAN ( x) & Operator(x) = Quantas} II = n. The inference goes I, 2
F=vv 3 ,
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II {xql,ghts: AMERICAN(x)
28 Ambiguity and Idiosyncratic Interpretation
where I.
2.
3·
I , 2,
and
3
are as follows:
ll {x€ flights: AMERICAN, (x) & Operator(x) = Quantas} ll = n. ll {x€ flights: AMERICAN2 (x) & Operator(x) = Quantas} ll = n. !l {x€ flights: AMERICAN, jAMERICAN2 (x) & Operator(x) = Quantas}!I = n.
6 D I S CU S S I O N The growing number of recent proposals in the area of reasoning with underspecified formulas notwithstanding, underspecification is often still only used as a way to speed up the disambiguation process or to cut down on computer memory needed for disambiguation. (See Bos 1996 for a recent example.) In this paper, we have sketched some ways in which reasoning with underspecified representations can be put to use. Doing this, a distinction has been made between theoretical and practical applications. The conclusions of our 'practical' discussion may trigger a number of objections, a few of which we will briefly try to pre-empt. I.
'The present account of ambiguous consequence does nothing to solve the combinatorial explosion problem.' This is correct. All the notions of logical consequence discussed in this paper hinge on enumeration of inter pretations (or paraphrases) of premisses and conclusion. But this is in accordance with the way in which the problem with interpreting ambiguous material was defined in the Introduction: the combinatorial explosion is only a secondary problem; the primary problem (i.e. the
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The number n is the number that the system can safely return to the user to answer the ambiguous question. '9 It may be good to compare this strategy with that of existing question answering systems. Such systems are confronted with basically two options: to 'throw a dice' or to query the user for clarification. In the first case, an unintended interpretation may be selected and a misleading answer generated. (This will not happen if all interpretations lead to the same answer, but traditional systems do not check whether this is the case.) In the second case, where the system asks something like 'Do you mean flights arriving in the US or flights flying in from the US?', the incorrect implicature will be that it matters which of the two interpretations is selected. For example, if the user selects the second interpretation and the system then answers 'Five', the user will be invited to infer that this answer depends crucially on the result of the clarification dialogue and that, consequently, the number of flights arriving from the US is either unknown to the system or unequal to S·
Kees van Deemter 29
problem of deadlock) is how to make sense of the notion of inference in an ambiguous domain. If and when this primary issue has been resolved, the question of finding equivalent, easily implementable, characterizations of the notion of logical consequence will come to the fore. 2.
3· 'Isn't reasoning with underspecifled expressions limited to polysemy?' The example worked out in section 5 · 3 concerned the polysemy of the word American. It may be plausible that people leave the ambiguity of polysemous words unresolved if the situation does not require total disambiguation, but does this also apply to lexical homonymy and to other (e.g. non-lexical) kinds of ambiguity? This is a difficult question, especially in so far as it focuses on human interpretive behaviour. It'has been argued that it is possible to make a linguistic distinction between types of ambiguity that do and types of ambiguity that do not require disambiguation (Pinkal 1 995, Poesio 1996). Ifwe assume that it is possible to make this distinction precise then it is still unclear that this constitutes a problem for the approach outlined in section 5·3· Consider a question by a user U involving a homonymous source of ambiguity, such as U: Is
this a picture of the pitchers?
and assume the system S
is
unable to determine whether pitchers refers
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'Reasoning with ambiguous expressions hinges on people's ability to perform supervaluational reasoning.' Incorrect. The idea behind this objection is that, presumably, people are bad at the kind of reasoning in which different interpretations have to be kept apart. First, this incorrectly assumes that inspecting the different possible interpretations is the only way to establish that a conclusion follows from certain premisses using the relation f=vv. That this is not necessarily the case may be made plausible most simply by looking at examples which do not hinge on ambiguity, such as the inference p f=vv p V q, where only q contains ambiguous material. Even if q is ambiguous between many interpreta tions, the irrelevance of q is so evident that the reasoning is easy to perform. But second, our discussion of the practical applications in section 5 does not assume that the user of these systems can perform the reasoning involved. Quite possibly, people have other resolution strategies at their disposal than present-day computers. The only thing our discussion in section 5,3 did assume was an ability on the part of the computer to perform supervaluational reasoning. In addition, it was claimed that using this ability is the best way for the computer to similate human behaviour. (See especially the closing remarks of section 5.)
30
.Ambiguity and Idiosyncratic Interpretation
to jugs or a baseball players. Suppose, furthermore, that both inter pretations led to negative answers and that, following the recipe of section 5 · 3· the system answered in the negative. In terms of direct information content, this would be a perfectly correct answer. On the other hand, it may be argued that this answer licences the inference that the ·system was unaware of the ambiguity of the sentence. If this is considered problematiC, however, the inference is easily blocked by the explicit acknowledgement that the system has found some 'importantly different' interpretations:
I'm not exactly sure what you mean, but the answer to your query must be negative either way.
S:
_
4· 'f=w is a very weak logic.' It has been noted that the logic arising from the
relation f=vv is weaker than most other systems discussed. Although this does not refute the logic, it might be seen as reducing its value for practical applications. Let us observe three things, however. Firstly, the logic based on the relation f=w allows more nontrivial and practically useful conclusions than one may at first realize. The reason is that many different kinds of ambiguities tend to lead to interpretations that are logically ordered. This is true, for example, for polysemy. Consider a word like write, as in Has John written any interesting papers recently? The verb may mean 'being the sole author of' or 'being one of the authors of', which is subsumed by the first interpretation. The same is true for quantifier scope ambiguities. Take any sequence ofn logical quantifiers:
(*) Cb x1 Q2x2 . . . <Jn xn cp,
where Q; is either V or 3. Then all n! interpretations of ( * ) are linearly ordered.
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This illustrates an important point, namely that the strategy outlined in section 5 · 3 leaves it open in what way the information is passed on to the user: it determines under what circumstances an affirmative/ negative answer may be given, but it does not say how this answer is .presented. In systems that allow follow-up questions, it can happen that a follow-up question contains the same ambiguity or refers ana phorically to material in the original question in which case a clarification dialogue may be needed after all. Just as likely, however, the follow-up question will contain sufficient information to decide which of the two interpretations is the intended one. In that case, the fact that a clarification dialogue has been avoided has led to a shorter, less complex dialogue, at no informational 'cost' to the user whatsoever.
Kees van Deemter
3I
F IPz F · F IPn!. For example, 3x'v'yRxy f= 'v'y 3xRxy. Now suppose either the strongest cp ,
"
, cp" ! is true or the weakest of cp 1 , , cpn! are false. In the first of cp 1 , case, it follows that all of cp 1 , , cpn! are true. In the second case, it follows that all of cp 1 , , cp" ! are false. Either way, all n! interpretations give the same result and no logical 'strength' is lost by quantifying universally over them. More generally, •
•
•
•
•
•
•
•
•
•
•
•
If IP; (where I � i � n!) is true then all IPj are true, for i � j � n!; and If !{); (where I � i � n!) is false then all IPj are false, for I � j � i. Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Analogous remarks apply to the case of polysemy.20 So, the relation f=w may be weak but it is not too weak to be useful. Secondly, we have seen that in some cases, it is possible to strengthen the relation of ambiguous consequence to one that is reflexive. This may be realistic, for example, in the case of short, well-written texts (Gale et a/. I 992). For example, by requiring that different occurrences of the same ambiguous material are interpreted in the same way, one may define 'coherent' versions of f=vv. For a discussion of the consequences of this move, which tends to upset other . structural rules such as monotonicity, see van Deemter (I99I, I 996). Thirdly, it is important to realize that, as has been shown in section 5 · 3· there are situations in which simply no strengthening of the logical consequence relation is warranted. In applications where the two occurrences of F stem from different authors-as when one user fills the database and another asks a query-there simply is no guarantee that any kind of coherence between the two occurrences exists. This is the kind of situation that is set aside for future research in Reyle (I995), but that is crucial in many practical applications, as we have seen.2' The situation is reminiscent of the so-called Schoenmakers paradox of distributed database theory. This paradox exploits the different ways in which the facts in standard databases can be interpreted. When two databases are combined, one of which contains the information p, while the other contains the information that p � q, then the inference q is only warranted if all the terms in p are defined in the same way in the two databases. Thus one may easily construct a case in which q could be inferred, using Modus Ponens, while the negation of q is also represented. If problems like this lead to a breakdown of logical principles (Modus Ponens, Reflexivity, etc.), then this may be regrettable. But to deny the problem and propose a more convenient logic that fails to reflect the facts that the logic is meant to .model would be a bad way of expressing one's regret.
32
Ambiguity and Idiosyncratic Interpretation
S · 'Is reasoning with underspecified expressions meant to replace disambiguation as a strategy to come to terms with ambiguity?' No, it is not. Ambiguities that can be resolved, by taking linguistic context, prosody (see e.g. Price et al. 1991), or even common sense knowledge into account, are probably
•
•
•
'P
& -, Pi
•
•
•
•
•
•
•
•
•
FV3 'P1
is a valid inference that can be used to perform disambiguation. Thus, while one type of ambiguous logic can sometimes replace disambiguation, another can come to its aid.
Acknowledgements Thanks are due to Uwe Reyle and two anonymous reviewers for pointing out some shortcomings in previous versions of this paper. KEES VAN
Received: 29.08.97 final version received: 09.05.98
DEEMTER Information Technology Research Institute. (ITRI) University of Brighton, Lewes Road Brighton BNz 4G] UK e-mail:
[email protected]
NOTES ' In
particular, well-formedness implies that the 'grammatically possible' inter-
pretations contain no type-conflicts. This gets rid of a considerable number
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resolved. Also, if the number of ambiguities in an utterance is limited and the ambiguity is easily explainable in nontechnical terms, then a clarification dialogue may effectively take care of the problem. Finally, if probabilistic information makes a number of remaining interpreta tions extremely unlikely and if the application permits occasional errors, then this may also be used to cut down on the number of interpreta tions. These methods will · sometimes allow one to hypothesize the speaker's intention with some degree of confidence. But in other cases, · the strategy outlined in this paper (i.e. the strategy of reasoning with ambiguous information) can prevent unnecessary deadlock. At this point it may be useful to return to what was said in Section 1 about charitable interpretation. Suppose, once more, that p1 , ,Pn are the only grammatically possible paraphrases of S, while cs f= -.p;. Let
Kees van Deemter 3 3 of logically
devious
quasr-mterpre
contraint on F a was discussed, namely
tations without significant effort. See section 2 for an example. •
This example is taken from the
Monotonicity.
TENDUM
follow-up
to
the
PHLIQA
quence is relaxed (i.e. made _extension
system
ally larger) then the same must be true
which focused on pragmatic aspects 3
for the notion of ambiguous conse quence based on it. If Q, and Q2 are
of interpretation.
'logical' quantifiers, as we have assumed,
Partial exceptions to this rule can be found
et al. 1987, Westerstahl et al. 199 3 , Asher & Fernando
then Monotonicity is equivalent with
in the literature (e.g. Fenstad
•
1 997) but not in actual systems, it seems.
This, of course, is true for other types of varieties of logical inference that are
1
11
V 1/J)),
where
MB
the
flavour. For an example involving a
meta level. See Poesio (I 996) or van
fallacy resting on lexical ambiguity, see
Deemter (I 996b) for more elaborate
van Deemter (I993).
comparison.
" A key assumption in these versions of of van
the sorites
Deemter (I 99 I, I 996b), an ambiguous
objects are
In
the
semantic
approach
argument is that if two
indistinguishable
in terms of,
for example, their size, then if one of the
two is 'small', the other must also be
biguous interpretation to each of the
'small'. The analysis of the sorites para
ambiguous constants in a formula. The
dox in van Deemter (I 993) hinges on
semantic approach becomes superior to
the idea that indistinguishability can
the syntactic approach when coherence
either be understood as an absolute notion
phenomena are modeled, but these will
or
as a
contextual
one,
in
which it matters whether the context
not be studied in detail here. (See the
provides sufficiently many other objects
end of section 5.2 for some sketchy remarks.)
to tell the two objects apart. (Only) the
Note that this leaves out some interest
first of the two is shown to lead to a
ing possibilities, such as the case where
valid sorites argument, while (only) the
Q
is the quantifier
most.
for a mathe
matical characterization of the
four
1
3
logical quantifiers, c£ van Benthem I 986. If the set
A consists of A , , . . . ,A., each
disambiguating
the
conclusion,
where f= denotes a version of
unambiguous logical consequence. In
van
Deemter
( I 996b),
another
to refute Fv3: Everybody slept or every body didn't sleep. Assuming the second
contingent,
then
Fa 1/J <*o.J (A, V . . . V An pB, V . . .
V Bm),
Reyle { I 995) uses the following example
disjunct to
be scopally ambiguous, he while
the
relation
FV 3
would wrongly cause it to be classified
this instantiation can also be written as 'P
second leads to true premisses.
observes that this sentence is intuitively
of which corresponds to a way of
9
gives
moved &om the object level to the
theoretic device that assigns an unam
8
plausibility
the notion of 'fallacy' its psychological
has
expression is associated with a model
7
.
that the criterion of
(Speaker, Hearer, disjunction
·
reviewers of this paper. See, for example, Mackie's contribution on 'Fallacies' in the Encyclopedia of Philosophy (J. L. Mackie I 967). Note
Note that this is very different from Intend (Speaker,
Boolean combinations of this kind were suggested by one of the anonymous
studied in linear logic (Troelstra 1 992).
c.p
6
Conservativity.
10
14
as a tautology. Nothing in
this argument hinges on the q. Consequently,
relation between p and
the argument can be duplicated for
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logics as well. Witness, for example, the
says,
{unambiguous) notion of logical conse
flight information system (Bunt 1 98 5), a
Monotonicity
informally, that when the underlying
34 Ambiguity and Idiosyncratic Interpretation simples examples such as the one where
Pitcher( j) is ambiguous between Base ball-player( } ) and jug( }), which are incompatible in the sense that no admissible model can verify both
'5
16
formulas, provided some Meaning Postulates forbid that something 1s both a baseball player and a jug. Nothing hinges on the particulars of this example, since the same point can be made using any ambiguous sentence.
7
the pronoun is resolved. " Reyle (1995) focuses on the very dif ferent situation, the goal of which is to draw (possibly ambiguous) conclusions from someone's (possibly ambiguous) mental state, to make his or her beliefs explicit. In such situations, it would make sense to assume certain prin ciples of coherence, similar to the
18
ment proved or rejected). Consequently, coherence between premisses and con clusion is not an issue in such systems. Coherence between expressions within the premisses, however, is an issue, and the same is true for coherence between expressions within the con clusion. Taking even this limited type of coherence into account would change
ones discussed above. On the other hand, why would one be interested in drawing ambiguous inferences about someone's mental state? Like in dis . course interpretation (c£ section 5.2), it often seems more useful to draw unambiguous conclusions from a mental state. As far as I can see, ambiguous conclusions only deserve a
the structural properties of the logic
place in applications in which these conclusions themselves are somehow 'given', for example when a user has
(especially
monotonicity
and
transi
tivity, c£ van Deemter 1991, 1 996b), but not the way the logic can be used
19
in a Question-Answering system. Note that it was assumed in section
a paper on long-distance dependencies?, one may observe that a formula corre sponding to a weakened question Has
someone co-authored a paper on long distance dependencies is false. Hence, the
answer must be negative no matter how
expressed an ambiguous query which the system then seeks to prove or disprove.
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A plausible strengthening of the PII would involve one and the same person (instead of different · people) at different moments. Note that the principle makes use of the (semantic) notion of an interpretation, instead of the (syntactic) notion of a paraphrase. Reformulation in syntactic terms is, of course, possible. It is unclear to me how the proposals in Reyle (1995, 1996) come to terms with such 'imperfections' in the notion of coherence. See Reyle (1996, p. 240) for a comparison between the treatments of coherence in van Deemter (199 1 ) and Reyle (1995). Usually, the premisses of a Question Answering system (i.e., the facts on the basis of which the system proves or rejects a statement) stem from another source than the conclusion (i.e., the state ·
1
·
2 that there is no separate interpreta tion of American which corresponds with the disjunction AMERICAN, (x) V AMERICAN, (x) . If such an interpreta tion were found to exists (which seems very unlikely) then this would destroy the unanimity between the different interpretations and consequently, a clarification dialogue would be needed before the query could be answered. Other ambiguities, such· as those arising from pronominal anaphora, cannot normally be ordered linearly according to logical strength, but in these cases it is often possible to find a simple weak ening that is false or a simple strength ening that is true. for example, to answer the question Has he co-authored
Kees van Deemter 3 5
REFERENCES
Proc. of 9th Amsterdam Colloquium,
ILLC, University of Amsterdam. van Deemter, K. {I996), 'Towards a logic of ambiguous expressions', in van Deemter & Peters {I 996). van Deemter, K. & Peters, S. (eds) { I996), ·
Semantic Ambiguity and Underspecification,
CSLI Publications, Stanford, CA. van Eijck, J. & Jaspars, J. {I995), 'Ambiguity and reasoning', report for the FraCaS Project.
Gale, W., Church, K. W. & Yarowsky, D. {I992), 'Estimating upper and lower bounds on the performance of word sense disambiguation programs', in Proc.
of ACL 1992.
Gorfein, D. S. (ed.) (1989), Rseolving Semantic Ambiguity, Springer-Verlag, New York. Fenstad, J. E., Halvorsen, P., Langholm, T., & Benthem, J. van, Situations, Language and Logic, Reidel, Dordrecht. Fernando, T. (1995), 'Non-monotonic consequences of ambiguity', in Proc. of Amsterdam Colloquium, December 1 995· Guha, R V. & Lenat, D. B. {1 990), 'Cyc: a midterm report', AI Magazine, I I , 3, 32-59· van Fraassen, B. C. (1969), 'Presuppositions, supervaluations, and free logic', in K. Lambert (ed.), The Logical Way of Doing Things, Yale University Press, New Haven, CT. MacDonald, M. C., Pearlmutter, N. J., & Seidenberg, M. S. {1994), 'The lexical nature of syntactic ambiguity resolution', Psychological Review, 101, 4· Mackie. (1967), 'Fallacy', entry in P. Edwards {Ed.), Encyclopedia of Philosophy. MacMillan, New York. Montague, R {1973), 'Universal grammar', in Thomason {1974). Moore, J. D. & Paris, C. L. { 1 994), 'Planning text for advisory dialogues: capturing intentional and rhetorical information', Computational Linguistics, 19, 4· Pinkal, M. {1995), Logic and Lexicon, Oxford University Press, Oxford. Poesio, M. (1 994), 'Discourse interpretation and the scope of operators', Ph.D. dissertation, University of Rochester, Dept. of Computer Science, Rochester, NY.
Poesio, M (1996), 'Semantic ambiguity and perceived ambiguity', in van Deemter & Peters {I 996). Price, P. J., Ostendorf, M., Shattuck Hufnagel, S. & Fong, C. {1 99I), 'The
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Alshawi, H . {I990), 'Resolving quasi logical forms', Computational Linguistics, 16, I 3 3-44. Asher, N. & Fernando, T. {I997}; 'Labelling representations for effective disambigua tion', in Proc. of Second Int. Workshop on Computational Semantics, Tilburg,January I 997· Bar Hillel, Y. (I 960), 'The present status of automatic translation of languages', Advances in Computers, I, 9 I - I 63. van Benthem, J. {I986), Logical Semantics, Reidel, Dordrecht. Bos, J. {I996), 'Predicate logic unplugged', in Proc. of Amsterdam Colloquium, Amsterdam, December I995· Bronnenberg, W., Bunt, H. C., Lands bergen, S. P. J., Scha, R., Schoerunakers, W., & Ut'teren, E. van {I 979), 'The question answering system PHLIQAI ', in L. Bole (ed.), Natural Communication with Computers, Vol. II, Carl Hanswer Verlag, Munich & Vienna: Bunt, H. {I98 5), Mass Terms and Model theoretic Semantics, Cambridge University Press, Cambridge. Buvac, S. {I 996), 'Resolving lexical ambi guity using a formal theory. of context', in van Deemter & Peters (I 996). van Deemter, K. {I99I}, 'On the composi tion of meaning; four variations on the theme of compositionality in natural language processing', Ph.D. dissertation, Amsterdam University, March I99 1 . van Deemter, K. {I993), 'The role of ambiguity in the Sorites fallacy', in
36 Ambiguity and Idiosyncratic Interpretation
'
Schubert, L. K. & Pelletier, f. J. {I982), 'from English to logic: context-free computation of 'conventional' logical American journal of translations', Computational Linguistics, 10, 165-76. Thomason, R H. (1974), Formal Philosophy: Selected Papers of Richard Montague, Yale University Press, New Haven, CT & London. Troelstra, A. S. {I 992), . Lectures on Linear Logic, CSLI Publications, Stanford, CA. Westerstihl, D., Haglund, B., & Lager, T. (1 993), 'A situation-theoretic repre sentations of text meaning: anaphora, quantification, and negation', in P. Aczel, D. Israel, Y. Katagiri, & S. Peters (eds), Situation Theory and its Applications, Vol. J, CSLI Publications, Stanford, CA, 375-408.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
use of prosody in syntactic dis ambiguation', ]. Acoust. Soc. Am., 90, s. December. Reyle, U. {I 99 3), 'Dealing with ambiguities by underspecification: construction, repre sentation, and deduction. journal of Semantics, 10, 2. Reyle, U. {I99S), 'On reasoning with ambiguities', in Proc. EACL 1995, Dublin. Reyle, U. ( I 996), 'Co-indexing labeled DRSes to represent and reason with ambiguities', in van Deemter & Peters {I 996). Ristad, E. S. & Berwick, R C. {I989), 'Computational consequences of agree ment and ambiguity in natural lan guage , journal of Mathematical Psychology, 3 3-
Jourtllll of&mantics
15: 37-82
© Oxford University Press
1998
Wh-questions in Underspecified Minimal Recursion S emantics MAR K U S E G G
Universitiit des Saar/andes Abstract
r I NT R O D U C T I O N In this paper, I introduce Underspecified Minimal Recursion Semantics (UMRS), a representation language that represents structural ambiguities by underspecification: ·rather than disjunctively enumerating all possible read ings of ambiguous expressions, the set of readings of such an expression is modelled by a representation that comprises all its possible readings. The advantage of such an underspecified analysis can be illustrated by comparing it to the naive 'generate-and-test' approach to semantic processing. In this approach, semantic construction enumerates the readings of an expression and passes them on to a resolution component, which-on the basis of contextual and world knowledge-filters out the plausible readings, if possible, a single reading. While the simplicity of this model is attractive, it is neither very efficient nor cognitively adequate. For instance, one may understand a sentence like ( r ) and can draw inferences from it without bothering to derive (even without being aware of) the range of its forty-two readings (Hobbs & Shieber 1.987): (r) A member of every department in most companies saw a few samples of each product From the standpoint of natural language processing, the advantage of the underspecified approach to structural ambiguities is that it considerably reduces the complexity of the analyses, which contributes greatly to their
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In this paper, I present Underspecified Minimal Recursion Semantics {UMRS), a representation language that represents structural ambiguities in terms of underspecifica tion. It is argued that this kind of approach allows for transparent semantic representations and a straightforward syntax-semantics interface. UMRS is a semantic metalanguage, whose expressions describe expressions of an object language and (possibly underspecified) dependences between them. The potential of UMRS will be illustrated by employing it as the semantic component of an HPSG description of wh-questions.
3 8 Wh-questions in Underspecified Minimal Recursion Semantics
2 THE UMRS F O RMALISM In this section, will first give a brief introduction to the UMRS formalism, outline how ambiguity is captured in UMRS in terms of underspecification, and discuss the features of UMRS that distinguish it from other underspecified semantic representation formalisms. 2. I
Basics of UMRS
The UMRS formalism represents structural semantic ambiguities by underspecification, not of disjunction.' UMRS has roots in the MRS
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computational tractability. Underspecification yields not only more compact semantic representations but also allows for simpler syntax semantic interfaces. Thus, in the analysis of examples like (I), there is no need to write complex rules to associate one single syntactic structure with a host of semantic structures, or, alternatively, to preserve an I : I -relation between syntactic and semantic structure at the cost of associating different readings of syntactic structures with different derivation histories as e.g. in the tradition of Montague Grammar. Within the last decades, several formalisms for underspecified semantic representations have been proposed to describe ambiguities in compact, underspecified representations, e.g., the algorithm of Hobbs ·& Shieber (I987), Underspecified Discourse Representation Theory (UDRT; Reyle I 993), or Quasi Logical Form (QLF; Alshawi I 992), Minimal Recursion Semantics (MRS; Copestake et al. I 997), or Underspecified Semantic Description Language (USDL; Pinkal I996). Like in UMRS, in these approaches the underspecified treatment of scope ambiguities plays a prominent role. To illustrate UMRS and to show the potential of this approach, it will be applied to the notoriously difficult field of wh questions. I will show that UMRS can account for the semantics of wh-questions in a transparent way, and, what is more, allows for an extremely simple syntax-semantics interface even in the case of the interaction of wh-elements with quantifiers. The paper is structured as follows: after an introdu.ction to UMRS in section 2, section 3 is devoted to wh-questions and the problems they pose for semantic representation formalisms. Finally, in sections 4 and s I will show that UMRS allows a straightforward compositional derivation of the semantics of wh-questions that represents ambiguities in this domain in terms of underspecification.
Markus Egg 39
NP
(2)
everyone_rei HANDEL rn BV
rn
HD_ARG Q]
come_rel HANDEL Q] INST rn at;g l
rn
The feature BV ('bound variable') specifies that the relation in which it appears is a function that ·binds a variable in its scope. The value of this feature in a function relation R must be co-indexed with the value of a feature of a relation in the scope of R. The feature INST models the main argument of the object language expression that the metalanguage relation denotes. E.g. the INST value of verbal relations corresponds to a main eventuality argument. Features are introduced by subtypes of the general type for relations that subsumes all UMRS metalanguage expressions. For instance, the feature HD_ARG is introduced by. a type scope_rel that subsumes all relations for scope-bearing expressions (see ·appendix B for the relevant parts of the type hierarchy I assume in this paper).
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formalism.2 It was used for the semantic construction in an HPSG grammar in the first phase of the German VERBMOBIL project. UMRS is a metalanguage: it contains entities that denote expressions of an appropriate object language and specifies (possibly underspecified) dependences between these entities. The entities. are called 'relations' and interpreted as types in a typed feature structure formalism. Semantic representations in UMRS are flat lists of relations. I use an extension of the predicate calculus (abbreviated as 'PC') as object language. Dependences between relations on a UMRS list are specified in terrns of a feature HANDEL that appears in every relation. Its value serves as an address for the relation. If the HANDEL value of one relation is co-indexed with the value of a functional feature in a second relation, this means that the second relation has the first one as its immediate argument. The set of functional features models the potential of an expression to act as a function upon other expressions. It comprises e.g. HD_ARG, which models the scope of an expression, or RESTR, which stands for the restriction of a quantifier. These functional features are ordered, for instance, HD_ARG is higher on this ordering than RESTR. Consider e.g. the (simplified) UMRS representation of Everyone came (2). The representation and the verb representation stand in a function argument relationship, as the former's HD_ARG value Q] is co-indexed with the latter's HANDEL value.3
40 Wh-questions in Underspecified Minimal Recursion Semantics
lntersective modification is specified in UMRS by co-indexing the
HANDEL values of modifying and modified constituent. To be well formed, the INST feature value of the modifier must be co-indexed with
the value of a feature of the modified constituent. The translation of this is co-indexation is conjunction. E.g. the UMRS representation of ( 3 ), and its translation into predicate logic is pretty'(xz) 1\ girl'(xz).
prettygirl
(3)
( [pretty_rel ] [girl_rel ] ) HANDEL III INST [1]
'
HANDEL III INST [1]
TL1 : [L1 U L:�.] =[L1](.Xxn[L2]) if the following conditions hold: L1 contains only an operator relation R1 and any relation that ts functionally dependent on R1 via some functional feature F1 =/:- Fz Fz is the highest functional feature F of R1 such that there is a relation in L1 U L:�. whose HANDEL value is co-indexed with the value of F the BV value of R1 is [!!] Lz contains only all the relations that are functionally dependent on R1 via Fz Functional dependency via a feature F is defined recursively: Rz is functionally dependent on R via F if the HANDEL value of Rz is coindexed with the F value of R1 or •
•
• •
1
•
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UMRS can represent the semantics of expressions as a list of only loosely connected relations. This allows other relations to intervene scopally, which facilitates accounting for complicated data. This is illustrated in my analysis of wh-questions in section 4· The translation of UMRS representations like (2) leads recursively from the translation ofUMRS lists L to the translation of disjoint parts of this list L1 and L:�..4 For unambiguous UMRS structures, the translation rules TL1 and TL2 define the recursion steps. They cover the case of function argument structure and intersective modification structure, respectively. They are mutually exclusive in that only one of them may apply to a given UMRS structure. Successful application of the procedure partitions a UMRS list into singleton lists. These singletons are then translated by a mapping M that maps each metalanguage relation on to the corresponding object language expression. This allows the recursion to bottom out. In TL1, the ordering on the set of functional features is crucial to guide the order in which the translation of an expression (e.g. a determiner) that yields a function with more than one argument is applied to its arguments.
Markus Egg 4 1
the HANDEL value of R2 is coindexed with th� value of some functional feature of an R3 that is functionally dependent on R, via F
•
lntersective modification is translated b� the rule TL2: . U Lz . . . U L,] = [L r ] 1\ [Lz] . . . [L,] 1f the following conditions hold:
TL2 : [L,
•
• •
The mapping M for singleton UMRS lists onto object language expressions must crucially preserve co-indexations within UMRS structures: Most of the action on the UMRS level has to do with getting these co indexations right, as they model important dependences between relations that matter in the object language, too (e.g� there is a co-indexation between the BV value of the main relation of an and the value of the appropriate argument feature in its governing verb). This preservation of co-indexations will be modelled in the following by reusing in M the numbers of the UMRS indices as subscripts of the variables that correspond to the indices in the respective object language translations. This preservation of the coindexations is e.g. crucial for the ..\-abstraction that is introduced in the translation rule TL1• This abstraction is determined solely by the BV value of the function: the argument relation does not reveal which of the variables of its translation must be abstracted over (there may be more than one available). Only the coindexation of the value of the corresponding feature with the BV value carries this information. Hence, abstracting over the right variable in the translation of the argument presupposes preserving the co-indexation between the Bv value of the function and the value of the corresponding feature of the argument. As an example for TL1 and TL2, consider the translation of the UMRS representation of everybody came yesterday:
NP
(4)
Jorall_rel HANDEL
[I]
[�'" 'd l
come_rel HANDEL
0 , HANDEL I}] , INST INST RESTR I}] 0 ARGI HD_ARG [I] BV
[
-"1 ]
Y""'J.y
III , HANDEL [I] ill INST ill 0
·
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All L; ( I :S i :S n ) contain only a relation R; ('main relation') and any relations that functionally depend on R; the HANDEL values of the main relations are identical . one of the main relations R; {the one of the modified expression) is related to every other main relation � (those of the modifying expressions) by a co-indexation of the INST value of every Rj with the value of some feature in R;
42
Wh-questions in Underspecified Minimal Recursion Se?Iantics
[�"'"-"/ ]
Jorall_rel HANDEL BV
RESTR
[I] [I] , HANDEL m m INST [I]
HD_ARG [I]
come_rel HANDEL [I]
Ax2
m
ARGI
[I]
l"'"''r
1
forall_rel HANDEL BV
RESTR
HANDEL [I]
m
INST
( [\/ [=�" �] )] ) person rei
[I] [I] [I]
Ax,
HD_ARG [I]
come_rel Ax2
HANDEL [I] INST
m [I]
ARGI =
[\ [ ] )] yesterday_rei
(\
HANDEL [I]
INST
m
-\Q-\P'v'x2 .Q(x2) -+ P(x2)(-Xx2 .person'(x2)) (-Xx2.come' (x2)(s4)
1\
yesterday' (s4))
At the beginning of the translation procedure, only TL1 is applicable. The first element of the resulting partition of the list is once more the input for 1L1 , whereas the second element is processed by TL2• As the example shows, I translate verb relations as formulae of type t, with their arguments represented as free variables. The translation rules allow the correct translation of verb-argument structures no matter in which order the semantic representations of nominal arguments are applied to the semantics of their governing verbs. See section s for detailed analyses which crucially rely on this aspect of the translation rules. The translation rules entail that in a sentence with fully specified scope
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INST
[ -"1]
Markus Egg 43
and modification relations, there is a function-argument chain (called 'main FA chain') in which each element Rn + 1 ( n E N) in the chain is functionally dependent on its predecessor Rn via the highest functional feature of Rn. Finally, note that there are non-singleton UMRS lists for which neither TL1 nor TL2 is applicable. Consider e.g. the cyclic structure (s): (s)
([
][
rell rel2 HANDEL co ' HANDEL CD HD_ARG CD HD_ARG co
])
2.2
Structural semantic ambiguities in UMRS
UMRS represents semantic structural ambiguities by specifying for each operator the range of its potential arguments. Relations for operators have two additional list-valued features HOUT and HNON. They list the HANDEL values of relations that can be immediately subordinated to the relation in question (the value of HoUT) or the HANDEL values of those that cannot (the value of HNON) . The HD_ARG value of an operator relation must be an element of the list that is equal to the HOUT value minus the HNON value. If there is more than one element on this list, the scope of the operator is underspecified. The value of HOUT is determined globally: In appropriate domains (scope islands), potential arguments (as specified in the lexical entries) are collected in a list. This list is percolated all over the domain and co-indexed with the HOUT value of every operator relation within this domain. E.g. every argument has the HANDEL value of its governing verb on the HOUT list. Thus, in the feature structure (6) below, the relations that model the determiners eVery and a (forall_rel and exists_rei) include in their HOUT value 1 20 I the verb
NP
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Here TL2 fails because the HANDEL values of the two relations are not coindexed. TL1 fails, too, since its first and fourth condition cannot both be met. If we assume that TL1 partitions (s) into L1 and L2 such that L1 contains reli and L2, reh, this is in accord with the first, second, and third conditions of TLI. But, then, L2 violates the fourth condition of TLI : It does not contain everything that is functionally dependent on rel 1 via its HD_ARG feature, because relr itself is not part of it. By similar reasoning, the translation procedure shows that structures in which two functions have the same immediate argument are not interpretable. If such an uninterpretable non-singleton UMRS list L" appears in a recursion step of the translation procedure for an UMRS list L, L is not well-formed in that it fails to denote an expression of the chosen object language.
44 Wh-questions in Underspecified Minimal Recursion Semantics
relation HANDEL value [}]. For each operator, its HNON value restricts possible arguments locally. Especially, each operator's HNON list comprises its own HANDEL value, as no operator is its own argument. For instance, the HNON value of the Jorall_rel comprises [2] , its own HANDEL value. (6)
0< � • 0 • 0 > HOVT 0 0(0u 0) [HIN
HINHOVT
coNT i um
coNT i usZT
0
[HIN HINHOUT
0 (� , > ] l
HOliT r:::-1 �
coNT i usZT
0(0u[D)
HO_ARC
HINHOUT
[HIN txists_rtl
HANDEL
CONT, USZT
0
IV IUISTII
HOVT HNON
HD_ARC
0 [""'man rd l
GJ 0 0 (0 )
1
KANDEL INST
0 GJ
HINHOVT HOUT
(� ) 0
]
lovt_rtl
HANDEL � CONT, USZT
0
INST ARGI ARCl
0 0 GJ
(6) illustrates this mechanism for Every man loves a woman. The list 1 20 I of HANDEL values of potential arguments comprises the HANDEL values of the determiners and the verb. The lexical items are the terminal nodes in the structure (6) (the construction of the semantics is omitted in (6)). They specify the potential arguments in HINHoUT I HIN. HINHoUT I HIN values of daughters are appended in the mother, the top node of the domain co indexes the value of HINHOUT I HIN with HINHoUT I HoUT. HINHoUT I HoUT values of mother and daughters are co-indexed, and lexical items coindex the HINHOUT I HoUT value with the HOUT value of all operator relations in their usZT value. (6) represents the ambiguity of operator scope by underspecifi.cation. It comprises two disambiguated readings: The immediate argument of
NP
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[
HINHOt.rf
]
Markus Egg 4 5
Jorall_rel is either love_rel or exists_rel as its HD_ARG value is an element of ([I], ffi] } (its HOUT minus its HNON value). If the verb relation is chosen, exists_rel must have Jorall_rel and not love_rel as its immediate argument (two functions may not have the same immediate argument). If exists_rel is chosen as the argument of Jorall_rel, exists_rel must have love_rel as its argument; if it had Jorall_rel as its argument, we would get an ill-formed
•
•
•
L1 contains only an operator relation R1 with the BV value [ill and any relation that is functionally dependent on R1 via some functional feature F. =I HD_ARG. The HANDEL value of R1 matches any relevant restrictions. R1 determines the new relevant restrictions. L� is the same as L2, except that the HANDEL value of R1 is added to the HNON list of all relations of L2 that have this feature.
The relevant restrictions mentioned in the third condition are either a type restriction or an exclusion set of HANDEL values. The condition is that the HANDEL value of R1 matches the type restriction and may not be an
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cyclic function-argument chain like in .(s). (TL3 below spells out the disambiguation process in detail.) In sum, the relative scope of the determiners is open in (6), but both have (immediate or not immediate) scope over the verb, as desired. UMRS structures are interpreted by translating them into an object language. For scopally fully specified UMRS structures, the translation rules TL1 and TL2, which were laid out in detail above, are employed. For UMRS structures that exhibit scope ambiguities, the translation must shoulder an additional task: it nondeterministically determines the scope of operators whose scope is not yet fixed. Above all, it reconstructs the main FA chain for each reading of an ambiguous UMRS structure. Rule TL3 applies to scopally underspecified UMRS 'structures. Once the (possibly recursive) application of TL3 · to an UMRS list L with scope underspecification has transformed it into a structure that contains only fully specified parts of L, these parts are processed by TL1 and TL2• TL3 specifies the step from the translation of an underspecified UMRS list L to the translation of its parts L1 (a scopally underspecified operator and any relations functionally dependent on it) and L2 (the rest of the list).5 To put it simply, each of these steps picks a scopally underspecified operator (plus any accompanying material) from the list, translates it, and applies it to the translation of the rest of the list (with a A-abstraction determined by chosen operator's BV value). Further restrictions rule out ill-formed disambiguations. More formally:
46 Wh-quesrions in Underspecified Minimal Recursion Semantics
2. 3
UMRS and other app roaches
Several other formalisms have been developed to describe scopally ambiguous semantic structures in underspecified, non -disjunctive repre sentations, among them UDRT (Reyle 1 993 ), QLF (Alshawi & Crouch 1992), MRS (Copestake, Flickinger, & Sag 1997), and USDL (Pinkal 1996) . A number of features distinguish UMRS from these approaches. The first difference of UMRS is that it expresses scope underspecification in terms of immediate subordination only (rather than in terms of not necessarily immediate subordination). This means that the basic scope relation is 'x has scope over y and everything else that has scope over y must also h�we scope over x', whereas the other approaches use a subordination relation ·�· that can be paraphrased as 'x has scope over y but there may be intervening material'. Scope ambiguity of a constituent is described in UMRS by underspecifying its immediate argument. Hence, cases of · not necessarily immediate scope relations must be handled differently. In the analysis of wh-questions I will show that the restriction of compatibility between the HD_ARG value of a function and the HANDEL value of its argument (as expressed in the second condition ofTL3) can be exploited for this goal: suitable typings of HANDEL and HD_ARG values of scopally underspecified relations allow the expression of such scope relations (see e.g. the discussion of the wh-operator in section 4·J.I).7 This makes the representation more compact, as the list of relations constitutes the core semantics by itself, one does not need an additional explicit list of scope relations in the core .like e.g. in UDRT. Moreover, the mechanism of typing HANDEL and HD_ARG values of scopally underspecified relations can be used for other phenomena, too, hence, some variant of it
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element of this exclusion set.6 The relation R1 that is chosen for evaluation determines the new relevant restrictions in the following way: if the HD_ARG value of R1 carries a type restriction, this becomes the new relevant type restriction. The HNON value of R1 becomes the new exclusion set. If no choice of R1 is possible for TL3 such that its HANDEL value matches the relevant restrictions, the structure is ill formed and the translation procedure must reset one or more of the nondeterministic choices. If there are no alternative choices left, the translation procedure fails. This rule prevents ill-formed disambiguations of UMRS structures (which would be too difficult to filter out in the metalanguage itself): cyclic function-argument chains as well as branching function-argument chains (in which more than one function has the same immediate argument) are ruled out.
Markus Egg 47
3 THE SEMANT I C S O F WH- QUES T I O N S This section is devoted to the semantics of wh-questions and presents the challenges that wh-questions pose for semantic representation formalisms. I start with a brief review of the approach of Karttunen & Peters {198o) (henceforth KP), which is based on Karttunen (1977) and Hamblin (1973). · This approach is reductionistic in that it interprets wh-questions as the set of all propositions that are possible answers to the respective questioiL8
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may be necessary anyway. For instance, in this paper I will use it to model the fact that NPs that are quantified into wh-questions must be read de dicto {see section 4.3.2). A further feature of UMRS is that it can represent the semantics of constituents not only by atomic relations but by whole lists of relations. The scope relations between elements of these lists may be underspecified, which opens up various ways of integrating them into the semantic representation of larger constituents. The aim of this highly flexible construction of complex constituents is to make possible simpler semantic representations in the lexicon and a simpler syntax-semantics interface. I will illustrate this feature of UMRS with · the analysis I propose for the interrogative operator in section 4· While this feature plays an important role in UMRS, it could in principle be integrated into other underspecified approaches to structural ambiguities, too. Nevertheless, fully exploiting the flexibility of this feature of UMRS in semantic construction seems to be difficult for approaches that describe not necessarily immediate scope relations in terms of the relation ·�· while it is straightforward for an approach like UMRS, which captures these scope relations by suitable typings of HANDEL and HD_ARG values. See section 4.3.1 for an example for this claim {the integration of the semantic representations of the interrogative operator and of the wh-elements). The translation formalism for UMRS (see the preceding subsections) is similar to the one of QLF {Alshawi & Crouch 1992) in that it operates recursively on structures of the representation language. For an ambig uous structure, the . translation nondeterministically selects one of its readings. The difference to the QLF translation is that UMRS structures denote object-level representations, whereas QLF structures receive a model-theoretic interpretation. With this brief comparison ofUMRS to other underspecified approaches I conclude the overview of UMRS. In the following section, the semantics of wh-questions will be outlined, before I illustrate UMRS by employing it for the description of wh-questioris.
48 Wh-questions in Underspecified Minimal Recursion Semantics
Wh-phrases are rendered as existential quantifiers Qike indefinite NPs). This nicely models the common ground between them, e.g. they are both acceptable in there-insertion contexts (Higginbotham 1997). If propositions are interpreted as properties (or sets) of possible worlds or eventualities, the semantics of a question like (7) is (8 ), the set of propositions that characterize eventualities s by the property 'x is coming at s', if x is a person in the given domain:
(7) Who is coming?
(8) .Xp 3 x(person'(x) 1\ p = .Xs .come'(x) (s))
(9) Who got which mark? (10) .Xp 3x1 (person'(x1 ) 1\ 3x2(mark' (x2) 1\ p
3.1
=
.X s . get' (x1 , x2) (s) ))
Questions and answers
The view of KP that questions should denote the set of their possible answers was challenged by authors like Higginbotham & May (19 8 1) (HM) and Groenendijk & Stokhof (19 8 2) (GS) (see also Higginbotham 1997; Groenendijk & Stokhof 19 8 4, 1997). They note that it is difficult to express the notion of 'partial answer' in this approach. It is a general observation that anything that narrows down the range of possible answers counts as an answer to a question (as opposed to an irrelevant remark). Complete answers to a question are thus a special case of answer. E.g. the following sentences all qualify as an answer to (7). None of them, however, except ( I I a), is an element of the KP answer set. This begs the question of how to distinguish partial answers to a question from irrelevant remarks.
( I I ) (a) John is coming
(b) At most two people are coming (c) No one is coming (d) At least two people are coming
HM and GS therefore separate the denotation of questions from possible answers to these questions. The semantics of questions gives rise to exhaustive partitions of the set of possible worlds in their analyses
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KP extend this approach to multiple wh-questions. In their semantic representations, all the wh-elements appear outside the equation between propositions, the rest of the sentence, within it. Thus, the representation of (9) is ( 1 o), the set of propositions of the type 'x gets y', if x and y are persons and marks, respec�ively, in the given individual domain:
Markus Egg 49
{presuppositions within questions would delimit the set to be partitioned). Consider e.g. GS's analysis of the intension of (7):
( 1 2) ..\w..\w'( ..\x .come'(x) (w') = ..\x.come'(x) (w))
3.2
The syntax-semantics interface
Once the semantic representation of a linguistic expression has been decided upon, one must show that it is possible to derive this representation by the interaction of the assumed syntactic theory with a suitable syntax-semantics interface. In this subsection, I will illustrate by the example of the KP analysis of the multiple wh-question (9) that the development of an appropriate syntax-semantics interface for wh-questions is a rather involved issue. The treatment of multiple wh-questions illustrates the two main features of the KP approach to wh-sentences: First, the semantic contribution of the
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At any given world w", ( 1 2) denotes the set of all worlds in which the set of walkers is the same as in w" (or, alternatively, the proposition that the set of walkers is the same as in w"). If we assume that there are just two individuals a and b in all possible worlds, there are four options for the set of walkers in w ". Consequently, the set of possible worlds is partitioned in four subsets, depending on whether the set of walkers in a world is 0, {a}, {b }, or {a , b } . On the basis of such a partition, the definition of answerhood is very straightforward. HM and GS state that a felicitous response to a question should narrow down the range of possibilities (the range of the partition of possible worlds) that is expressed in the semantics of a question. Formally: the meaning of such a response is regarded as a further restriction of each element in the set of possibilities. This should result in contradictory restrictions for at least one possibility, which is hence ruled out. Complete answers are special in that they rule out all but one possibility. For our example this means that if a is the individual called john', { I I a} rules OUt the possibility that the set of walkers is empty, or contains only the individual b. {I Ic}, on the other hand, removes all possibilities except the one that the set of walkers is empty, hence, is a complete answer. Although the notion of answerhood is not encoded directly in the KP analysis of wh-sentences, I think it is still possible to follow the argumenta tion of Chierchia (1 993, 191£} in favour of KP proposition sets as the semantics of questions (modulo type raising), although one can no longer regard these proposition sets as sets of possible answers, as GS and HM have shown. This means that the relation between questions and answers must be spelt out explicitly, which I will do in the appendix A.9
so Wh-questions in Underspecified Minimal Recursion Semantics
Q2 QNP2 Xm QNP. Xn ________-r---
( I J)
. 1
which mark
Q1
�S I �
who
Syntactic question nodes get different semantic analyses: The lowest question node Q. introduces the .\-binder of a propositional variable and the equation between propositions (I4). Higher question nodes like get the semantic interpretation (I S ) · This expression binds the .\ abstraction over propositions in its argument and introduces a new one. This imitates inserting wh-elements between the two parts of the wh operator.
p
Q2
( I 4) { I S)
[[QQz.]] .\.\pp[[QQNP2NP.]]((.\.\xxm[n(pQ.]([ps)]))) =
=
=
This analysis illustrates that the development of a syntactic analysis and a suitable syntax-semantics interface is a first challenge for analyses of wh questions. Ideally, all wh-questions should be described in terms of one single syntactic structure with an invariant semantic interpretation for each type of syntactic node. When further phenomena are integrated into the semantic analysis of wh-questions in the following two subsections, the topic of syntax-semantics interface will come up again.
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wh-operator breaks down into two parts: (i) a binder of a proposttton variable (in KP, a .\-abstractor), which models the analysis of questions as answer sets, and (ii), an equation of propositions that characterizes the members of this answer set. Second, semantic representations of wh expressions are modelled as existential quantifiers that take scope over the equation and below the binder in the wh-operator semantics. This begs the question of how to model these features in the derivation of the semantics of multiple wh-questions. In order to 'squeeze in' more than one wh-expression between the two parts of the wh operator for multiple wh-questions, it seems to be necessary to complicate the syntactic analysis and the syntax-semantic interface considerably. KP assume a syntactic question node for each wh-expression. Thus, simple and multiple wh-questions get different syntactic analyses. They analyse (9) as ( I J):
Markus Egg 5 1
3 · 3 De re
vs.
de dicto
readings
In this subsection, I will discuss the distinction of de re vs. de dicto readings of wh-expressions like which man. The difference shows . up in examples like (16): (16) John knows which man walks
(17) (a) A w 1 (Ax.walk' (x) (w ' ) A man' (x) (w ' ) = Ax.walk'(x) (w) A man' (x) (w) ) (b) A w1 ( -Xx.walk'(x) (w ' ) A man' (x) (w) = Ax.walk' (x) (w) A man' (x) (w) ) ·
GS represent the semantic contribution of wh-expressions in terms of A-abstractions rather than in terms ofquantifiers. E.g. for which man walks, the abstract would at a given world w be AX0 .man' (x0) (w) A walk' (x0) (w). These abstractions, then, are embedded inside the equation that is the core of the question semantics. This analysis of wh-expressions by A-abstraction directly yields de dicto readings of wh-expressions. . De re readings are the result of a special mechanism in GS's approach, which assumes the framework of Montague Grammar (MG). First, one needs syntactic N variables one, (analogous to the he� NP variables assumed for quantifying in MG). These variables function as ·place-holders for the N constituent of a wh-phrase in the derivation of a wh-question. Second, there is a syntactic rule that combines sentences and N into a sentence. This rule replaces a syntactic variable one, by the N ·constituent. The corresponding semantic rule integrates the N semantics 4> into the sentence semantics 'If; by abstracting in 'If; over the variable that is the semantic contribution of
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If the wh-expression which man is understood de re, John knows of all individuals that are men whether they walk, but need not be aware of the fact that each of them is a man. In the de dicto reading of the sentence, he also knows of each individual in the set of walking men that he is a man. The KP analysis can only derive de re readings of wh-expressions, as these expressions are interpreted as indefinite quantifiers, which restrict the answer set but are not part of it. GS note (and Zimmermann 198 5 proves) that there is no direct way for the KP approach to derive these de dicto readings, because it assigns to wh-expressions the semantic type of NPs. GS can express de dicto readings of wh-questions like which man walks. They let (16) in its de dicto reading denote in a world w the proposition (17a) that the intersection of men and walkers is the same as in w. In contrast, the de re reading of this sentence in a world w is the set of worlds w ' (17b) such that the intersection of individuals that are men in w and walkers in w ' is the same as the intersection of men and walkers in w:
52
Wh-questions in Underspecified Minimal Recursion Semantics
and applying the result to ¢. This application ensues that the world parameter of the N semantics is determined independently of the semantics of the sentence. In (I 7b), this pertains to the two instances of the semantic representation of whose world parameters are both set to the world w at which the sentence is evaluated. Chierchia (I993) shows that it is possible in his analysis, too, to derive readings. For readings, he also relies on a syntactic rule that combines sentences and N constituents. These analyses are problematic in that they necessitate a very peculiar extension of syntax by adding a rule that combines a sentence and an N. This technique of relating semantic ambiguities to different derivation histories of identical syntactic structures is used in MG to obtain a I : I relation between syntactic structures and readings of a semantically ambiguous expression. Bur the underspecified approach can preserve a I : I -relation between syntactic and semantic structures without having to assume these otherwise unmotivated syntactic ambiguities, by describing the readings of a semantically ambiguous syntactic structure in terms of one single underspecified semantic representation. Note also that the solution as it stands runs into problems, because it integrates the semantics of the N constituent of the wh-phrase into the core of the question by conjunction. This is problematic for sentence pairs like in ( I 8) and (I9):
onen,
man,
de dicto
Which bachelors are bachelors? Who is a bachelor? Which men are bachelors? Which bachelors are men?
In the GS representation of example (I 8a) (attributed to Stanley Peters), there are two conjoined instances of the proposition bachelor' (x) , which boil down to one. This, however, makes the semantics of (I 8a) identical to the semantics of (I 8b). Similarly, commutativity of the conjunction would bring it about that the representations of (I 9a) and (1 9b) become indistinguishable. Higginbotham's (I997) approach, too, represents the semantics of wh questions as a partition on the set of possible worlds. His analysis overcomes the problem posed by examples like ( I S) or (I9): While the wh-element is introduced into the core of the question, it functions only as a restriction on the propositions that are used for the construction of the partitions of possible worlds (see section 3·4·3 and Higginbotham I997 for details). The solution I will propose in section 4.3.2 sticks to the KP analysis in that it analyzes wh-questions as indefinite quantifiers. Yet it is possible to extend this analysis to cover readings as well. The reason for this is
de dicto
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( I 8) (a) (b) (I9) (a) (b)
de re
Markus Egg 5 3
that UMRS is very flexible representation. 3 -4
m
combining the parts of a semantic
Quantifying into wh-questions
Quantifying into questions is yet another phenomenon that a fully-fledged analysis of the semantics of wh-questions must take into account. E.g. (2o) has, apart from the reading in which one asks for the mark which everyone got, an additional reading, the so-called '(pair) list reading', which asks for pairs of persons X1 and marks x2 such that x1 got x2 : This reading is related to a multiple wh-question (in the case of (2o), (9)) in that both share the same complete answer. However, Higginbo tham (1 997) has shown that they are not equivalent in that they have different partial answers. He illustrates this by the following example: In a situation in which there are three people, anyone who knows of two of them what they said but has no information about the third can assert (2 1) but not (22): (2 1) I have some information about who said what (22) I have some information about what everyone said Other quantifiers can be quantified into wh-questions as well, as Belnap's example (23):
m
(23) Where can I find two unicorns? In one reading of (23), called 'choice reading' by Groenendijk & Stokhof (1984), one asks for information about the position of any two unicorns. An A is appropriate answer to this reading could be B, Such readings add an additional level of complexity in that they do not denote unique questions but whole families of questions. E.g. for (23), any family member is a question on the whereabouts of two unicorns. This entails that the type of their semantic representation must be more complex than merely sets of propositions. If one wants to assign a uniform type to all wh-questions, the type of a simple wh-question like (7) must be lifted. In addition, the problem of readings reappears for quantifiers that are quantified into wh-expressions, as these quantifiers must be understood Like HM and GS I analyse the list reading of (2o) and the choice reading of (2 3) as quantifying into wh-questions. My use of the term 'quantifying in'
unicorn behind the house.
Unicorn in the garden and
de dicto/de re
de dicto.
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(2o) Which mark did everyone get?
54 Wh-questions in Underspecified Minimal Recursion Semantics
3 -4. 1 KP's approach
The list reading of (2o) cannot be described by a straightforward extension of the KP approach. The direct way of expressing in this approach that, according to this reading, not everyone must have the same mark would be to give the universal quantifier everyone wide scope over the existential quantifier as introduced by the wh-element which mark: (24) .\p\fx 1 (person' (x . ) --+ 3 x2(mark'(x2) 1\ p = .\s.get'(x . , x2 ) (s))) But if there is more than one person in the individual domain, (24) denotes the empty set rather than the desired set of propositions of type .\s .get'(x" x2 ) (s) (with x. , a person and x2, a mark): for every person X1 , a proposition p of the set denoted by (24) would have to be equal to the proposition 'x1 gets x2 at s' (x2, a mark). However, this condition cannot be fulfilled, as no proposition can be equal to 'x1 gets X2 at s' for more than one pair of values for x1 and X2 (KP).
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refers to the same class of phenomena as in MG (syntactic structures that are associated with more than one reading which is due to scope under specification of quantifiers). However, the use of this term is not meant to imply that I subscribe to the MG account of these phenomena (relating different readings of one syntactic structure to different derivation histories of the syntactic structure). Chierchia (1993) is sceptical of the interpretation of sentences like (2o) as instances of quantifying in. He gives two arguments against such an analysis: first, he claims that in these analyses it is impossible to rule out quantifying into yes/no questions. Second, he doubts that standard quantifying in and rules like the ones proposed by Higginbotham (1997) and Groenendijk & Stokhof (1 984) for quantifying into wh-questions have enough common ground to be grouped together under the same heading. His first argument against such analyses is not uncontroversial, see e.g. Higginbotham (1997). But even if quantifying in yes/no questions is impossible, this can be accounted for in the proposed analysis (see section 4·3- 1). Furthermore, I will show in section 4.3.1 that there is more common ground between standard quantifying in and quantifying into questions in the proposed analysis than in Higginbotham's (1997) and Groenendijk & Stokhof's (1984) analyses, which justifies subsuming . them under the common denominator of quantifying in. In sum, a comprehensive analysis of wh-questions must be able to account for quantifying into wh-questions and, in addition, to describe the relation between multiple wh-sentences and quantifying universal quantifiers into wh-sentences. Let us now briefly review a number of analyses of quantifying into wh-questions.
Markus Egg 5 5
Karttunen { I 977) concludes that wh-expressions must have widest scope in a wh-question and that quantifying into these questions must be analysed in terms of a 'performative approach' to questions. I.e. direct questions Q are interpreted as indirect questions of the type 'I want you to tell me Q' (see Groenendijk & Stokhof I 997 for an extended discussion of the performative approach). This move makes possible quantifying in in the usual way; the resulting analysis for (20) would roughly be 'For each person, tell me what mark he got'. However, KP show that this solution cannot be generalized to list readings They suggest of wh-questions that are complements of verbs like accounting for these examples by a rule that maps universal quantifiers that are quantified into wh-questions on to their duals. As this rule maps universal quantifiers on to existential ones, (2o) can be assigned the same semantics (10) as (9). However, this rule does not cover quantifying into wh questions in general, e.g. it does not account for Belnap's example (23).
to wonder.
Engdahl {I986) accounts for list readings by analysing wh-expressions in terms of functions J from (n-tuples of) individuals to individuals. The restriction of a wh-expression (in (2o), the predicate mark') characterizes the range of such a functionf. She proposes the analysis (25) (simplified) for the list reading of (2o): (25) Ap 3f(\ix( mark' (J(x)) ) A p
=
As'Vx( person'(x) ---+ get'(x, J(x)) ) )
This technique scopes the universal quantifier below the equation between propositions. (25) denotes the set of propositions that are equal to the proposition that every person gets some mark, viz. the mark assigned to him by a suitable function f. This approach identifies both the list and the 'functional' reading · of a sentence like (2o). It does not try to represent the ambiguity between list readings and functional readings in one single underspecified reading: In this analysis, list readings functional readings. In functional readings, what is asked for is a set of functions that maps the individuals in the quantifier's restriction onto individuals that belong to the wh-expression's restriction. E.g. for (2o), a functional reading is forced in the question-answer pair (26).
are
(26) Which mark did everyone get? The mark he dreaded most to get. Mathematically, functional readings subsume list readings, as functions can be interpreted as sets of ordered pairs of individuals (such pairs are asked for in list readings). List readings are then a special case of functional
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3 .4.2 Engdahl's approach
56 Wh-questions in Underspecified Minimal Recursion Semantics
readings in that the language happens to lack an expression for the function
f in the case of list readings. This means that J must be characterized by an explicit listing of its ordered pairs. However, as Groenendijk & Stokhof (1984) and Chierchia (1993) show, quantifying into wh-questions cannot be identified with functional readings:10 The functional and the list reading of a wh-sentence contribute to the truth conditions of larger constructions independently of each other. Consider e.g. Max may know the exhaustive list of lover-loved pairs without being aware of the function that maps the first element of such a pair on the corresponding second element. The reverse might also hold. Moreover, if one adopts the argumentation of Groenendijk & Stokhof (1984) against relating singular forms of wh-expressions with uniqueness presuppositions, the uniqueness condition on values as introduced by the functions J is an additional feature that distinguishes functional and list readings: while this condition holds for functional readings, it is too strong for wh-readings. E.g. in the list reading of (27), the pairs that are asked for are taken from the Cartesian product of persons and students: it is possible for a person in the relevant domain to see more than one student.
Max knows whom everyone loves:
Finally, Engdahl's explanation does not account for the fact that the distribution of list readings is narrower as the one of functional readings, since downward monotone quantifiers 1 1 typically disallow list readings but not functional readings. Thus, (28) can be answered by but not by Bill a list like
The i r PM Max admires Clinton, Mary, Helmut Kohl ...
3 ·4·3 Higginbotham's approach
Higginbotham (1997), Groenendijk & Stokhof (1984), and Chierchia (1993) propose analyses for quantifying into questions that describe these cases with expressions that have lifted types. To show how these analyses work, I will outline the basics of the first of these analyses. Higginbotham assumes that simple wh-questions (modulo type lifting, whose motivation is to assign all wh-questions the same semantic type) denote partitions of possible worlds. Elements of this partition are characterized by sets S of predicates. E.g. for simple wh-questions of the type X Y?, such a set S contains for any individual x in the given context such that x E [X] either the proposition P(x) or its negation, where P is the semantics of Y. (Nothing else is an element of such an S.)
Which
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(27) Which student did everyone see? (28) Which politician do few people admire?
Markus Egg 57
If we assume that there are-_just three people a, b, and c. Higginbotham's (1997) analysis of {7) yields a'tpartition like (29), where ¢ stands for the property of coining:
{29) {{¢(a), ¢(b) , ¢(c) } , {-.¢(a) , ¢(b) , ¢(c) } , {¢(a) , -. ¢(b) , ¢(c) } , {-.¢(a) , -. ¢(b) , ¢(c) } , {¢(a), ¢(b) , -. ¢(c) } , {-.¢(a) , ¢(b) , -.¢ (c)} , {¢(a) , -. ¢(b) , -. ¢(c) } , {-.¢{a), -. ¢(b), -.¢(c) } }
Who do two people love?.
does love?.
(3 o)
Who loves whom? Who
{ {love' (a, a), love' (a, b) , love' (a, c) , love' (b, a) , . . . } , { -.love'(a, a), love'(a, b) , love'(a, c) , love'(b, a) , . . . } , {-.love' (a, a) , -.love' (a, b), -.love' (a, c) , -.love' (b, a) , . . . } } .
The semantics of the latter question is a singleton set whose member comprises three partitions (one for each individual). The partitions are like (29) , with ¢ = y . love'(xi , y) where Xi is replaced by the respective individual. The member of the singleton set is given in {3 1 ).
(3 1 ) { { {love' (a , a), love' (a, b), love' (a, c) } , {-.love' (a, a) , love' (a, b), love' (a, c) } , . . . , {-.love' (a, a) , -.love' (a, b), -.love' (a, c)} } , {{love' (b , a), love' (b, b) , love' (b, c)} , · {-,love' ( b, a) , love' ( b, b) , love' ( b, c) } , . . . , } , { {love' (c, a) , love' (c , b), love' (c, c)}, {-.love' (c, a) , love' (c, b) , love' (c, c)} , . . . , } }
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For quantifying into questions, the picture is more complex. Higginbo tham (1997) describes it via a set of sets of partitions. I will intrqduce his analysis here only informally, for the details of the formal apparatus, I refer to the original article. Consider e.g. the choice reading of If we again assume that there are only three people in the domain, the semantics of the question without the quantified in element can be described by a partition which is like {29), if¢ = Ay .love'(xi , y) . Then the resulting set of sets of partitions S' contains three members, as there are three possibilities of picking two individuals from the set of people. If E1 is the element of S' in which the chosen individuals are a and b, E. must contain for both a and b a partition which is like (29), with ¢ = AY .love' (a, y) and ¢ = AY .love' ( b, y), respectively. This analysis models the similarity between and everybody In our small three-person universe, the semantics of the former (after type lifting) · is a singleton set whose member has as its sole element the partition ( 3 o):
58 Wh-questions in Underspecified Minimal Recursion Semantics
Higginbotham (1997) assumes that to alljwer a family of questions is to answer every question in one of its memoers. E.g. in one must answer a pair of questions A and (A and B refer to persons). Then it follows that the list reading of B and the multiple wh-question have the same complete answers. For the multiple wh-question, a complete answer picks out one element from the partition (3o) that is the sole member of the sole element of the semantic representation of the question. This element specifies all the and only the lover-loved pairs. For the list reading, the family of questions has only one element (3 1 ), too, but one that has a partition for every person. A complete answer to the list reading picks for each person a partition member that specifies all the and only the persons he loves. The union of these partition members equals the partition member for the first question. Higginbotham (1997) achieves the construction of these semantic structures by two special interface rules. The first one combines an N constituent and a sentence into a wh-sentence. The second rule is ternary and combines a determiner, an N constituent and a wh-sentence into a new wh-sentence. In both rules, one has access to . the N constituent within a wh-phrase or within an NP that is quantified into a wh-sentence. The motivation for such rules is that the corresponding semantic rule can directly manipulate the semantics of this N constituent. By this move, one readings for wh-phrases and for quantified-in NPs. The can derive price, however, is that the syntax-semantic interface is complicated by these additional rules.'2 In the UMRS analysis of wh-questions and quantifying into wh questions, I will do without such special rules. This considerably simplifies the syntax-semantics interface. What is more, this restriction makes possible an underspecified representation of the ambiguities introduced by quantifiers in wh-sentences. As I will show in section 4, this approach relies crucially on the flexibility of combining semantic material in UMRS representations.
lovleo?v,e? Who does everybody love?
Who d o t w o pe o p l e Who does love? Who does Who loves whom?
de dicto
3·5
The assumed semantic representation of wh-questions
On the basis of the discussion in the preceding subsections, I assume the following semantic representations for (wh-)questions:
(32) (a) Is it raining? (b)
>.Q.Q(>.p.p >.s.rain'(s) =
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which,
Markus Egg 59
(33) (a) Who is coming? .
.
(b) ..\ Q.Q(..\p 3 x.person' (x) (s') 1\ p = ..\s.come'(x) (s))
(34) (a) Which student gets which mark?
(de re) (de dicto)
(b) ..\ Q.Q(..\p 3 x 3y. student'(x) (s') 1\ mark' (y) (s " ) 1\ p = ..\s.get'(x, y) (s) )
(3 s ) (a) Which student gets which mark?
(b) ..\Q.Q(..\p 3 x 3y.student'(x) (s') 1\ mark'(y) (s " ) 1\ p = ..\ s . student'(x)(s) 1\ mark'(y) (s) 1\ get'(x , y) (s))
(36) (a) Which mark does every student get? (wide scope of the non-wh quantifier)
(b) ..\Q \Ix .student' (x) (s ') Q(..\p 3y.mark'(y) (s " ) 1\ p = ..\s. student'(x) (s) 1\ mark'(y) (s) 1\ get'(x, y) (s)) -t
.
(b) ..\ Q32x. student'(x}(s') 1\ Q(..\p3y.mark' (y) (s " ) 1\ p :-- ..\s. student' (x) (s) 1\ mark' (y) (s) 1\ get' (x, y) (s) )
de re de dicto
In orc!_er to distinguish and readings, properties that model N semantics are assigned a situation or possible world readings, the binding of this parameter is parameter, too. (For left open, I assume here some kind of contextual binding along the lines envisaged in En� 1 986). Consequently, relations that denote properties like being a student must carry a situation feature SA ('situation argument'), too. This calls for a slight adaption of the translation rule · TL2 for modification structures. The situation arguments of the main relations of the modifiers and of the modified constituent must be identical. However, in the case of underspecified modification, this condition cannot be anticipated in the semantic construction. Hence, TL2 must coindex . the situation arguments of these main relations. (ph) and (3 3 b) are merely lifted versions of the standard KP analyses, the set of sets of sets of propositions of the type 'it is raining' and 'x is coming' (x, a person), respectively. The difference between (34b) and (3 5h) is that in the reading the semantics of the N constituents within the wh,.phrases appear twice, once as the restriction over the elements of the
de re
de dicto
proposition set, and once more inside these propositions to express their
dicto
de
character. For quantifying into wh-questions, the complex types are indispensable: (36b) denotes the set of sets Q' . Each member of Q' comprises for every student x the set of propositions of the type 'student x gets mark y'. This
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(37) (a) Which mark do two students get? (wide scope of the non-wh quantifier)
6o Wh-questions in Underspecified Minimal Recursion Semantics
entails that Q' is a singleton set. Compare this representation to the one of (3 5 a): The difference here is that for (3sb), the member of the resulting singleton set has only one element, the set of propositions of the type 'student x gets mark y'. This models the difference between (3 sa) and (36a), as noted by Higginbotham. Finally, (37b) stands for the set of sets Q ". Every member of Q " comprises for two students one set of propositions each. These propositions are of the type 'student x gets mark y'. '32' is merely an abbreviation: 32x.P(x) � 3y3z.y =/= z 1\ P(y) 1\ P(z) .
The analysis of wh-questions in UMRS is presented in four parts: After a short outline of the syntactic analysis of wh-questions that is assumed in this paper, I will discuss the representation of the interrogative operator in UMRS. Next come some comments on the possibilities of avoiding overgeneration in the underspecified treatment of ambiguity in UMRS. After these preliminaries, the analyses for wh-sentences are spelt out in detail.
4. 1
The underlying syntactic analysis of wh-questions
The syntactic analysis of wh-questions in the HPSG framework which is assumed in this paper was proposed by Feldhaus (1996). In this subsection, I will briefly outline the essential features of this analysis. I will presuppose a working knowledge of HPSG and refer to Pollard & Sag (1994) for a comprehensive description of the HPSG framework. The essential features of Feldhaus's (r996) analysis are: •
•
a new head-interrogative schema (HIS) licenses fronting of a wh-phrase in a sentence wh-elements interact with other phenomena (e.g. word order, intonation, other lexical information . . . ) to determine the value of a MOOD feature. This feature plays a prominent role in the HIS. The HIS is depicted in (38):
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4 THE C ONSTRUCTION O F COMPLEX WH:- Q UE STIONS IN UMRS
[SVNSEM phriU<
1 . . . , NONLOC
[
rum/oc INH I sLASH eset
]
l
Markus Egg 6 1
[ l [ u u o c A T ] M oo o [sign ] SYNSEM SYNSEM SUBCAT phrast
:...
we i
I LOC
�
eliSI
finite _ wh-mterrog
•
•
S contains a trace (in TO-BIND I SLASH) to be bound by W: co-indexing the INR I SLASH and TO-BIND I SLASH values means that the trace is bound in the HIS; coindexing the INH I SLASH and the LOCAL value of W says that this LOCAL value binds the trace of S. The sentence mood of S must allow the fronting of a wh-phrase. This is for S. S may contain additional encoded in the MOOD value wh-phrases in situ. W cannot be a finite sentence (though pied piping is covered in this schema, see below). There may be only one wh-phrase in sentence initial position: The mother node in the HIS must have an empty INH I SLASH value, which prevents recursive application of the schema. (This condition is lang�age-specific.)
wh-inter og
•
•
This schema is based on a detailed account of how the MOOD value of a sencence is derived. In this derivation, various phenomena interact (for details, see Feldhaus I 996, 99f£). The presence of a wh-element somewhere within a constituent leads to a MOOD value of type for the whole constituent. This allows has the MOOD value since for pied piping: e.g. the MOOD value of is assigned this value lexically. Based on this mood determination ·one can also express the · condition that wh-phrases must be licensed by a sentence-initial wh-phrase. And, finally, the MOOD value also opens an easy way of expressing selection restrictions of sentence-embedding verbs. Yes/no-questions and wh-questions include in their semantics the same interrogative operator. I assume that, for wh-questions, this interrogative
wh-in whinictehrpaograktive which
wh-inter ogative, in situ
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In prose: a wh-phrase W and a saturated sentence S (verb with an empty SUBCAT list) form a sentence, if the following conditions are met:
62 Wh-questions in Underspecified Minimal Recursion Semantics
4.2
The interrogative operator in
UMRS
The interrogative operator is represented in UMRS as a list of three relations qi_rel, q2_rel, and q3_rel that are only loosely connected (the BV value (1] of qi_ref is the INST value of q2_re/, the BV value of [1) of q2_ref and the INST value of q3_rel are coindexed, too). These indices correspond to the set of sets of proposition sets ([1]), and to the proposition set ([1)) that play a prominent role in the PC analysis of wh-questions introduced in section 3· The three relations are scopally underspecified operators, hence, they have an AN_ARG feature whose value is not yet fixed. (In (39), I omitted the features HOUT and HNON.)
(39)
q l_rel HANDEL INST
OJ
0 0 HD_ARG nwh_JJ [2] BV
q2_rel HANDEL nwh_JJ I]J INST 0
q3_rel HANDEL wh rn INST [2]
HD_ARG
HD_ARG nwh_Jr �
BV
[2]
wh [i]
BV
�
The relations q i_rel, q2_rel, and q3_rel together represent the semantics of the interrogative operator. Semantic construction integrates these relations into larger semantic representations. In the representations of fully specified wh-sentences, all wh-phrases must have scope between q2_rel and q3_rel. Therefore, the HD_ARG value of q2_rel is not yet specified. It can be co-indexed only with the HANDEL value of a wh-element, if there are any, or else with the HANDEL value of q3_rel. Similarly, the position between
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operator is the semantic contribution of the HIS. I follow Copestake, Flickinger, & Sag ( 1997) here in that the semantic contribution of a phrase is interpreted as the union of the contributions of the daughters, and of the mother. This approach assumes only one interrogative operator per sentence no matter how many wh-phrases there are in the sentence. No further machinery is needed for the syntax-semantics interface of wh-questions. Note in particular that the integration of the semantics of the fronted wh-phrase into the semantics of the whole sentence takes place in the construction of the head daughter of the HIS and is passed on to the fronted wh-element via the coindexation of its LOCAL feature with the trace in the head daughter. Thus, Feldhaus's head-interrogative schema lays the syntactic ground work for an interface between syntax and semantics that allows an analysis of wh-questions in terms of one single syntactic structure with an invariant semantic interpretation for all types of syntactic nodes.
Markus Egg 63
and can only be filled by NPs that are quantified into the question, if there are any. This is secured by the types of the HANDEL and HD_ARG value of the three relations, an issue to which I will turn in section 4·3 below. For the re.mainder of this subsection, the types of HANDEL . and HD_ARG values can be ignored. Such a representation in UMRS exploits its flexibility in introducing and combining semantic material. This kind of representation is more flexible than e.g. an attempt to describe the interrogative operator directly in an extension of a predicate calculus: there, semantic lexical entries are indivisible and allow no other material to intervene during semantic construction. Thus, UMRS yields a simple semantics even for the complex wh-question cases. The translation of the three relations is spelt out in (4o). The complexity of the types of the translations is necessitated by quantifying into questions. But, nevertheless, the semantic representations of the relations are very simple. In the translations in (4o), I use the indices of (39) to show the parallels between the UMRS decomposition and the PC translation.
qi_rel p_rel
[[qq2i__rreeil]] [q3_rel]
=
t t t ) ) , ) , ( s, tit) ,rta)ining? rain
between the parts of the interrogative operator. Hence, the translation of (with INST value (ID, which means these relations plus a relation for that its translation is rain'(s8 )) gives the desired semantics, viz., the set of sets of the set of propositions of the type 'it is raining'. Recall that in the translation of an UMRS function -argument structure the function triggers .-\-abstraction over the value of its BV feature for the translation of its argument: = q (.Xss . rain'(ss)))))) ain .-\sg .r '(s8 ))
(41) .-\Q.Q(.-\Qz (.XP.Q2 (P) ( .-\p7 ( .Xq =
.-\Qz .Qz ( .Xp7 . p7
=
As an illustration of the interaction o f the parts of the interrogative operator semantics with the semantics of wh-elements, consider the reading of (3 3 a). I omit the typings of the HANDEL and HD_ARG values:
de re
(42)
(
,, _.
HAHDEL
INJT IV
HD_ARG
[2] 0 0 G
f2_rtl
HD_AlC
0 0 0 0
f3_rtl
IIAHDEL INST
av
HD_ARC
wlt_nl
0 0 B 0 0 usn G G 0 HANDEL IV
.
HD_AlG
I
[� · I HANDEL INST
G G
C4mt_rtl HANDEL I
ARG
0)
0 B
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t ) , t ) , ·t ) , t )
.-\Q2 .Q2 (argument and range of type ( ( ( ( s, = .-\P.Q2 (P) (type ( ( ( s, (b) (c) = .Xq.p7 = q (type For simple yes-no questions like Is no material intervenes
(4o) (a)
64 Wh-questions in Underspecified Minimal Recursion Semantics
whco_mree_l rel,
q2_rel q3_rel,
If we assume that has scope between and and that has highest and narrowest scope (c£ section 4·3 to see how this is achieved), (42) translates as the set of sets of the sets of propositions of the type 'x, 2 is coming' (x, 2 , a person):
qi_rel
(43) .AQ2 .Q2 {.Ap7 3 x ,2.person'(x,2) l\ p7
=
ASg . come' {xl2)(ss ))
In .the following, I will employ a two-dimensional notation of feature structures. E.g. (42) would be written as follows:
3
wh{HI I , BV12, RI4, HAI 3 ), person{H14, come(H9, I8, A12))
h2),
In this section, I have introduced the semantics of the interrogative operator. It consists of three only loosely connected relations. This allows NPs that are quantified into wh-sentences and wh-elements to interact scopally with the parts of this interrogative operator. 4· 3
Constraining structural semantic ambiguities in
UMRS
The question of how to constrain potential ambiguities and how to derive and constrain the readings within wh-questions has been postponed until now. I will show that both these tasks can be handled by and values. the typing of UMRS represents operator scope ambiguities by listing for each operator its potential immediate arguments. These lists depend on the value of the top node of a scope domain, which is coindexed with every operator relation's value within this domain (see section Thus, all operators of a domain have nearly the same list of potential arguments: their value minus their value. Thus, as presented so far, this approach would overgenerate considerably, even if some unwanted structures (e.g. cyclic function-argument chains) are ruled out by the translation rule TL3 for UMRS structures.' 3 This problem affects UMRS representations of wh-questions, too: The desired readings of these UMRS structures should respect an ordering in the main- FA chain ('<' abbreviates 'has immediate scope over'):
de dicto/de re HANDEL HD_ARG ROUT ROUT HANDEL qi_rel
HINHOUT I ROUT 2.2).
q2q3_r_elrel HANDEL qi_rel ROUT
< quantifiers (from quantified in NPs) < wh-representation, < . . . < wh-representationn < other material of the sentence
< <
But, so far, very little has been done to enforce this ordering. The only possibility is not to put the value of on the list, which
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(44) ( q i {HI , l2 , BV2, HA10) , q2{H3 , 12, BV7 , HA4) , q (H 5 , I7, BV8 , HA6 ) ,
Markus Egg 65
ensures that it must receive widest scope within a wh-sentence. Apart from this move, one can merely mark and and the relations for wh-elements and quantifiers indiscriminately as potential arguments within values on to the domain-specific list their domain (by putting their of potential arguments via the lexical value). This allows other, unwanted orderings, e.g. one in which outscopes wh-elements. The solution is to appropriately type the and values of the involved relations. This technique allows restricting the combinatory potential of scope bearing elements and, what is more, it can also be used for readings of wh-phrases the derivation (and constraining) of and quantifiers.
q2_rel qJ_rel HANDEL IDNHOUTJ HIN q3HANDE_relL HD_ARG de re vs. de dicta
Scope relations for wh-phrases and quantifiers in wh-questions
The mechanism of typing and values of relations is exploited in the UMRS account of wh-questions to guide the scope relations for wh-phrases and quantifiers. Recall that the compatibility of the value of an operator relation and of the value of its immediate argument relation is enforced for . scopally underspecified operators and their arguments in the third condition of the translation rule 1L3• In the process of translating UMRS structures with scope ambiguities, relations are selected for translation one after the other. The order of these choices determines one of the scope possibilities included in the underspecified representation. Following 1L3, each relation chosen for translation must have a value that matches the relevant type restriction (if there is any). And, if an operator relation is chosen and its value carries a type restriction, this becomes the new relevant type restriction. That is, every chosen value whose type is compatible with the relation must have a value of the operator relation that becomes its type of the immediate function by being chosen for translation immediately before. Reconsider the semantics of the interrogative operator (only relevant types are shown, see appendix B for the full type hierarchy of values):
HANDEL HD_ARG
HD_ARG
HANDEL
HANDEL
HD_ARG
HD_ARG HANDEL
(45 ) ( q r ( H r , I2 , BV2 , HA9nwh ), q2 (H3 nwh ' 12 , BV7, HA4wh ), q 3 ( H5 wh ' I7 , BV8 , HA6nwh ) )
HANDEL wh_hanHANDEdeHD_ARG l, L nwhHD_ARG _handep_rl, el
Here there are a number o f typings of involve two incompatible subtypes type. The former type appears as the
handel
and values. They and of a general value of and the
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4- 3 - 1
66 Wh-questions in Underspecified Minimal Recursion Semantics
q2_rel < wh-representation 1 < . . . < wh-representationn < q3_rel Consider again the UMRS analysis (46) [= (44)] of the simple wh-question (3 J a). Only relevant typings are shown: ( qr (Hr , 12, BV2, HA10nwh ) , q2 (H 3 nwh l 12, BV7, HA4wh) , q 3 (H5 wh ' I7 , BV8 , HA6nwh ) ,
wh(HI I wh ' BV1 2 , R14, HA1 3 wh) , person(Hr4, I 1 2 ) , come(H9nwh , I8 , Ar 2) )
Potential scope arguments are listed in the HOUT value ((ll , rn , (2] , [IT] ) . Due to the typing o f the HD_ARG value of wh_rel, its only potential argument is q J_rel (the sole other relation with a HANDEL vafue of type wh_handel in HoUT). But then, q2_rel must have wh_:_rel as argument, with qr_rel being the top and come_rel, the bottom element in the FA chain. Thus, the typing of HANDEL and HD_ARG values models that (46) is scopally unambiguous. To express the same constraint on the ordering of the parts of the interrogative operator and the wh-relations in terms of the subordination relation ':S' as used e.g. in UDRT (where subordination is not necessarily immediate), two conditions are needed: q2 ::; X and X ::; q3 for any wh relation X. However, the compositional derivation of the second condition seems problematic: If we assume that the preposed wh-phrase, the question operator, and a sentence with a trace are the syntactic building blocks of wh-sentences, how can the semantic composition extract from the semantic information that is associated with these building blocks exactly those parts that enter into this scope interaction? This problem does not show up in UMRS where the scope relations need not be determined in the process of composition but are predetermined lexically by typing HANDEL and HD_ARG values of the scopally interacting relations. In this respect, the UMRS
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HANDEL value of q3_rel, the latter type, as the HD_ARG value of qr_rel and q 3_rel and the HANDEL value of q2_rel. If in addition all wh-elements have HANDEL and HD_ARG values of type wh_handel while all HANDEL and HD_ARG values of non-wh-elements like verbs and quantifiers are of type nwh_handel, wh-relations must and nothing else can take scope in between q2_rel and q3_rel. This typing blocks unwanted orderings in the main FA chain of the UMRS representation of wh-sentences. E.g. it rules out that a wh-element (whose relation has a HD_ARG value of type wh_handel) takes as its argument the main verb of a wh-sentence (which is represented by a relation with a HANDEL value of the type nwh_handel). In short, the following part of the main FA chain in wh-questions is fixed by this simple typing:
Markus Egg 67
representation has an advantage over the representation ofscope relations in terms of the subordination relation ·�·. In a similar fashion, the scope possibilities for quantifiers in wh-sentences can be controlled. E.g., the structure (47) is the UMRS analysis of (36a). Again, only relevant typings are shown: mark(H9, 18) , (47) ( qi (HI , I2, BV2, HA2o,wh ) , q2(H3 nwh ' 12, BV4, HA2I wh ) , forall(HIOnwh' BVI I , R12, HA24nwh ) , q3 (H5 wh' I4, BV6 , HA22n wh ) , student(HI2, I I I ) , wh(H7wh ' BV8 , R9, HA23wh ) , get(HI 3 nwh ' 16, A, I I , A28 )) Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
As sentence (36a) is ambiguous between a standard wh-question and a list reading one would expect (47) to comprise two different main FA chains. This prediction is borne out. The HOUT list of every scope-bearing relation's HANDEL value in (47) is (Q] , [i] , [l] , ITQJ , ffi] ). Again, the typing of the HANDEL and HD_ARG values ensures that the only possible argument of wh_rel is q3_rel and that wh_rel is the immediate argument of q2_rel. This brings the HOUT list of the remaining scope-bearing relations down tO ( Q] , ITQJ , ffi]) . For forall_rel, this shortened HOUT list comprises the two linguistically attested scope possibilities, which are compatible with the typings of the HANDEL and HD_ARG values: It may have get_rel or q2_rel as argument. In either case, the remaining scope relations (qi_rel < q2_rel, q3_rel < forall_rel, and q i_rel < Jorall_rel, q3_rel < get_rel, respectively) follow directly. This illustrates how UMRS represents quantifying into wh questions without overgeneration. The basic technique for modelling the ambiguity of (36a) is to leave underspecified the scope position of a quantifier relation. This allows the use of standard syntax and syntax-semantics interface rules instead of special ones. What is more, it is the very same technique that was used for the derivation of standard quantifying in cases like Every man loves a woman in section 2.2. The fact that one single technique can account for both phenomena agrees with subsuming them both under the heading of quantifying in. This might answer Chierchia's (I993) worry that the operation that combines quantifier NPs with wh sentences is too different from standard quantifying in to be subsumed under this heading, too. I conclude this section with some remarks on how quantifying into yes/ no questions could be ruled out in the proposed analysis. The schema that licenses yes/no questions syntactically would contribute the same semantics (39) as the schema that licenses wh-questions. But in the case of yes/no questions, the HD-ARG value of q i_rel would be restricted to the HANDEL
68 Wh-quesrions in Underspecified Minimal Recursion Semantics
value of qz_rel, which bars quantifying in, since the scope position for quantified in relations is no longer available. In sum, subtyping the HANDEL and HD_ARG values makes it possible to reduce the range of readings for underspecified UMRS structures to avoid overgeneration of inappropriate readings of wh-sentences. 4· 3 .2
De re and de dicto
readings
• •
typing HANDEL and HD_ARG values (like in the case of wh-expressions) an appropriateness condition on feature structures that allows a local type inference on feature values
The proposed solution is based on a quantifying in analysis. The technique that is used to derive the de dicto/de re ambiguity turns on the UMRS flexibility in underspecifying the composition of the semantic representation of a sentence. This flexibility overcomes the fundamental problem of deriving de dicto readings in a KP-like approach to wh-question semantics.
Distribution of de re and de dicto readings. To guide the distribution of de re and de dicto readings, the basic idea is to introduce a cross-classification of quantifier relations. De dicto readings are modelled by a special subtype of quantifier relations that allows for a more flexible relation between the semantics of a determiner and the semantics of its syntactic N sister. De re readings, on the other hand, need no further semantic machinery, they can be expressed in the usual way, viz., by co-indexing the RESTR value of the determiner relation wit_!! the HANDEL value of the relation that represents the associated N semantics. '4 Formally, apart from the standard distinction of different kinds of quantifiers there is another, exhaustive partition of quantifier relations into the two incompatible subtypes quant_dr_rei (which is involved in de re readings, this type corresponds roughly to the quantifier relation as assumed so far) and quant_dd_rel (which appears in de dicto readings). See appendix B for a comprehensive view of the resulting (cross-classifying) hierarchies of quantifier relations and HANDEL values. As an example, consider the two subtypes offorall_rel (slightly simplified): 4· J.2. I
.
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The last step in the derivation of the desired readings is the distinction between the de re and de dicto readings. Recall that the phenomenon had two aspects: Wh-phrases may be read de re or de dicto, and quantifiers that are quantified into questions are read de dicto. This phenomenon is handled by a combination of two mechanisms:
Markus Egg 69
{48)
forall_dr_rei HANDEL
nwh_dr
BV
rn rn
RESTR HD_ARG
nwh_J,
m
forall_dd_rel HANDEL BV
[±I
D_RESTR HD_ARG
nwh_dd
rn rn nwh_JJ
[D
!II
(49)
( q i (HI , l2 , BV2, HA2onwh Jd) , q2 ( H 3nwh dJ • 12, BV4, fiA2 Iwh ) , q 3 (Hswh,l4, BV6 , HA22nwh_J, ) , wh(H7wh • BV8 , PA9, HA2 3 wh ) ,
mark(H9, 18) , forall(Hionwh • BVu , PA12, HA24nwh ) , student(HI2, h 1 ) , get(H 1 3nwh_dr • 16 , A , I I , A2 8 ) )
Crucial are the types of the HANDEL and HD_ARG values in this structure. The HD_ARG value of q i_rel and the HANDEL value of q2_rel are typed dd_handel. This is one prerequisite for expressing that a quantifier relation that takes scope between them must be understood de dicto: if the quantifier relation is the immediate argument of qi_rel, its HANDEL value must. be of the type dd_handel as well (due to 'IL3). This in turn triggers a local type inference on the basis of the condition that only subtypes of quantifier_dd_rei have this HANDEL value. The inference enforces a specifi cation of the quantifier relation to the one of its subtypes that is a subtype of quantifier_dd_rei. The scope position between q2_rel and q3_rel is not restricted in a similar way, the HD_ARG value of q2_rel and the HANDEL value of qJ_rel are neutral to the distinction dd_handel/dr_handel. That is, relations whose scope position is between q2_rel and q3_rel are not fixed with respect to the de re/de dicto distinction by obtaining this scope position. As this position is taken by the wh-relations, this models the observation that wh-expressions allow either a de re or a de dicto reading. The HD_ARG value of q3_rel as well as the HANDEL and HD_ARG values of all other relations in the lexicon must be typed dr_handel.
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The distinction between the subtypes of quantifier relations is twofold: first, they are distinguished by the types of their HANDEL and HD_ARG values (dd_handel and dr_handel, respectively, again a partition of the general handel type), second, they show different specifications {RESTR and D_RESTR, respectively) of a feature P_ARG that is coindexed with the HANDEL value of the relation that models the associated· N semantics. This distinction will be discussed in detail in section 4·3.2.2: The typing determines the distribution of de dicto and de re readings of quantifiers. I will use (49), the UMRS representation of {36a), to show how this mechanism works (only relevant types are shown).
70 Wh-questions
in Underspecified Minimal Recursion Semantics
If we now consider possible scopings in (49), we find once more that the scope relations q2_rel < wh_rel <: q3_rel are fixed. But, nevertheless, two main FA chains are possible, depending on whether theforall_rel takes scope between q 1_rel and q2_rel, or between q3_rel and get_rel. These two options model the underspecification of the scope of the NP everyone: It may be understood as quantified into the question or as a part of the core of the question. The lexical entry of the Jorall_rel is compatible with both readings. Its HANDEL and HD_ARG values are of the type (nwh_)handel, as it is underspecified with respect to the partition quantifier_dr_rei/ quantifier_dd_rei. If the first scope option is chosen, the Jorall_rel must be specified to Jorall_dd_rel. That is, whenever a quantifier is quantified into a wh-question, it must be read de dicto, which is exactly what we want. On the other hand, if the quantifier takes scope below q3_rel, it follows analogously that it is interpreted de re, because, due to TL3 and the partitioning of the type quant_rei, it must be specified to Jorall_dr_rei. This approach opens an easy way of describing the scope behaviour of determiners in the lexicon. While in principle quantifier relations would be unspecified w.r.t. the quant_dd_rel and the quant_dr_rei partition (which means that their scope behaviour within wh-questions is not restricted), more specific typing is possible to indicate restrictions in the scoping behaviour within wh-questions. For instance, Groenendijk & Stokhof's {1984) observation that downward monotone quantifiers strongly disallow quantifying into wh-questions could be modelled by typing them lexically as quant_dr_rel, which makes it impossible for them to take scope between qi_rel and q2_rel. Similarly, lexeme-specific restrictions on the de re/de dicto distinction could be expressed. E.g. if NP wh�expressions like who and what, whose restriction ('person' and 'thing', respectively) is not given in terms of an explicit N constituent, have only de re readings, this could easily be modelled in our approach by lexically typing them as quant_dr_rel, while it would be difficult to express this restriction in an approach like the one of GS which treats the de dicto readings of wh-elements as basic. .
4.3.2.2 Representation and interpretation of de re and de dicto readings. The second distinction between the two classes of quantifiers
that is modelled by the partition of quant_rel into quant_dd_rel and q_uant_dr_rei concerns the relation between a quantifier and its associated N semantics. So far, I have assumed that quantifier relations have a feature RESTR whose value is coindexed with the HANDEL value of the relation that models the associated N semantics. This is a function-argument relation that is processed in the recursive procedure of translating UMRS structures.
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·
Markus Egg 7 1
The existence of de re and de dicto readings of NPs, however, shows that this analysis covers only the de re interpretation of NPs. Hence, a more general representation of quantifiers is called for, in order to express the observation that quantifiers may be related semantically to their associated N semantics in various ways. To this aim, I assume an underspecified relation that models all kinds of quantifiers. The difference to the quantifier relations as assumed so far, however, is that instead of a RESTR feature it has a P_ARG feature. The schematic UMRS representation of the semantics of NPs looks like this: ( s o)
[
"'''_rei ITJ rn , HANDEL ..._,, INST [}] rn 1}] [±]
]
The value of the feature P_ARG in the quantifier relation is coindexed with the HANDEL value of the relation restr_rei, which stands for the associated N semantics, and whose INST value is coindexed with the Bv value of the quantifier. Since the P_ARG value indicates the relation that represents the restriction for the quantifier relation, the translation of this relation must be assumed as the restriction of the quantifier in the translation of l,JMRS structures like (so). However, it is not yet determined whether this relation is to be taken as an argument of the quantifier relation at the UMRS level or not. This interpretation of the P_ARG value overcomes the problem noted for examples like (1 8 ) and (19), because it applies only to the semantic contributions of restrictions of wh-elements, which hence distinguishes them from the semantic contributions of constituents that belong to the core of a wh-question even if such a constituent has the same semantic representation as the restriction of a wh-element. . Partitioning this quant_rei type into quant dd_rei and quant dr_rei leads not only to a mcire restrictive typing of the HANDEL and HD_ARG values, but also to a specification of the P_ARG feature. For quant_dr_rel, it becomes the RESTR feature, which indicates a function-argument relationship between a quantifier and its associated N semantics, as has been assumed so far. In the case of quant_dd_rel, the P_ARG feature is specified to the feature D_RESTR (for 'domain restriction'). This feature models the loose relation between a quantifier and its associated N semantics in a de dicto reading, but does not indicate a function-argument relation between quantifier and associated N semantics on the UMRS level. _
_
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quant_rel HANDEL BV P ARG HD_ARG
72
Wh-questions in Underspecified Minimal Recursion Semantics
(5 I)
quant_dd�rtl HANDEL BV
HOUT D_RESTR HO_ARG
IIJ 0 [II JJ
nwh_J,
JJ
0
,
[TI & member{[I})
[
restr
rtl
HANDEL
nwh_J,
INST
0
[TI & member{[Ij)
l
In the examples given in this paper, the ROUT list always comprises only one HANDEL value of type nwh_dr_handel (the HANDEL value of the main verb). Hence, we need not bother with the determination of underspecified modifier attachment in this paper.
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This procedure begs two questions: First, how can a relation R that models the associated N semantics of a quantifier but is no argument of the quantifier at the UMRS level be integrated into the UMRS structure? In order to get a well-formed, translatable structure, one must establish a dependence between R and some element of the main FA chain. Second, how can R be introduced in the core of the question (in UMRS terms, below the q3_rel ) to express the de dicta character of the NP? The answer to both problems is to interpret the relation R as a modifier. This means that it is conjoined to another relation. This other relation must belong to the core of the question. Technically speaking, one must coindex the HANDEL value of the relation R with the HANDEL value of a suitable relation below q 3_rel. The technical apparatus for this procedure is available in UMRS, because it can also handle cases of modifier attachment ambiguities in an under specified way. In this section, I will introduce as much of this apparatus as necessary and refer the reader to Egg & Lebeth (I995) for the fully worked out treatment of modifier attachment ambiguities. This analysis uses the HOUT list of (HANDEL values of) potential arguments that is the basis for scope underspecification in UMRS for underspecifica tion of modifier attachment, too. Modifiers can be underspecified with respect to their attachment site by leaving open their HANDEL values but constraining them to be a member of the ROUT list. In the relations that stand for quantifier expressions, the value [!!] of the feature ROUT lists the potential arguments for scope-bearing operations; We state that quant_dd_rel specifies its D_RESTR value as an element of[!!] . If we in addition specify the type of the D_RESTR value as nwh_dr, this means that the HANDEL value of the relation of the associated N semantics must be coindexed with the HANDEL value of a relation that takes scope below q3_rel, as desired. (5 I) is the schematic representation of the semantics of the de dicta reading of an NP:
Markus Egg 7 3
Before turning to the detailed examples of UMRS analyses of wh questions, I will briefly recapitulate the main features of the proposed analysis. •
•
•
•
In sum, the UMRS approach allows for a transparent analysis of the semantiCs of wh-questions that captures ambiguities by underspecification and needs only a simple syntax-semantics interface. This illustrates my claim that such an approach considerably reduces the complexity of linguistic analyses.
5 ANALYSES O F WH- SENTE NCES I N UMRS
.
In this section, I give detailed examples for the UMRS analysis of whquestions. After a de dicta reading for the wh-phrase in a simple wh-question I present a multiple wh-sentence and, finally, an analysis for a wh-sentence with a quantifying in reading. The first example is the sentence (5 2) :
(52) Which student is coming? Its UMRS representation is the following. I have already assumed that the subtype of the wh-relation is chosen that models de dicta readings: (5 3) ( q i (H I , I2, BV2, HAJ nwh JJ ) , wh_dO(H I I wh dd , BV12, DRI Jnwh-dn HAI4wh-JJ ) , q2(H4nwh-dd ' 12, BV5 , HA6wh ) , student (H I J nwh-dr & member{16), I12, SA17) , come(H I Snwh_dn I9, A12) ) q3 (H7wh ' Is , BV9, HA1onwh J, ) ,
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•
all wh-questions are described in terms of one single syntactic structure (Feldhaus's head-interrogative schema) the ambiguities between de re and de dicta readings of wh-phrases as well as the ambiguities caused by non-wh-quantifiers in wh-sentences (quantifying in or not) can be represented in an underspecified way the similarity between wh-expressions and indefinites can be modelled like in KP's analysis by representing wh-elements in terms of existential quantification all N constituents can be treated uniformly in the syntax, i.e. they become part of an NP structure, which then is integrated into larger structures. In particular no syntactic rules for combining sentences with N constituents are necessary to derive the distinction between de dicta and de re readings quantifying into declarative sentences and into wh-sentences follows the same rules
74 Wh-questions
in Underspecified Minimal Recursion Semantics
[ (q1) ] (AQ2. [ (q2 ) ] ( Ap5 . [ ( wh_dd ) ](Ax12 . [ (q 3 ) ] ( A s9 . [ ( student, come ) ] ) ) ) ) TL2 turns [ ( student(HI S , li2 , SAI7 ) , come{HI S, I9, A1 2) ) ] into [ ( student(HI s , 112, SA9) ) ] 1\ [ ( come(H1 s , l9, A12) ) ] . Here the situation
argument of the nominal relation is identified with the one of the verb. The translation of the UMRS structure (s 3) was successful, as it managed to break down the list into singleton lists. These singletons have defined translations into object language, which respect the coindexations between re�ations in the UMRS · list:
[ (q1) ] AQ2 .Qz [ (q2 ) ] = A P.Q2 (P) [ ( wh_dd ) ] A P 3 x1 2 . student' (x12)(s .7 ) 1\ P(x12) [ (q J ) ] A q . p s = q [ ( come) ] = come' (x12) (s9) [ ( student ) ] = student' (x12 ) (s9) =
=
=
Note that the. translation of the wh_dd_rel contains the restriction of the wh-expression. This is due to the coindexation of the HANDEL value of the relation that stands for this restriction with the D_RESTR value of the wh_dd_rel. The translation of ( 5 3) is (54), the set of sets of proposition sets such that there is a student x12 and the propositions are of the type 'student x12 is coming':
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The value � of the feature HOUT in all operator relations, which comprises the HANDEL value of potential arguments, is ( [±] , [l] , IJil , [}i]). The typing of HANDEL and HD_ARG values forces the wh_dd_rel to take the q3_rel as its argument {the only other relation with a HANDEL value of type wh in HoUT). Then q2_rel can have only the wh_dd_rel as its argument. Finally, q i_rel must have widest, and come_rel, narrowest scope in order to integrate all relations into the main FA chain. The only successful application of the translation rules to (s 3) is the one in which TL3 chooses the functions in the order that corresponds to the only feasible main FA chain in this UMRS representation. In addition, student_rel must act as a modifier of a relation whose HANDEL value is on HOUT. However, the only element of the HOUT list with a suitable typed HANDEL value is the come_rel, hence, there is no underspecification of modifier attachment. Note that student_rel comprises a situation argument to allow for de dicto readings of NPs. Successive application of TL3 gives us the following structure:
Markus Egg 75
(54) .X Q2 . Qz ( .Xp5 3x l 2 .student'(x �z ) (s �7 ) A p5 .Xs9 . student' (x12 ) (s9) A come' (x12 ) (s9))
=
The second example illustrates the derivation of a multiple wh-question (read de re).
(55) Which student got which mark? q 3 (H I 7 wh , I5 , BVI 8 , HAI 9nwh_dr) , (56) ( qi (HI , 12, BV2, HA3 nwh dd ) , get( H2 onwh dr ' 1 1 8 , A1 8 , A2 I J ) , q2(H4nwh dd' 12, BV5 , HA6wh ) , wh_dr( H7wh d,, BV8 , R9, HA1 0wh J, ) , �udent( H9, I 8 , SA21 ) , wh_dr( HI2 u,:_dr BV1 3 , R 1 4:, HAISwh_J, ) , mark(H14 , I q , SA22 ) ) The value of the HOUT feature for the scope bearing expressions in this UMRS structure is ([±] , [1] , (11] , ITZJ , 1 20 I ) . Since there are two wh relations in this sentence, either one may be the immediate function for the q3_rel. In either case, the remaining wh-relation must be the function of the first one. But then q2_rel must be the immediate function ofthis second wh-relation. There is no other way of integrating the wh-relations into the main FA chain of the UMRS structure. The two scoping options noted for the wh-relations are semantically equivalent, hence, I will assume the one in which the subject has scope over the object and ignore the other one. The remaining scope relations follow directly (qi_rel < q2_rel and q3_rel < get_rel). The recursive application of TL3 must again consider the constraints on possible scope orderings as expounded in the last paragraph. The result is the following: '
Applying TL 1 to [(wh_dr , student )] and to [ (wh_dr, mark)] and translating the singleton sets of the resulting structure yields (57), the set of sets of proposition sets such that there is a student x8 and a mark x13 and the propositions are of the type 'x8 gets X1 /: .XQz . Qz ( .Xp5 3xs 3xwstudent' (xs ) (s2 1 ) A mark'(x1 J (s22 ) Ap5 = .Xs�s -get' (xs ) (x1 J (s � s ) ) The last example (5 8) involves an ambiguity . which is due to a quantifying NP in a wh-sentence. It may either take scope over the sentence, i.e. be quantified into the wh-sentence, or take scope inside the core of the question. The underspecified UMRS representation that comprises these two readings is given in (59).
(58) Which mark did every student get?
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[ ( q1 ) ] ( .X Q2 . [ ( q2 ) ] ( .Xp5 . [ ( wh_dr , student ) ] ( .Xx8 . [ (wh_dr, mark)] ( .Xxw [ ( q3 ) ] ( .Xs�s - [ ( get ) ] ) ) ) )
76 Wh-questions in Underspecified Minimal Recursion Semantics
---+
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(59) ( q 1 (H I , 12, BV2, HA3 nwh dd ) , q 3 (H17wh ' I s , BV1 8 , HAI9nwh_J, ) , q2 (H4nwh dd • 12, BVs , HA6wh ) , get(H2onwh-dr ' 1 1 8 , A 1 8 , A2 I J ) , forall ( H7�wh • BV8 , PA9, HAwnwh ) , student(H9nwh dr ' 18, SA2 1 ), wh_dd(H1 2wh�dd • BV1 3 , DRI4 nwh_dr & member( I I ), HA1 5 wh_dd ) , mark(H1 4nwh dr & member(u), h 3 , SA22) ) The value of the ROUT feature [ill for the scope bearing expressions in the UMRS structure (59) is (GJ , Il] , [TI] , [ITJ , I 201). By the same reasoning as for the other examples, it follows that the order q2_rel < wh_dd_rel < q3_rel must be part of any main FA chain from the set of readings described in (59). For the forall_rel, thus, the list of HANDEL values of available arguments is ([i], 1 20 I). That is, we have a choice. The relation may either take scope directly over the get_rel (inside the core of the question), or it may take scope between q i_rel and q2_rel (which models quantifying into the question). However, the typing of the HANDEL and HD_ARG values of the other relations leads in either case to a specification of the forall_rel: In the first case, it is specified to 'forall_dr(H7nwh_d, BV8 , R9, HAwnwh_dr)'; in the latter case, to 'forall_dd(H7nwh dd • BV8 , DR9nwh dr & member( I I), HAIOnwh JJ ) '. This models the observation that it must be understood de dicto if iti.s quantified into the question. Thus, there are two different successful ways of recursively applying TL1 to ( s 9). In the case of direct scope offorall_rel over the verb, the result is [ (q1 ) ] ( AQ2 . [ ( q2 ) ] ( Ap5 . [ ( wh_dd ) ] ( Ax i 3 . [ ( q 3) ] ( A s1s . [ ( forall_dr, student ) ] ( A �s . [ ( mark, get ) ] ) ) ) ) ) TL 1 and TL :�. account for the remaining non-singleton lists forall_dr, student ) and ( mark, get ) , respectively. The semantic result ( then is (6o), the set of sets of proposition sets such that there is a mark x1 3 and the propositions are of the type 'every student got the mark x1 / This models the first reading of sentence (5 8): (6o) A Q2 . Q2 ( Ap5 3�1 1 . mark' (x13 ) (s22 ) t\p5 = �1s'v'xs(student' (xs ) ( s21 ) mark' (x1J (s1 s ) t\ get' (xs , X13 ) (s1s ) ) ) In the second reading of (58), we encounter quantifying into questions. Here the forall_rel has scope between qi_rel and q2_rel, which enforces its specification to forall_dd_rel. The recursive application of TL3 yields [ ( q1 ) ] ( A Q2 . [ ( forall_dd ) ] ( Axs . [ ( q2 )] ( Ap5 . [ (wh_dd ) ] ( A x i J " [ ( q 3 ) ] ( A s1 8 . [ ( student, mark, get ) ] ) ) ) )
Markus Egg 77
In this case, both determiner relations specify their associated N semantics as modifying relations, which, due to the typing of their HANDEL value (type nwh_dr), can only modify the verb relation in this reading of (s8). The semantics of_ this reading, then, is (61), the (singleton) set whose member comprises for every student x8 a proposition set such that there is a mark x1 3 and the propositions are of the type 'student x8 gets mark
xi 3 ':
(61) >. Q2'v'xs.student'(xs) (s2 1 )
�
Q2 (>.p5 3xl3 .mark'(x� 3) (s22)/\
p 5 = A S1g .student' (xs ) (s 1s ) 1\ mark' (x1 3 )(s 1s ) 1\ get' (xs , X 1 3 ) (s 1s ))
6 · CO NCLUS I O N In this paper, I have presented Underspecified Minimal Recursion Semantics (UMRS), a representation formalism that accounts for structural ambiguities in terms of underspecification. UMRS was applied to the description of wh-questions to illustrate its properties: UMRS makes possible an underspecified representation of structural ambiguities. It also allows for a rather simple semantic representation, because of its high flexibility in combining the semantic contribution of constituents that build complex syntactic constructions. Finally, the semantic construction can do with a very simple syntax-semantics interface. Acknowledgements I thank R. Blutner, A. Feldhaus, P. Ruhrberg, and two anonymous referees for valuable comments on earlier versions of this paper. MARKUS EGG
Universitiit des Saar/andes Computerlinguistik, Gebiiude D-66041 Saarbrucken Germany e-mail:
[email protected]
1 7-2
Received: 29.08.97 final version received: o 1 .04.98
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The examples in this section illustrate the UMRS analysis of wh questions. My aim was to show that UMRS allows on the basis of a fairly simple syntax-semantics interface a straightforward . analysis of wh questions and makes possible an underspecified representatipn of ambi guities in this domain.
78 Wh-questions in Underspecified Minimal Recursion Semantics
A QUESTI O N S AND ANSWERS I n this section, I propose a definition o f the relation between questions and answers. This proposal is merely an integration of the insights of the approaches ofHM and Groenendijk & Stokhof (1984) with the analysis of questions in terms of KP answer sets: while the KP analysis of questions as sets of propositions (modulo type raising, which was necessitated by quantifying into questions) is retained, the notion of relevant answer to a question is no longer defined by this set of propositions. Like HM and GS, I assume that questions express a range of possibilities in their semantics, and. define relevant or felicitous answers to a question as those that narrow down this range of possibilities. First I assume a modified question denotation Q' that builds on top of an answer set Q (Lahiri 199 1). It comprises the conjunctions of all nonempty elements of the power set of Q: =
>..p 3p '( p '
E
p(Q)\0 1\ p = A p ')
Following HM and Groenendijk & Stokhof (1984), the semantics of a response (in the form of a proposition) is conjoined with the predicates in Q', which characterize the set of possibilities, and any resulting contradictions are removed from this set. However, the formal spellout is different, because the elements in sets as defmed in (62) are not mutually exclusive. But, still, if a response is a felicitous answer to the question, adding its semantics to the members of Q' returns a set with fewer members than Q'. The loss of elements can come about in two ways: Either the semantics of the response is incompatible with an element of Q', which means that this element is removed, or conjoining the semantics of the response to different elements of Q' yields identical results. In many cases, this procedure returns a proper subset of Q'. As an example, consider (63) [= (7)] and the answers (64} [= ( r r )] : (63) Who is coming? (64) (a) John is coming (b) At most two people are corning (c) No one is coming (d) At least two people are corning If we assume that there are three individuals a, b, and c in every possible world, the set Q' for (63) is (6 s ) (p 1 , p, , and p3 stand for 'a, b, c is coming', respectively): (6 s ) { p. , p. , p3 , p. A p., p. A pJ • P• A pJ , f• A p, A pl } If the answer is (64a), and a is the individual called john', p 1 is conjoined with all elements of Q'. The result is a subset of Q', which can be glossed as 'all the remaining possibilities are such that John is coming (possibly apart from someone else)': (66) { p. , p. 1\ p. , p. l\ p3 , p. 1\ p, A p 3 } (66) is a subset o f Q', because conjoining p 1 with every element in Q ' maps its second and fourth element on to the same result ( p 1 1\ p , ) . For (64b), the result is that adding this information to all members of Q' is incompatible with p 1 1\ p, 1\ p p which is consequently removed. Hence, the resulting set is again a proper subset of Q'. In the case of (64c), the information is incompatible with all members of Q'. Hence, the result is 0, which means that all of the possibilities are negated. For answers like (64d), the information is compatible with all members of Q'. The
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(62) Q'
Markus Egg 79 reason for this is that an element of Q' like p , only gives information about one individual in the domain but does not say anything about the oth�r individuals. This is ·different &om an exhaustive approach, in which the partitions contain information on every individual. In our example (where there are only three persons), this answer means (p , 1\ p,) V { p, l\ p 1 ) V { p , l\ p 1 ) . The resulting set is the following: (67) { ( p , 1\ p,) V ( p , l\ p 3) V ( p , l\ p, l\ p 3 ) , ( p , 1\ pz) V ( p, l\ p 3 ) V ( p , l\ p 2 1\p3 ) , ( p , A pJ V ( p. A p3 ) V ( p , l\ p 2 1\ p3 ) , p , 1\ p. , p , l\ p3 , pz l\ p3 , p , A p2 A p3 } Hence, we need an additional rule to derive the status of {64d) as an acceptable answer. This rule says that in an answer set {q , V q ., q . , q. , . . . , qn } the first member can be deleted, as all the members of the disjunction are already present in the set. Consider e.g. the first element of {67). As p , 1\ p2, p , 1\ p p and p , 1\ Pz 1\ p3 are elements of (67), too, the first element of (67) can be deleted. Similar reasoning applies to the second and the third element of (67). I.e. the resulting set Q" {6 8) is a subset of the answer set Q', which gives the desired result that {64d) is an appropriate partial answer to {63), too. ·
B THE RELAT I O N HIERARCHY This appendix summarizes the hierarchy of relations I have assumed in this paper. First, I give the hierarchy of HANDEL values, which is used to constrain the range of possible structural ambiguities ill UMRS representations. I assume a cross-classification of the opposition wh_handel and nwh_handel on one side (involved in the distinction of wh elements and non-wh-elements) and dd_handel and dr_handel (involved in distinguishing de dicto and de re readings of NPs) on the other side. Cross-classifications are indicated by dashed lines: handel
wh_handel
nwh_handel
wh_dr_handel
nwh_dr_handel
dr_handel
dd_handel
wh_dd_handel nwh_dd_handel
I assume a general relation for scope bearing constituents. Immediate subtypes of this type are the relation for qua�tifiers and the relation for operators. Quantifiers have the additional feature P_ARG. The value of P_ARG is co-indexed with the HANDEL value of a relation that models {together with any relations that are functionally dependent upon it) the semantics S of an N constituent.' 1 This coindexation expresses that the N semantics S models the restriction of the quantifier. Operators, on the other hand; introduce an INST feature. The three parts of the interrogative operators qi_rel, q2_rel, and q3_rel are subtypes of operator_rel. Other classes of operator relations represent the semantics of modal verbs, frequency adverbs, or negatiorL
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(6 8) { p , 1\ p. , p , 1\ pp pz i\ Pl • P• A p. A pj
So Wh-questions in Underspecified Minimal Recursion Semantics scope_rel
HANDEL
m m HOtrr m HNON ([]] ) HD_ARG [II BV
[
]
quant_rel
P_ARG
li]
[
operator_rei INST li]
]
[ � quanr_rtl
P_ARC H0\11'
fo
[aisu_rd ~ l[ l HD_ARC
...it
0 ������� G
wh_rd
HANDI!L
....
HD_ARC
..
1WTil
HD_ARG
HD_ARC
..w�� 0
-"
6
0 [!]
Jorall_dd_rd
wh_dr_rtl KANDEL
J
.... - -
[ �
(indif_rtl)
HANDEl
�
.._..
0
0
-'-* 0
KANDEL D_R HD_AIC
...._410 _._,.0& member( [D J ... �[!]
Two instances of cross-classified quantifiers are given in the hierarchy. The relation Jorall_dd_rel models every as it emerges in cases of quantifying in an NP with a universal quantifier into a wh-sentence (de dicto reading). On the other hand, wh_dr_rel represents which in the cases of the de re reading of which-NPs.
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For quant_rel, I assume a cross-classification (again indicated by dashed lines). Its left part introduces the different types of quantifiers, e.g. the universal quantifier or which. I assume that the indefinite article can be grouped together with which (under indef_rei), because they both involve existential quantification. The right part of the cross-classification partitions quantifier relations into those that act as functions on their associated N semantics S (hence, lead to de re readings of NPs), and those that force S to become a modifier (and which therefore yield de dicto readings of NPs):
Markus Egg 8 I
NOTES 1
•
3
s
6 7
8
9
1° Chierchia {I993) analyses quantifying
1 1
'3
••
•s
into wh-questions in terms of functions from (n-tuples of) individuals to indi viduals, too. However, he distinguishes the semantics of list readings and functional readings, hence, the fol lowing arguments against Engdahl's analysis do not apply to his approach. In the following, I will omit functional readings from consideration. For downward monotone quantifiers P, A E P entails B E P, for all B such that B � A. The analyses of Chierchia (I993) and Groenendijk & Stokhof (I984) have the additional feature that they rule out list readings for downward monotone quantifiers (like in (28)). The reason is that thei� analyses employ the notion of 'minimal witness set' (see Barwise & Cooper I98 I}. Syntactic structure may further restrict operator scope possibilities (see e.g. Aoun & Li I993, or Frey I993). This topic is outside the range of this paper, but Egg & Lebeth (I996} show a first integration of such syntactic information. I will use the statement that an N semantics and a quantifier Q are 'associated' as an abbreviation for the syntactic description that the N seman tics is the semantic contribution of the N constituent that is the syntactic sister of the determiner whose semantics is Q. If the N semantics is complex, the coindexation pertains to the HANDEL value of the relation in the N semantics on which all other relations in the N semantics are functionally dependent. To keep the presentation readable, I will in the following ignore this complexity and talk about 'the' N relation. This constituent is the syntactic sister of the determiner whose semantics is the quantifier relation.
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•
UMRS is special in that it also captures ambiguities of modifier attachment as in An appointment was scheduled in March 'In March, the scheduling of an appointment took place/An appoint ment for March was scheduled' {see Egg & Lebeth I 99S. I 996}. The name 'UMRS' should not be mis understood as implying that there is no underspecification in MRS. I assume a verb semantics with an addi tional argument position for possible worlds or 'eventualities' as in Davidson (I 967). Here and in the rest of the paper I neglect the semantics of tense and aspect. This disjointness will be presupposed in the following definitions. Translations of UMRS structures are written with double brackets ([ ] ) around them. TL3 is presented in a simplified form: I assume that operators are scopally underspecified w.r.t. their highest functional feature only and leave out of consideration the possibility of modifying scope bearing relations. See sections 4·3-I and 4.3.2 for examples of the use of such type restrictions. Immediate subordination can be expressed in terrns of the subordination relation ::=;, due to its antisymmetry. Consider for instance a relation rei that is given by 1, : rel(12). (This is the notation of Reyle I993; relations are labelled, subordination relations are expressed as relations on labels. The argument of rei is characterized by its label 12.) The fact that a relation whose label is 13 is the immediate argument of rei can be expressed by a conjunction of the two subordination relations 12 ::=; 13 and 11 ::=; 12• KP assume as the semantics of a wh question only the · set of all true asked propositions. I omit this detail. Lahiri {I99I} shows that for a subgroup of wh-questions this goal can also be obtained by mapping KP answer sets on to partitions.
82 Wh-questions in Underspecified Minimal Recursion Semantics
REFE RENCES Alshawi, H. (ed.) {I 992), The Core Language Engine, MIT Press, Cambridge, MA & London. Alshawi, H. & Crouch, R {I992), 'Monotonic semantic interpretation', in Proceedings of the 30th ACL, 3 2-9. Aoun, J. & Li, Y. {I993), Syntax of Scope,
I, I 8 I-234· Copestake, A., Flickinger, D., & Sag, I. {1997), :'Minimal recursion semantics: an introduction' CSLI, Stanford Uni versity, available under .ftp : / /ftp csli . stanf ord . edu/l inguistics/
sag/mrs . ps . gz.
Davidson, D. (r967), The logical form of action sentences', in N. Rescher {ed.), The Logic of Decision and Action, Pittsburgh University Press, Pittsburgh, 8 I-95· Egg, M. & Lebeth, K. { 1 995), 'Semantic underspecification and modifier attach-· ment ambiguities', in J. Kilbury & R Wiese (eds), Integrative Ansiitze in der Computerlinguistik (DGjS/CL'95), Dussel
dorf, I9-24. Egg, M. & Lebeth, K. (I 996), 'Semantic interpretation in HPSG', · paper pre sented at the 3rd Conference on HPSG, Marseilles, 20-22 May I 996. En\;. M. {I986), Towards a referential analysis
of
temporal
expressions',
Linguistics and Philosophy, 9, 405-26. Engdahl E. (r986), Constituent Questions: The Syntax and Semantics of Questions with Special Reference to Swedish, Reidel, Dordrecht.
Feldhaus, A. {I996), 'Fragen iiber Fragen:
Eine HPSG-Analyse ausgewiih.lter Phano mene des deutschen w-Fragesatzes', Master's thesis, Universitiit Tiibingen. Frey, W. ( 1 993), Syntaktische Bedingungen
fiir die Interpretation: Uber Bindung, implizite Argumente und Skopus, Akademie Verlag, Berlin.
& Stokhof, M. {I982),
'Semantic analysis of wh-complements', Linguistics and Philosophy, s. I 75-23 3 . Groenendijk, J. & Stokhof, M . {I984), 'Studies on the semantics of questions and the pragmatics of answers', Ph.D. thesis, University of Amsterdam. Groenendijk, J. & Stokhof, M. {I 997), 'Questions', in J. van Benthem & A. ter Meulen (eds), Handbook of Logic and
Language, Elsevier, Holland, I 0 5 5 - I I 24. Hamblin, C. {I973), 'Questions in Monta gue grammar', Foundations of Language, IO, 4 1- 5 3 · Higginbotham, J . {1997), 'The semantics of questions', in S. Lappin (ed.), The Hand book of Contemporary Semantic Theory,
Blackwell, Oxford, 3 61-8 3 . Higginbotham, J. & May, R ( 198 r ), 'Ques tions, quantifiers, and crossing', Linguistic Review, I, 4 I -80. Hobbs, J. & Shieber, S. {I 987), 'An algo rithm for generating quantifier scoping', Computational Linguistics, I 3 , 47-63. Karttunen, L. {I 977), 'Syntax and semantic of questions', Linguistics and Philosophy, I , 3-44· Karttunen, L. & Peters, S. (r98o), 'Inter rogative quantifiers', in C. Rohrer (ed.), Time, Tense, and Quantifiers, Niemeyer, Tiibingen, I 8 r-205. Lahiri, U. {1991), 'Embedded interrogatives and predicates that embed them'. Ph.D. thesis, MIT. Pinkal, M. (I 996), 'Radical underspecifi cation', in P. Dekker & M. Stokhof (eds), Proceedings of the 1oth Amsterdam Colloquium, Amsterdam, 587-606, ILLC. Pollard, C. & Sag, I. {I 994), Head-driven Phrase Structure Grammar, CSLI and Uni versity of Chicago Press. Reyle, U. {I 99 3 ), 'Dealing with ambiguities by underspecification: construction,
representation, and deduction', journal IO, I 23-79· Zimmermann, T. { I 9 8 5 ), 'Remarks on Groenendijk and Stokhof's theory of
of Semantics,
indirect questions', 43 I -48.
sophy, 8,
Linguistics and Philo
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
MIT Press, Cambridge. Barwise, J. & Cooper, R {I98 I), 'General ized quantifiers and natural language', Linguistics and Philosophy, 4, I 59-2I9. Chierchia, G. { 1 993), 'Questions with quantifiers', Natural Language Semantics,
Groenendijk, J.
Journal oJSnnantia
15: 8]- 1 13
© Oxford University Press
1998
Bridg ing N I C H OLAS ASHER
University of Texas at Austin ALEX LAS CARIDES
University of Edinburgh Abstract
I
INTRODUCTION
We aim to offer a formal model of bridging. We take bridging to be an inference that two objects or events that are introduced in a text are related in a particular way that isn't explicitly stated, and yet the relation is an . essential part of the content of the text in the sense that without this information, the lack of connection between the sentences would make the text incoherent. Examples ofbridging are illustrated in texts (I-4):
( I ) I met two interesting people last night at a party.
The woman was a member of Clinton's Cabinet. (2) In the group there was one person missing. It was Mary who left. (3) John partied all night yesterday. He's going to get drunk again today. (4) Jack was going to commit suicide. He got a rope. In ( I ), the woman generates the presupposition that there's a unique salient worrian in the context. The context doesn't supply one explicitly. However, the hearer draws the implicature that the woman is one of the two people the speaker met last night, and therefore, to guarantee the uniqueness of this antecedent, the other person must have been a �aiL In fact, without this inference the text would be incoherent, because there would be no
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In this paper, we offer a novel analysis of bridging, paying particular attention to defmite descriptions. We argue that extant theories don't do justice to the way different knowledge resources interact. In line with Hobbs (1979), we claim that the rhetorical connections between the propositions introduced in the text play an important part. But our work is distinct from his in that we model how this source of information interacts with compositional and lexical semantics. We formalize bridging in a framework known as SDRT (Asher 1993). We demonstrate that this provides a richer, more accurate interpretation of definite descriptions than has been offered so far.
84
Bridging
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connection between the objects or events described in the two sentences. So this implicature is a bridging inference. While work on bridging inferences has typically concentrated on definite descriptions (e.g. Poesio 1994; Poesio, Vieira, & Teufel 1997), other presupposition triggers generate bridging inferences too (Clark, 1977). For example, the it-cleft in (2) conveys the presupposition someone left. The hearer draws an implicature that the person missing from the group left, and, indeed, Mary is that person. This inference is a bridging inference, since (2) would be incoherent without it: there would be no connection between the events or the objects. In (3), the presupposition triggered by again is that John got drunk before today. A bridging inference occurs here too: one infers that this previous occurrence of getting drunk is concurrent with the event of partying mentioned in the first sentence. Without this inference, one cannot compute how the events are connected, resulting in incoherence. Karttunen (1974), Heim (1983, 1992), and van der Sandt (1992) have developed accounts of how presuppositions are satisfied in context. But these theories don't handle bridging, and so they don't explain the relevant inferences for (1-3). Indeed, it won't be possible to model all cases of bridging by refining presupposition satisfaction, because bridging occurs in the absence of presupposition triggers (Clark 1977). Consider the example (4) taken from Charniak (1983). Here, there is an inference connected with the indefinite description a rope: one infers that it is to be used in the suicide. Without this link; there is no connection between the contents of the sentences, leading to text incoherence. As such, it's a bridging inference. And yet since it occurs in the absence of presupposition triggers, it can't be explained in terms of presupposition satisfaction. In this paper, we will provide a formal theory of bridging based on the conjecture that it is a byproduct of discourse interpretation. In particular, bridging is part of the task of computing rhetorical connections between propositions introduced in a discourse. For example in (4), information conveyed by the second sentence is computed to be an elaboration of the information given by the first sentence. Part of this computation involves the inference that getting a rope is part of the plan to commit suicide: the rope is the intended instrument. A similar inference is involved with (2): the information in the second sentence serves to elaborate the first, and computing this involves inferring that Mary is the member of the group that's missing. Our theory will be specified in a formal representation of discourse semantics known as SDRT (Asher 1993), which incorporates rhetorical relations. An accompanying formal theory of pragmatics known as DICE (Lascarides & Asher 1 993) models how the construction of this discourse
Nicholas Asher and Alex Lascarides 8 5
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semantics is influenced by a wide variety of information. By mixing these ingredients, we hope to furnish a richer theory of bridging than has been attempted so far, where domain knowledge, compositional semantics, lexical semantics, and rhetorical relations all play a central role. This conjecture that bridging is a byproduct of discourse interpretation isn't new. Hobbs (1979), Hobbs et al. (1993), and Sperber & Wilson (1986) also propose this. But we approach discourse interpretation differently. Bridging for Hobbs et al. and Sperber & Wilson is part and parcel of figuring out the intended message or full understanding of the message. They equate the semantics of discourse with the task of integrating the clause that's currently being processed with the interpreter's beliefs. For Hobbs et al. (1993), this integration is a matter of abduction, whereas for Sperber & Wilson (1986) it is a matter of relevance. . We approach discourse interpretation differently. For us, bridging is a byproduct of computing the discourse structure of a discourse, which we view as a necessary precondition for discourse interpretation, as the interpretation of a discourse is for us compositional: a function of interpretation of the discourse's parts and how they are put together (viz. the discourse structure).' We have argued elsewhere and will largely presuppose here that we need a logic different from the simple lambda calculus of standard semantics in order to construct discourse structure. But our notion of interpretation is still essentially tied to the goals of truth conditional accounts of meaning. For us there is a big distinction between getting the semantic form of the message and full understanding of it. A theory of discourse interpretation as we see it has two tasks: first, to specify a structure that has a coherent interpretation, and second to offer a model-theoretic int.erpretation of that structure. Full under standing takes the full structure and integrates it with the beliefs of the interpreter, and as such comes after discourse interpretation. In our view, we're after the linguistic content of the message (pragmatically and semantically determined). In contrast, Hobbs et al. and Wilson are after an integration of the content with beliefs-a theory of how beliefs are updated as a result of information present in the discourse. They are more ambitious than we are, but in turn we think that what they're after can't be analysed illuminatingly in detail with the general ideas about inference that they have. From a computational perspective, there are also differences between our approach and theirs: full interpretation as pursued by Hobbs et al. and Sperber & Wilson involves inferences which aren't recursively enumerable (and perhaps shouldn't be). But the task of building a coherent discourse structure for interpretation which encompasses bridging inferences-must be feasible for computa tion�! agents, if understanding is possible. As we will indicate below in
86 Bridging
section 4, the problem of computing bridging inferences is a decidable one our theory. Bridging also occurs in the absence of definite descriptions, but in line with most research, we will focus our attention on cases involving definite descriptions. We will assume an existing compositional analysis of definite descriptions (Chierchia 199 s) and build a formal theory of bridging which is compatible with it: Although we think that from our discourse perspective Chierchia's analysis isn't quite right, we won't argue for that here. And our underlying theory of bridging in SDRT won't depend on the details of Chierchia's semantics.
We aim to provide a theory of how objects denoted by definite descriptions are related to previously described objects. For example: (s)
Lizzie met a dog yesterday. The dog was very friendly. (The dog in (sb) is identical to the dog mentioned in (sa)). (6} I took my car for a test drive. b. The engine made a weird noise. (The engine in (6b) is part of the car mentioned in (6a)). I've just arrived. (7) b. The camel is outside and needs water. (The camel in (7b) is used as transport in the arrival mentioned in (7a)). a.
. b. a.
a.
As we've stated, we will use Chierchia's (1995) compositional semantics of definite descriptions as input to the bridging which occurs at the discourse level. Chierchia treats definite descriptions as anaphoric: The N denotes an N that's related in some anaphorically determined way B to an antecedent u. Chierchia (1995) and von Fintel (1994) have suggested that the Russellian uniqueness condition holds for definite descriptions so long as one includes this relation B, because it serves to restrict the domain. So Chierchia's analysis of the N is given in (Sa). We will exploit the anaphoric resolution processes that already exist in DRT (Kamp & Reyle 199 3 ) to model bridging. So we will assume the (roughly) equivalent representation of definites in (8b):
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2 PRELI M I NARIES A N D S O ME S I MPLE EXAMPLES
Nicholas Asher and Alex Lascarides 87
(8} a. .XQ.Q (tx(B(x, u} 1\ N(x))) X, u, B Q(x, e) N(x} B(x, u) B =? b .Xe.XQ u=? .
z N(z) B(z, u)
B is an underspecified relation (as marked by the condition B = ?), which must be further specified through connecting to the discourse context. Chierchia doesn't spell out this process. We intend to do this.2 Taking van der Sandt's (I992} view that presuppositions are anaphora (and so presupposed content can be viewed as those OR-conditions contain ing '?'), this analysis assumes that the presupposed part of definites is minimal: there is some antecedent (u) which is related in some way (B ) to the individual referred to by the definite. How does one compute the value of B? Van der Sandt's (I992) theory of presupposition satisfaction in DRT gives us one clue. He suggests that presupposed content binds to an antecedent of the same content which is in an accessible part of the DRS representing the prior discourse context, if it can. This amounts to a preference for resolving B to identity. We will formally encode this preference. It provides a nice account of (s), for example. It predicts that B and u get resolved respectively to identity and the discourse referent introduced by the indefinite a dog, thereby capturing the intuition that the dog mentioned in (sb) is the same one that's mentioned in (sa). But there are alternatives t() B being identity. Clark (I977) provides a taxonomy of relations that include, among others: set membership (as in (I}}; necessary parts; probable parts (as in (6)); inducible parts (as in (7)); reasons (as in (9)); causes (as in {Io}); consequences (as in (I I}}; and concurrences (as in (3)). (9) John had a suit on. It was Jane that he hoped to impress. ( I o) John had a suit on. It was Jane who told him to wear it. ( u ) John fell. What he broke was his arm. We will build on Chierchia's analysis by spelling out a detailed formal
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=? §
88 Bridging
theory via SDRT {Asher 1993) and DICE (Lascarides & Asher 1993) of exactly how B gets resolved to such connections. In contrast to von Fintel (1994), we will use rhetorical relations to do this. We explain why in the next section.
3 THE NEED F O R RHETORICAL RELAT I O N S
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Bos et al. (1995) develop a theory o f bridging by extending van der Sandt's work with lexical knowledge. The strategy is to include more information about word meaning in the discourse context, so that definite descriptions can link to objects that are introduced as part of this additional information. They assume a generative lexicon (Pustejovsky 1 991, 1 995), where lexical semantic information and real-world knowledge are not seen as necessarily distinct Instead, linguistic processes have limited access to world knowledge, which could therefore interact with knowledge of language and become conventionalized in various ways. In particular, lexical entries for artifacts have a qualia structure, which represents a limited amount of information about that artefact: what it's made up of, what one does with it, and so on. Bos et al. use the qualia structure to perform bridging inferences. They amend van der Sandt's model of presuppositions as follows: if it cannot be hound by identity to an accessible antecedent, then one tries to link it to elements of the qualia structure of entries in the accessible parts of the DRS. So in (6), the engine links successfully to the QUALIA : CONSTITUENCY value of the lexical entry for car, which in turn is in the accessible DRS representing the discourse context (6a), because this value in the lexical entry contains an engine (to reflect the fact that cars have engines as parts). However, this extension to van der Sandt's theory has shortcomings. First, it fails to model bridging inferences in the absence of presupposi tion triggers (e.g. (4)). Secondly, although lexical semantics is a useful source of information for modeling bridging, it isn't sufficient. To illustrate the problem, consider (7). It's implausible to assume that the inference that I arrived by camel is achieved solely through lexical semantic information. For then the lexicon would essentially contain arbitrary domain knowledge, and consequently productive lexical phenomena would in general overgenerate word senses (c£ Verspoor 1996). There is a wide variety of knowledge that's used to support the bridging inference in (7). First, one uses the meanings of the words: for example, arrive is a motion verb, and so it is plausible to assume that there was a mode of transport. Second one uses world knowledge: for example, camels can be
Nicholas Asher and Alex Lascarides 89
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used as a mode of transport. But crucially, one uses the above lexical knowledge and world knowledge, as opposed to other knowledge, because this knowledge must be utilised to meet the coherence constraints imposed by the way (7b) connects to (7a). (7a) is stative and, according to Lascarides & Asher (1993), states normally provide background information. If this were the case here, however, then the camel being outside would temporally overlap the arrival, thereby blocking the camel from being part of the arrival. But another coherence constraint on Background is that the constituents must have a common topic (Lascarides & Asher 1993). And if one is forced to assume that the camel has nothing to do with the arrival, then a suitable topic can't be constructed, leading ultimately to discourse incoherence. Intuitively, one tries to interpret constituents to obtain the best possible discourse coherence. Here, assuming the camel isn't the mode of transport leads to discourse incoherence. On the other hand, assuming the camel is the mode of transport allows us to interpret the discourse coherently-my arrival caused the camel to be outside, and so the propositions are connected by Result. Thus, if we formalize the coherence constraints of different rhetorical relations, together with the principle that you aim for discourse coherence, one can compute the link between the camel in (7b) and its discourse context. Verifying coherence constraints imposed by the rhetorical relation that connects the sentences together has two important effects. First, it brings certain lexical knowledge and world knowledge into play. Second, it adds semantic content to the constituents that are connected (c£ Asher 1 993). We now know that the object described in (7b) isn't just a camel; it's a camel that I used as a mode of transport in the arrival event mentioned in (7a). Thus the added semantic content is a brid�ing inference in this case. Grosz & Sidner (1986) offer an account of how connections between sentences in discourse serve to constrain the world knowledge that is brought into play in discourse interpretation; a feature we have just claimed is essential to bridging. They define a close relationship between the discourse segmentation of task oriented dialogues and the intentional structure of the plan that underlies the task described. Poesio (1993, 1994) merges Grosz & Sidner's framework with a situation theoretic semantics to account for how focus affects the denotation of definite descriptions. Tracking focus and allowing this to influence the available antecedents is a compelling idea. It enables one to capture the intuition that the uniqueness constraint on definite descriptions is closely related to the notion of saliency. For example, Poesio (1 994) tracks the motion in (12) below, to infer that the focus of attention at the time when (12b) is processed is Dansville:3
90
Bridging
{12)
a. John took engine EI from Avon to Dansville. b. He picked up the boxcar and took it to Broxbum
(12) a. John took the engine E I from Avon to Dansville. b'. He also took the boxcar. In contrast to (I 2a, b), the natural reading of {I 2a, b') is one where the boxcar is in Avon. Presumably this is because of the different way that the sentences connect together, which in tum results in different spatia temporal effects in the semantic content. But these spatial differences between Narration and Parallel aren't represented in the theory of discourse structure that Poesio adopts. Just as before, tracking the motion in (12a) leads to the focus of attention being Dansville at the point when ( 12b') is processed. And so as in ( 1 2a, b), this predicts that the boxcar mentioned in ( 1 2b') is in Dansville, contrary to intuitions. Computing that the boxcar was in Avon by recognizing John's commonsense plan won't help either, since to recognize this plan involves computing the rhetorical connection that we've described between the sentences, and yet in Grosz & Sidner's theory, recognizing commonsense plans is primary to constructing discourse structure. One can view changes to semantic content caused by rhetorical connections as closely related to the concept of focus. The added content affects what's being talked about, and hence what's salient. So a general theory of how discourse structure affects semantic content can be viewed as contributing towards a general theory of focus. We will use this feature to model bridging inferences, by formalising the process in SDRT {Asher I993). Note that these inferences about the content of the description remain
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By doing this, he is able to infer that the boxcar is in Dansville-that is, he infers additional semantic content for (12b) as a result of tracking focus through the discourse structure. Such an account is fine as far as it goes. However, it lacks a detailed formal, general theory of how the semantic content of constituents can be modified in the light of the way they connect together in the discourse structure.4 But this flow from discourse structure to the addition of further semantic content is an essential feature of bridging. Moreover, Poesio's account of how motion determines focus produces the wrong results for other examples that feature other rhetorical relations. This is because Grosz & Sidner's model of discourse structure includes only two discourse relations-dominance and satisfaction precedence. This is too coarse-grained to handle the different semantic effects that different rhetorical relations can have on bridging. So, for example, the rhetorical relation in ( 12a, b') is Parallel rather than Narration:
Nicholas Asher and Alex Lascarides 91
when the boxcar is replaced by a boxcar. So once again, bridging occurs in the absence of presupposition triggers. We've given texts where different rhetorical relations have different effects on bridging. Text { I 3) provides evidence that rhetorical coherence can even override default world knowledge during bridging.
(13) a. John moved from Brixton to St. John's Wood. b. The rent was less expensive.
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Matsui {I995) tested subjects' judgements on where the rent was less expensive in (I 3 ). All the subjects knew the world knowledge that rents tend to be less expensive in Brixton than in St.John's Wood. But in spite of this, the majority of informants judged that in (I 3), the rent being talked about was in St. John's Wood, thereby drawing conclusions which conflicted with their world knowledge. Arguably, information about how the sentences connect together conflicts with the world knowledge, and ultimately wins over it. So if computing bridging ignores discourse structure, then the world knowledge would trigger the wrong results in (I 3). We will explain { I 3) in terms of the rhetorical relation that's used to connect the constituents. (I 3 b) is stative, and so supports a Background relation. However, intuitively, one prefers explanations of intentional changes (in this case, moving house), to simple background information that sets the scene for the change. Assuming that we always want to maximise discourse coherence, then even if default world knowledge conflicts with this, we infer both Background and Explanation for these texts. But the Explanation that John moved because the rent was less ,expensive is phmsible only if the rent was less expensive in the place he went to: St. John's Wood. The above texts where rhetorical information affects bridging pose challenges for extant theories. We need to analyse definite descriptions in a theory where information flow from rhetorical relations to the semantic content of constituents is taken into account. So we propose to use SORT {Asher 1993), where this information flow is a distinguishing feature. SORT is a theory of discourse semantics designed to explore systematically the interface between semantics, pragmatics and discourse structure. To date it has been used to model several phenomena on the semantics/pragmatics interface (e.g. Asher I993; Asher & Lascarides I994, 1995, in press; Lascarides & Asher 1993, Lascarides & Copestake I997, Lascarides & Oberlander 1 993). Here, we will use it to interpret definite descriptions and to offer a new picture of bridging in general. SDRT has three main advantages for our purposes. First, the way discourse structure affects and is affected by semantic content has. already been studied extensively in this framework, and an adequate account of definite
92 Bridging
4
A CRASH C O URSE I N S D R T
Broadly speaking, there are two components to SDRT. First, there is a formal language with a compositional semantics, in which the content of discourse is represented (Asher 1993). This is an extension of Discourse Representation Theory (oRT): discourse is represented as a segmented DRS (soRs), which is a recursive structure of labelled DRss that represent the clauses, and these labels are linked together with rhetorical relations, such as Narration and Parallel (c£ Hobbs 1985; Polanyi 1 985; Thompson & Mann 1987; and others). The second component to SDRT is a formal theory of pragmatics known as DICE (Discourse in Commonsense Entailment) (Lascarides & Asher 1 993), which is used to build the SDRS of the text or dialogue. It uses a variety of knowledge sources to do this: for example, lexical and compositional semantics, domain knowledge and cognitive states. DICE is a type of 'glue' logic, because it specifies how SDRSS connect together with rhetorical relations� The glue logic differs from the logic of 'information content' (i.e. the logic of the SDRSS themselves), whose validity problem is at least recursively enumerable (Asher 1996). DICE exploits a much weaker language (Lascarides & Asher 1993): it's a quantifier free fragment of a first order language augmented by a weak conditional operator > (P > Q means IfP, then normally Q). The logic is decideable. All axioms in DICE for computing rhetorical relations are of the form given in (14), where r, a and f3 label soRSs ( r, a , /3) means f3 is to be attached with a rhetorical relation to a, where a is available in the SDRS
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descriptions must make use of these effects. Second, the basic semantic framework which underlies soRT (oRT) has already proved useful in specifying constraints on the interpretation of definite descriptions (van der Sandt 1 992; Bos et al. 1995). We will build on this work here. Finally, one of the main features of SDRT is the underlying axiomatic theory DICE (Discourse in Commonsense Entailment) which allows us to infer rhetorical relations, using semantic content and world knowledge as clues (Lascarides & Asher 1993). DICE is distinctive in that it deals in a principled way with cases where different knowledge sources give conflicting clues about how to interpret a text. We will use this axiomatisation to provide a novel analysis of bridging that records the influence of background knowledge on the process, and we will use DICE's tools for conflict resolution to model why the default world knowledge is 'ignored' in (1 3).
Nicholas Asher and Alex Lascarides 93
labelled r that's built so far; some stuffis a gloss for relevant information, and R is a rhetorical relation: (14) ( ( r , a , {3 ) /\ some stuff) > R ( a, {3)
5
( ( r, a, {3) 1\ event(ea) !\ event(e13)) > Narration(a, {3) Consequence of Narrat ion: Narration( a, {3) ea -< e13
•
Narrat i on:
•
Temporal
-+
Narration also constrains spatia-temporal trajectories of objects. Asher et al. (1996) derive the following constraint from Narrat ion and commonplace assumptions about eventualities: •
Spat ial Consequence of Narrat i on:
(Narration ( a, {3) !\ actor(x, a) !\ actor(x, !3)) loc(x, source(e/3)) = loc(x,goal(ea))
-+
In words, if Narration( a, {3) holds and a and {3 share an actor x then the location of x is the same at the end of ea and the onset of e13.6 There's also an axiom which states that narratives have a distinct common topic. We will introduce further axioms in later sections of this paper. A distinctive feature of SDRT is that if the DICE axioms yield a nonmonotonic conclusion that R(a, {3) holds, and information that's necessary for this to hold isn't already in the constituents Ka or (e.g. -< Narration( a, {3) is nonmonotically inferred, but the formula ea e13 and information about the spatial location of actors are not in Ka or in then this content is added to K13 in a constrained manner through the SDRS Update process. Asher & Lascarides (1998) give the detailed formal definition of discourse update for hierarchically structured contexts. An
K13
K13),
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While the glue logic and language are distinct from their counterparts at the level of information content, the glue language nevertheless exploits some aspects of information content in axioms of the form just given. To this end, we have devised an information transfer function J.L from SDRSS into the DICE language, which allows DICE to use information about content to compute the rhetorical relation. Roughly, for each labelled SDRS 1r: Kn, J.L takes conditions inside the SDRS Kn and turns them into predicates of its label 1r. So J.L (Kn) ( 1r) is a set of formulae of the form ¢>(1r), where ¢> is a predicate. Some stuff in (14) will be formulae of this kind. For example, the schema Narrat ion states: if {3 is to be attached to a and a and {3 describe events, then normally the rhetorical relation is Narration. The Temporal Consequence of Narrat ion is a coherence constraint on Narration in that it constrains the contents of the connected constituents: if Narration( a, {3) holds, then a's event precedes {3's.
94 Bridging
(12) a. John took engine E1 from Avon to Dansville. b". He picked up a boxcar c. and took it to Broxburn. First, we use the grammar to build DRss Ka. and K13 for the ( 1 2a) and ( 1 2b"), and these receive the labels a and {3 respectively. The pronoun in K13 is resolved to John because in soRT the · only available antecedents to pronouns are those that are DRs-accessible in the current constituent (in this case, K13), or those that are DRs-accessible in the constituent Kcr to which K13 is going to be attached. So John is the only choice. Defeasible Modus Ponens on Narrat ion yields Narration( a, /3). Modus Ponens on Axiom on Narrat ion yields e0 -< e13 (i.e., John's taking engine E 1 from Avon to Dansville precedes his picking up a boxcar), and Modus Ponens on the Spat i al Consequence on Narrat ion yields that the shared actor John is in Dansville when he begins to pick up a box car, because this is the location of the goal of e0• By the lexical semantics of picking up (see Asher & Sablayrolles 1995), the location of the source of this event is the same as the location of its goal, and the object that's picked up is at this location. So the boxcar is in Dansville when it's picked up. The definition of soRT Update guarantees that the content that's inferred as a result of the DICE inference that the text is narrative is added to K13 in the soRs for ( 1 2a, b"). In particular, the information that the boxcar is in Dansville is added to K13, and this can be viewed as · a bridging inference, because it amounts to a relation between an object mentioned in the current clause and one mentioned previously, which arose out of coherence constraints on the discourse. Thus in contrast to Bos et al. (1995), soRT can model bridging inferences in the absence of presupposition triggers.
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informal, simpler definition does for our purposes, however. Informally, Update(Kn Ka, KfJ) is an SDRS in which three things are added to the SDRS Kr: (a) /3 is added to Kr's list of discourse referents; (b) R( a , /3) is added to Kr's conditions, where R(a, /3) follows nonmonotonicall� from DICE; and (c) {3 : KJ is also added to K/s conditions, where K{J is just like the SDRS KfJ, save that information cp that's necessary for R( a, /3) to hold and that wasn't already in Ka. or KfJ has been added. In what follows, we will specify constraints on Update. And in certain cases, we will replace one update task with another. So Update(Kr, Kcr, K13) : = Update(Kr', Ka.' , Kf3 ') means: replace the task of updating Kr with K13 via attachment to Kcr with the task of updating Kr with K/3' via attachment to Kcr'· As an illustrative example, consider (12a, b"):
Nicholas Asher and Alex Lascarides 95 s
B R I D G I N G WITH SORT
. We will use SDRT to resolve the underspecified conditions in Chierchia's analysis of definite descriptions. In effect, computing the bridging inference will occur as a byproduct of SDRT update.
5.1
SDRT
We now define how the anaphoric binding relation B and antecedent u, which are introduced by the compositional semantics of definites, are resolved in terms of the function Update introduced in section 4· There are four rules that define this. They· are not part of the DICE language. Rather, they are meta-rules about how" the semantic content of underspecified constituents and the function Update interact. The first rule captures van der Sandt's intuition that one uses identity to resolve bridging if one can. The second captures the intuition that bridging inferences must be plausible. The third captures the intuition that if updating the discourse with (underspecified) information adds semantic content which can act as a bridging implicature, then this added information is indeed a bridging implicature. And the last rule captures the intuition that we favour bridging implicatures that maximise discourse coherence. First some notation: l K means that the SDRS K is well defined; that is, it contains no unresolved conditions of the form x = ? and every DRS in K is attached to another with a rhetorical relation. Furthermore, K[¢] is a formula, which is true if the SDRS K contains the condition ¢, and K[¢' / ¢] is a term which denotes the SDRS which results from replacing ¢> in K with ¢' . The first rule is given below. It states that if SDRS update with the binding relation B specified to identity is well-defined, then SDRS update must set B to identity. •
If Possible Use Ident ity:
{K,a[B = ?] /\ 1 Update(K,. , Ka , K,a [>.xAyx = y/B]) ) --+ (Update(Kn Ka , K,a) : = Update(Kn Ka, K,a[>.xAyx = y/B] ) )
This aXiom reflects the preference noted by van der Sandt, for standard anaphoric binding over the alternatives. However, the condition this axiom imposes on standard anaphoric binding is stronger than van der Sandt's. In van der Sandt's theory, a presupposition will bind in any context where there's an accessible discourse referent satisfying the same content, and the result is satisfiable and informative. In contrast, I f Possible Use Ident ity permits this binding only if van der Sandt's conditions hold,
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·
Building the bridges in
96 Bridging
and one can compute a rhetorical relation with the result. Van der· Sandt's weaker condition on binding is problematic in an example such as (I s):7
(I S) a. Boggs stood calmly by as Ryan struck out the hitter with a 95-mph pitch, b. then he stepped up to the plate and c. he hit the pitch out of the park.
( 1 6) A foreign president visited the White House, but the President was busy.
But we believe resolving B to identity in (x6) doesn't produce a well defined soRs, and so If Possible Use Ident ity doesn't apply in this case: If we do identify the President with the president mentioned in the first sentence, then the coherence constraints required by the relation Contrast, which is monotonically inferred from the cue word but, are violated, much in the same way as they're violated in (17), if one assumes that he refers to the foreign president. (17) ?A foreign president; visited the White House, but he; was busy. As we've seen, specifying B as identity doesn't always yield a well defined soRs. In this case, we allow the discourse context to guide us to a suitable specification for B. All the following rules suppose that • ! ( Update(Kr, Ka , Kp[A.xAyx = y/B]) ) holds. In general, there are many ways the underspecified parameter B could be made precise; some of these may be more plausible than others. We see here an important role for world knowledge. It specifies certain plausible ways of filling in the underspecified parameters in the presupposed material (c£
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In van der Sandt's analysis the pitch in ( I sc) will bind to the 95 mph pitch mentioned in ( 1 sb), because his theory fails to account for the effects of temporal constraints. Moreover, we have shown elsewhere (Lascarides & Asher 1991, 1993) that an adequate account of the temporal constraints on discourse requires reasoning about discourse structure. In contrast, our theory will detect that the binding relation B in the representation of the pitch in (1 sb) cannot be identity, because the result will violate the temporal coherence constraints on Narration which, by Defeasible Modus Ponens on Narrat ion, binds the propositions together in this discourse. Instead of B resolving to identity, the three axioms below for computing B will ensure that B resolves to 'thrown-by' and u to Ryan. Note that If Poss ible Use Ident ity is monotonic rather than default. Giles Fauconnier (pc) has offered (x6) as a potential counterexample to its monotonicity: Resolving the binding relation to identity in ( 1 6) doesn't produce the intended reading.
Nicholas Asher and Alex Lascarides
97
Beaver . 1994). To represent this we introduce a conditional operator: P >o Q should be read as 'If P, then it's plausible to assume Q'. This specifies a weaker connection than >; it stipulates what is plausibly the case, rather than what is normally the case. In essence Bridge s are Plausible below will restrict bridging as follows: the bridge must be built from > consequences of the semantic content of the constituents. That is, a bridge must be plausible: 0
•
Bridges are Plausible:
( .B[B = ¢ ; u :_ x/B = ?; u = ? ] /\ (r , a, ,B ) 1\ R(a , .B)) � (( JL (KT ) ( r ) 1\ JL (Kf3 ) (,B) 1\ R( a ; ,8)) >o (B = ¢ 1\ u = x)_)
(7) a. I just arrived. b. The camel is outside and needs water. b'. ?The fleas are outside and need water. An axiomatization of >o would involve extensive discussion of common sense reasoning with world knowledge, and so we gloss over it here.8 However, if one believes that all bridging relations are constrained to fall within Clark's (1977) taxonomy, then one could capture this within this axiom Bridges are Plausible: one could assume that >o is constrained so that the formula on the RHS of in Bridges are Plaus ible holds only if the bridging relation ¢ is one of those that falls within Clark's taxonomy; i.e. ¢ must be a part-whole relation, or a set membership relation, or a causal relation, etc. This would amount to the assumption that only those relations within Clark's taxonomy form plausible candidates for bridging. There would be computational advantages to restricting ¢ this way, because this would provide a monotonic restriction on the search space of candidates for bridging. However, we remain agnostic as to whether Clark's taxonomy of bridging relations provides an exhaustive list of plausible bridging relations. There may be rich discourse contexts in which world knowledge permits a plausible bridging relation that lies outside this taxonomy. Our third rule governing bridging inferences is D i s course Structure (DS) Determines Bridging. This rule captures the intuition that when the rhetorical relation used to connect the constituents gives us a particular �
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In words, if B and u are resolved to ¢ and x respectively, and .B is attached to the constituent a in . T with a rhetorical relation R, then the semantic content of this (updated) discourse must make these bindings plausible. We'll see in section 7.2 that this rule will prove important when distinguishing (7a, b) from (7a, b') (it's not plausible to assume fleas were the mode of transport):
98 Bridging
way of resolving B, we do it that way. More formally, let J..L (Kf3 ) (f3) -+.J..L (K
DS Det ermines Bridging:
Suppose: ( ) 1-L(Kr ) (r) /\ i-L(K�J) (/3) /\ (r, o:, /3) � R(o:, /3) a
{b) � 1-L(K�J) (/3)
-+* 1-L(K¢) ( ¢); and (c) � (R (o:, /3) /\ !-L (Kr) (r)) > !-L (K¢) ( ¢ ) Then Update(Kn Ko: , K13) : = Update(Kn Ko: , K¢)
(12)
John took engine EI from Avon to Dansville. b. He picked up the boxcar and took it to Broxbum. a.
We can use DICE to infer that (12a, b) is narrative even before determining the underspecified elements B and u in (12b); we then use Narration's coherence constraints to infer that the boxcar is in Dansville, and this added content suffices to produce a plausible way of resolving B = ? and u ? (B resolves to in and u to Dansville). DS Determines Bridging ensures we resolve them this way. The details of this analysis are given in the next section. DS Determine Bridging deals with the case when the coherence constraints imposed by the rhetorical relation that's inferrable from the underspecifled constituent {3 produces a plausible bridging inference. But the underspecified constituent {3 doesn't always contain sufficient information to determine the rhetorical relation; hence it may not be enough to determine the bridging inference. To deal with such cases, we state a rule which captures the intuition that people interpret text so as to maximize discourse coherence. It is a more restricted version of the Interpretation Constraint in DICE that was introduced in Lascarides et al. (1996) for modelling word sense disambiguation, and this more restricted rule suffices for our purposes. As background to this rule, we assume that rhetorical relations between constituents may be partially ordered with respect to the semantic content =
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In words, if we can infer the rhetorical connection R between the discourse context r and the underspecifled constituent {3, and this relation R allows us to infer a particular resolution K
Nicholas Asher and Alex Lascarides 99
of the context. This reflects the fact that given the semantic content of the clauses, some rhetorical relations will produce a 'closer connection' or 'better coherence' than other rhetorical relations. We encapsulate this by introducing the following partial order: Explanation > r, a Background means that it would be preferable to interpret {3 as an explanation for a, rather than background information-although both alternatives may be coherent, one is better than the other-and this is partly because of the content of T and a.9 The following rule then captures the following: resolve the underspecified element B so as to maximize discourse coherence: •
· Maximize D i scourse Coherence:
(a) J.L(Kp) (/3) �* J.L(Kp, ) (/3, ); and (b) (T, o:, /3, ) 1\ J.L(Kr ) (T) /\ J.L(Kp, ) (/3, ) � R, (o:, /3, ); and (c) R , is the > r, a maximal rhetorical relation of attachment Then Update(Kn K0 , Kp) : = Update(K71 K0 , Kp, ) . If
6 MODULARITY O F D I S C O URSE PROCE S S I N G Both our theory and Hobbs et al.'s theory use rhetorical relations to help compute briding inferences, and they are quite similar in spirit. However, there are several important differences. First, Hobbs ignored compositional semantic information and lexical semantics in computing the antecedents to definite descriptions, and he doesn't specify how to translate NL definite descriptions into logical form. We do. The main difference, however, concerns modularity. For both linguistic and computational reasons, DICE exploits a logic that is distinct from the logic of information content (that is, the logic of SORT). Indeed, the former
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It does this because in words, the rule ensures that . if {3, resolves B and produces the best coherence, then one must replace {3 with {3, in the update. Maximize D i scourse Cohere.nce will be used in the analysis of (1) and (7) in section 7.2. Note that these rules for computing bridging by reasoning about soRT update are fully declarative and monotonic. They therefore don't make any assumptions about whether rhetorical relations are inferred first, or whether bridging relations are inferred first. However, such orders could be imposed in an implementation of this theory: for example, one could guide the implementation so that one attempts to compute rhetorical relations on the underspecified constituent before one computes a bridging relation; and failing that, one reasons about bridging relations, and then tries to compute rhetorical relations on the resolved constituents.
100
Bridging
logic is not only separate, but weaker than the latter logic. In contrast, in Hobbs et al 's abductive framework, the logic of the information content and the logic for computing rhetorical relations are one and the same. Hobbs et al. (1993) use weighted abduction to interpret discourse: one makes assumptions that explain the data at least cost, from a knowledge base that includes all information, both linguistic and non-linguistic. Using abduction on semantic content and background knowledge to guide pragmatic inference is intuitively compelling. But there are two technical reasons for splitting the logics of information content and information cohesion in the way we do. First, all the nonmonotonic frameworks, including Hobbs et al.'s abductive one, require some appeal to consistency tests to draw conclusions. But if one's base logic of information content is already that of first order logic, then adding consistency tests goes beyond the boundary of what is recursively enumerable. Our framework for computing rhetorical relations is also nonmonotonic. But the base logic is propositional rather than first order logic, because it is kept separate from the logic of information content of discourse (which is first order logic). So the logic for information cohesion we use here is decidable. Second, by modelling compositional semantics, background knowledge and discourse coherence principles within a single logic as Hobbs et al. do, one cannot separate the process of anaphora binding from the semantic content of the discourse as one would wish. Abduction requires some additive measure of cost ori the various assumptions made to compute a proof of the .discourse, and so inconsistent interpretations will always have the highest overall cost, and will be avoided if possible. Consequently, it's unclear how one should handle discourses where definite descriptions receive an unambiguous interpretation, which results in an inconsistency in the semantic content of the discourse (thereby making the discourse sound odd). For example, the woman and the election in (18b) unambiguously denote one of the people I met last night and the vote denoted in ( r8a) respectively, even though this results in an inconsistency that makes the discourse sound strange: .
It's not clear that Hobbs et al.'s abductive framework can account for examples like these, because the account will prefer accommodating the definite descriptions to binding it, in order to preserve consistency. In our account, binding definite descriptions to the discourse context is essential, because the compositional semantics of the definite anicle will demand it. In the above example, one would infer Elaboration between the constituents
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(18) a. I met two interesting people last night who voted for Clinton. b. The woman abstained from voting in the election.
Nicholas Asher and Alex Lascarides 101
7 APPLI CATI O N S TO EXAMPLES We now examine some examples in detail. In sections 7.1 and 7.2, we will concentrate on bridging inferences involving definite descriptions. In section 7·3· we will briefly discuss cases that involve other expressions. 7. 1
Bridging through discourse attachment
First, consider a case where discourse structure determines bridging: (12) a. John took engine E1 from Avon to Dansville. b. He picked up the boxcar c. and took it to Broxburn.
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because of the relationship between the woman and the two people. The coherence constraints on this relation won't be violated by the fact that one can't abstain and vote at the same time. However, the discourse is still predicted to be odd in soRT, because its representation is unsatisfiable. Finally, Hobbs et al. assign different weights to different predicates, in order to deal with cases like (1 3), where there are choices about what bridging inferences to draw, because of the conflicting clues from different knowledge sources. A notion. of cost for inferring information is very intuitive. But the meaning of the weights in the abductive logic is unclear; and so there are no general principles that explain when and how (default) information about rhetorical relations overrides default world knowledge. In contrast, the logic we use is designed to resolve conflicting clues about semantic content from different knowledge resources logically, rather than through the use of weights (see Lascarides & Asher 1993 for details). Reasoning among the knowledge resources will be handled 'automatically' by the logic (though we must take care in representing the axioms, so that the logic does this appropriately). So our approach is computationally more tractable while being more fine tuned to the linguistic phenomena. Sperber & Wilson's approach to bridging also deserves some comment, though the comparison between the two approaches is more difficult here than in Hobbs et al.'s case. Relevance theorists could, though they have not done so, adopt our linguistic assumptions and most of our framework. Their view is compatible with our modular view of discourse interpretation, in a way that Hobbs's approach is not. Their claim would then be that it is the principle of relevance that guides the resolution of the underspecified elements in our treatment of definite descriptions. But then detailed comparison at this point would be highly speculative, given that we are not sure how to use the relevance principle in reasoning about underspecification.
102 Bridging
The DRSS representing (12a) and (12b) are
a
and {3 respectively:
j, E1, a, d, e1, t1 , n
n, B, u, y, e2, t2, n pick-up(e2, j, y) hold(e2 , t2) t2 -< n B= ? (!3) u = ? B(y, u) bo:xcar(y) z boxcar(z) B(z, u)
=- §
Note that he in {3 resolves to John. This is because anaphoric constraints in SDRT make John the only choice, regardless of the rhetorical relation which connects a and {3. In this example, resolving B to identity makes the update undefined, because there is no boxcar in a, and so no resolution of u = ?. So according to OS Det ermines Br idging, we should check to see if we can attach {3 (as it stands) to a with a rhetorical relation, and if the results of this give us other values for u and B. The antecedent to Narrat ion is verified, since both ea. and e13 are events. So by Defeasible Modus Ponens on Narrat ion, Narration( a, !3) is inferred. Further inferences follow from this. First, by Modus Ponens and the Temporal Cons equent of Narrat i on, ea. occurs before e13; that is, the taking of the engine from Avon to Dansville occurs before a boxcar is picked up. Furthermore, as we showed in section 4, by the semantics of the
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John(}) engine-E1(EI) Avon( a) ( a ) Dansville(d) take(e" j, E1) from(e1 , a) to(e. , d) hold(e. , t. ) t1 -< n
Nicholas Asher and Alex Lascarides 103
phrases take to and pick up and the Spat i al Consequence of Narrat ion, one infers that the source of the picking up event is in Dansville and the object that is picked up is therefore also in Dansville. Hence, the boxcar is in Dansville. Thus, the coherence constraints on Narration allows us to infer a particular way of resolving B and u-viz. B is in and u is d. or Dansville (for simplicity, we have ignored conditions on when these relations hold, but they could be added to the formal representation of content). So DS Determines Bridging leads to the following revision of {3, and this gets attached · to a with Narration:
d, e2, t2, y, B, u, n
z boxcar(z) B(z, u)
=? §
Note that our final result {3. includes added content. We have resolved anaphoric conditions that were conventionally triggered by the definite. This added content was inferred in order to meet constraints on discourse coherence. It amounts to: the boxcar is located in Dansville and moreover, . it's the only one in Dansville. Poesi? accounts for (12a, b), but fails to model cases involving different rhetorical relations: (12)
John took the engine E 1 from Avon to Dansville. b'. He also took the boxcar. a.
His theory doesn't predict the boxcar in (12a, b') is in Avon. In contrast, our analysis captures the intuitive interpretation of ( 1 2a, b'). Briefly, as in the previous example, the attempt to specify the binding relation B to identity fails. The similarity in syntactic structure and the cue word also are clues in DICE that the discourse relation between (12a) and (12b) is Parallel. This doesn't have a spatial constraint like that represented in Spat i al
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pick-up(e2, j, y) hold(e2 , t2) t2 -< n in(y, d) boxcar(y) Dansville( d) source(e2, d) location(t2, y, d)
104
Bridging
7.2
Bridging before discourse attachment
We have looked at cases where inferring a rhetorical relation helps specify bridging inferences. The rule Maximize Discourse Coherence specified in section s.I enables us to specify bridging inferences so as to gain discourse coherence that wouldn't be there otherwise. In example ( r ), we fail to get a well-defined update if we specify the binding relation to identity. Furthermore, in contrast to texts like (12a, b), there isn't enough information in the underspecified constituent f3 repre senting (I b) to infer a particular rhetorical relation between it and a representing ( I a). {I) a. I met two interesting people last night at a party. b. The woman was a member of Clinton's Cabinet. This is because only Background in DICE applies, and so the only candidate relation is Background. But constituents related .by Background must have· a common topic. We can compute this using the technique discussed in Grover et al. ( I 994). That is, we generalize over the predicates and arguments in the propositions. Since we haven't resolved B and u, the woman is unconnected with the two people. And so computing a common topic in this way isn't possible, because the result is too general: something like things that were true yesterday. Hence Background can't be inferred between a and the underspecified {3. Neither can any other relation. Hence DS Det ermines Bridging won't apply. Instead, we must use Maximize D i scourse Coherence. That is, we 10
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Consequence of Narrat i on. Rather, the spatial constraints are computed on the basis of the way the different parts of the DRSS related in the parallel relation are mapped on to each other. This mapping is an essential feature of the coherence constraints on Parallel {Asher I 99J). For the sake of brevity, we omit the details of constructing the mapping here, but informally, the taking event in (12b') is matched with that in {I2a). The consequence is that, by the spatial constraints on Parallel, their sources and goals are taken to be the same, unless there's information to the contrary. This adds semantic content to the DRS representing (12b'); the source of the taking event in (12b') is Avon. So by lexical semantics, the boxcar is in Avon at this source. One adds this to the representation of the given information via DS Determine Bridging as before. And so one obtains an interpretation where the boxcar is in Avon rather than Dansville, and it's the only boxcar in Avon.
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105
Coherence.
(7) a. I just arrived. b. The camel is outside and needs water. b'. The fleas are outside and need water. Again, B can't be identity. The antecedent to Background is verified, but notice the difference with the following variants (7a', b") and (7a', b"'): (7) a'. John �rrived at 3 pm. b". A camel was outside and needed water. b"'. ?A camel is outside and needs water.
·
Background requires a distinct common topic, and one is readily able to construct this in (7a', b"): a camel's being outside and needing water can be understood to be a property of the place John arrives at, a description perhaps of the scene that he sees. The operation of generalization then would yield a topic like: properties of the place that John arrives at. But this seems to be blocked in the case of(7a, b) and (7a', b"'). We need an analysis of the effects of tense shift (from past to present) and words like just on discourse topics to model this. But exploring these effects would take us too far afield, and so we'll simply assume that Background is blocked in (7a, b) because a common topic can't be constructed. So we have to find another connection. Just as in ( r ), we must entertain various resolutions of the underspecified
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must investigate which resolution of (3 produces the best discourse, and resolve (3 to that. Suppose that {32 is a resolution of (3 where B and u are defined so that the woman y is separate from the two people mentioned in the first sentence. Then this produces just as bad a discourse as that betWeen a and (3 itself, for the same reasons. On the other hand, suppose that (3, is the resolution of (3 where the woman y in the DRS (3 is one of the two people I met last night. In other words, the binding relation B in (3, resolves to member-of, and u resolves to the discourse referent denoting the two people I met in a. Then the rules in DICE given in Asher & Lascarides ( 1995) allow us to compute Elaboration between these constituents a and (3,. This comes with different coherence constraints from Background: the topic is a. The discourse coherence is therefore much improved. So, the antecedent to Maximize D i s c ourse Coherence applies with respect to (3. , and so the discourse context a is updated via Elaboration with (3, . As before, we have gained further information: we now know that the woman is one of the two people I met last night, and only one of the people I met last night was a woman by the uniqueness condition that forms part of the compositional semantics of the definite. So the other one must have been a man. Our analysis of (7a, b) also uses the principle Maximize Discourse
ro6 Bridging parameters in /3 and see which option maxtmtzes discourse coherence. Suppose B and u are resolved so that the camel had some role in the arrival. By the constraint Bridges are Plausible given in section s.I, this must be a plausible role. The only one is that the camel is the mode of transport by which I arrived. This content enables us to infer a new rhetorical relation, with improved discourse coherence. We can infer that the camel being outside was caused by my arrival thanks to the spatial information in the compositional semantics of the change of location phrase arrive here, and so the rhetorical relation is Result. So Maximize D i scourse Coherence is
( I J)
a. John moved from Brixton to St. John's Wood. b. The rent was less expensive. a
Let the sentences ( I 3 a, b) be represented by the DRSS and {3 respectively. Once again attempting to resolve B to identity fails. But rent is a functional noun, and so in and of itself it suggests a value for B: it should be of, and the other term of the binding relation should be some object that can have rents. But there are no places that are mentioned in ( I 3a) that have rents. So .1 1 we must construct one through attempting to attach {3 to a As in the previous examples, one cannot compute a rhetorical relation between a and the (underspecified) {3. We need to know more about the connection between the rent mentioned in /3 and the content of a. There are at least two possible resolutions of u in {3. The first, /31 ' is such that - the constituent means: the rent of the place that John moved to, which is in St. John's Wood, is less expensive than the rent he paid in Brixton. The second, /3z, is such that the constituent means: the rent he paid in Brixton is less expensive than the rent of the place he moved to, which is St. John's Wood. /31 together a with the content of a yield Explanation( , /31 ) in DICE. They also yield a Background( , {31 ) , because Background is compatible with Explanation, and
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used to infer this new content to the definite description the camel, together with the Result relation between the constituents. (7a, b') is odd because one cannot infer that the fleas are the mode of transport. This is implausible, and so it's ruled out by Bridges are Plaus ible. Indeed, there is no plausible resolution of B and u that produces a coherent discourse, and so the SDRS can't be updated. (7a1, b"') is odd because the antecedent to Maximize D i scourse Coherence isn't verified-the semantic representation of (7b"') contains no underspecified elements. Therefore, even though (7b"') as it stands cannot attach to (7a'), we lack the means to- change its content. This demonstrates that although we capture bridging inferences for certain indefinites (e.g., (1 2a, b")), we don't overgenerate bridging inferences for them, resulting in discourse coherence where there shouldn't be any. Now consider the text (I J):
Nicholas Asher and Alex Lascirides
1 07.
{31 describes a state (i.e. the rent in St. John's Wood being less expensive). Moreover, in contrast to a and {3, we can compute a good topic for a and {3., since we now know the rent is connected to St. John's Wood. In contrast, {32 and the content of a yields only Background( a, {31 ), but it .cannot support Explanation (since moving to a more expensive house doesn't explain why one moved, at least, not on its own). Intuitively, one prefers an interpretation of a discourse that offers explanations of intentional behaviour that's described in the text-such as moving house-to an interpretation of the discourse where such behaviour is left unexplained. In essence, interpreters don't like miracles, or unexplained changes. We can model this via the partial order of rhetorical relations: Explanation > Background in this case. Therefore, the antecedent to the monotonic rule Maximize D i sc ourse Coherence is verified and one updates {3 to {31 • In other words, one infers the rent referred to in (IJb) is the rent that John pays in the place he moved to, which is in St. John's Wood. This consequent of Maximize D i s course Coherence is incompatible with the default world knowledge that rents in Brixton are typically less expensive than those in St. John's Wood. However, since Maximize D i scourse Coherence is a monotonic rule, it overrides this default world knowledge. This is as required, given the evidence in Matsui's experiments. In essence, Maximize D i scourse Coherence guarantees that maintaining discourse coherence takes priority over default world knowledge; a principle of discourse interpretation for which we have argued elsewhere in modeling word sense disambiguation {Lascarides & Copestake 1997; Lascarides et al. 1 996). r, a
Beyond definite descriptions
Bridging can occur in the absence of definites. We have already discussed how soRT captures the bridging relation in (12a, b"): (12) a. John took engine E I from Avon to Dansville. b". He picked up a boxcar. c. and took it to Broxbum. The bridging in (4), which we discussed in section similar manner: (4)
I,
in modelled in a
a. Jack was going to commit suicide. b. He got a rope.
The proposition representing (4b) must be attached to the one repre senting (4a) with a rhetorical relation. Let's assume that the content of
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7·3
108 Bridging
(2) In the group there was one person missing. It was Mary who left. Let us suppose that in line with Chierchia's analysis of definite descriptions, the compositional semantic analysis of it-clefts reflects the fact they're anaphoric, demanding a relationship B between the event e corresponding to the content of the presupposed information (here, that someone left} and an antecedent event e ' in the discourse context. Let us further suppose that by default someone leaving a group causes him to be missing from that group. Then this can be exploited to connect the two sentences in (2) with a rhetorical relation, and it also provides a way of resolving B via DS Determines Bridging. By the DICE axioms in Lascarides & Asher (1993), cause(e, e ' ) is inferred, where e ' is the eventuality that someone's missing from the group, described in (2a). Moreover, this resolution of B to cause yields discourse coherence: the second sentence specifies who left, and so DICE supports the inference that this elaborates content of the first sentence. Now consider the discourse (3):
(3) John partied all night yesterday. He's gomg to get drunk agam today. As with it-clefts, we assume again is anaphoric, in that its content includes the conditions B(e, e' ) , B = ? and e' = ?, where e is the event that forms part of the presupposed content triggered by again; in this case, e is the event that John got drunk (before today). B and e ' are resolved through discourse update. By generalizing over the two properties of times given in the two DRSS that represent the two sentences, we can construct a common theme that supports a Parallel relation between them (for more details see Asher
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(4a) allows us to infer by default that Jack has a plan to commit suicide. Let us further suppose that if Jack has such a plan, and he gets a rope, and we know these events are connected somehow (as they must be for a rhetorical relation to hold), then normally, getting a rope is part of the plan, and the rope is the suicide instrument. These defaults will lead to an inference in DICE that the rhetorical relation is Elaboration. And the definition of SDRT Update will add the information that the rope is an instrument in the suicide to the representation of (4b), since this content is essential for the coherence of the Elaboration. So just as in ( 1 2a, b"), the coherence constraints on rhetorical relations trigger additions to the semantic representation of (4), which amount to bridging inferences between the objects described in the text. Bridging inferences also occur with presupposition triggers other than the definite, e.g. the it-cleft in (2):
Nicholas Asher and Alex Lascarides
109
1993). To maximize the common theme, we infer that John got drunk at the party yesterday. And so computing the rhetorical structure of the discourse produces values for B and e ' via DS Determines Bridging: B is ' concurrent and e is the event described in the first sentence. We have only hinted here at how our theory of bridging contributes to the analysis of cases involving other expressions. For the formal details of how our axioms introduced in section 5.1 are involved in the analysis of presupposition triggers in general, see Asher & Lascarides ( 1998).
Bridging inferences involve a complex interaction between lexical and compositional semantics, world knowledge and discourse structure. We have shown that the coherence constraints imposed by different rhetorical relations have an effect on bridging, which cannot be accounted for purely in terms of focus or domain knowledge. We have modelled this effect in SDRT, a theory of discourse structure with the distinguishing feature that rhetorical connections can trigger a change to the semantic content of the propositions introduced in the text. Bridging inferences are a byproduct of computing how the current sentence connects to the previous ones in the discourse. Our account fully integrates compositional and lexical semantics and discourse structure. We use a well-defined logic which combines various know ledge sources to compute how new information integrates with the discourse context, paying particular attention to when these knowledge resources conflict. We demonstrated that by integrating compositional and pragmatic reasoning in this way, we provide a more refined account of bridging inferences than either compositional semantic accounts or AI accounts that exploit background knowledge in discourse interpretation can achieve on their own. Acknowledgements Various versions of this paper have been presented at the International Workshop on Underspecification which Vl(aS held at Berlin in 1996, the International Workshop on lexical semantics and acquisition which was hdd in Courmayeur, Italy in 1996, CUNY 1996, and seminars at the University of Texas at Austin and the University of Edinburgh. We would like to thank the people that attended these talks for their feedback. We would also like to thank David Beaver, Janet Hitzeman. Ali Knott, Rob van der Sandt, Frank
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8 CONCLUSION
·
I IO Bridging Veltman, and two anonymous reviewers for their helpful comments and suggests on previous drafts of this paper. Received 23.09.97 Final version received: I 5.05.98
NICHOLAS ASHER Dept. of Philosophy University of Texas at Austin Austin, Texas 7871z USA e-mail: [email protected] ALEX
N OTES ' In fact, we view the resolution of anaphora and the interpretation of presuppositions this way too (Asher & Lascarides I 998). We are aware that the proposed Russellian uniqueness condition is controversial, even when it comes in tandem with the restriction provided by B (x, u). We believe that one can uphold Russellian uniqueness in these citcurnstances, but it isn't essential to our account of bridging itsel£ We have also assumed here that the uniqueness condition is part of the asserted content, rather than being presupposed; the latter case would be represented by making the uniqueness condition anaphoric in some respect. We are in fact agnostic about what the correct status is for the uniqueness conditions of definites, but see Asher & Lascarides ( I998) for more detailed discussion of this issue. l In fact, this is a slightly modified version of the example in Poesio ( I994), in that we have put it in the past tense, rather than having a sequence of instructions.
•
•
s
6
We modify the example here because we want to ignore speech acts in this paper. Perhaps more seriously, these accounts also lack a general inference procedure for computing intentional structures from common-sense plans, and hence the ultimate discourse segmentation, which is assumed to be isomorphic to this intentional structure, is inferred by theory bound intuitions. For a detailed critique of this, see Asher & Lascarides (in press). Formulae like e0 and event(e0) are a notational 'gloss' for propositional formulae of the form
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LASCARIDES Centre for Cognitive Science and HCRC University of Edinburgh z, Buccleuch Place Edinburgh EH8 9LW Scotland, UK e-mail: [email protected]
Nicholas Asher and Alex Lascarides I I I 7 8
9
Thanks to Geoff Nunberg for this example. Note that this constraint involving >o is monotonic, and that > 0 can be axiomatized within a decidable system (e.g. conditional probability theory). If >0 is axiomatized using conditional probabilities, then the decidability of > remains unaffected. · Note that this won't affect the worst case complexity of DICE, and indeed from a practical perspective it may on occasion improve it because it will guide choices
10
1 1
about which rhetorical relation to aim for first when computing the discourse update. We don't formalize here the conditions under which a· topic is poor. For such a formalization, see Lascarides et al.
{I996).
For the sake of simplicity, we ignore the comparative nature of less, and gloss over the way one computes from the discourse context the set over which the comparison (or rental cost) is measured.
Asher, N . {1993), Reference to Abstract Objects in Discourse, Kluwer Academic Publishers, Dordrecht. Asher, N. (1996), 'Mathematical treatments of discourse contexts', in P. Dekker & M. Stokhof (eds), Proceedings of the
semantics and pragmatics of pre supposition', MS available from http:/I www.cogsci. ed.ac.uk-alex. Also to appear in journal of Semantics, Oxford University Press, Oxford. Asher, N. & Sablayrolles, P. (1995), 'A typology and discourse semantics for motion verbs and spatial PPs in French',
Asher, N. (forthcoming), 'The logical foundations of discourse interpretation'; inJ. M. Larrazabal (ed.), Logic Colloquium 1996, Springer Verlag. Asher, N., Aurnague, M., Bras, M., & Vieu, L. (1996), 'De l'Espace-temps dans l'analyse du discours', Semiotique:
Beaver, D. (1994), 'An infinite number of monkeys', Technical Report, ILLC, University of Amsterdam. Bos, J., Mineur, A-M., & Buitelaar, P. {1995), 'Bridging as coercive accom modation', Technical Report Number 52, Department of Computational Linguistics, Universitat Saarbruiicken. Briscoe, E. J., Copestake, A., & Boguraev, B. {1990), 'Enjoy the paper: lexical seman tics via lexicology', 13th International
Tenth Amsterdam Colloquium on Formal Semantics, ILLC Publications, University of Amsterdam, 2 I -40.
Numero Special Theories semantiques et modalisation, 9· Asher, N. & Lascarides, A. ( 1994),
'Intentions and information in dis course', in Proceedings of the ;znd
Journal ofSemantics,
·
12,
2, 163-209.
Conference o� Computational Linguistics Annual Meeting of the Association of (COLING-9o), Helsinki, 42-7. Computational Linguistics, Las Cruces, Charniak, E. (1983), 'Passing markers: a theory of contextual influence in lan USA, June 1994, 34-41. guage comprehension', Cognitive Science, Asher, N. & Lascarides, A. {1995), 'Lexical 7. 171-90. disambiguation in a discourse context', Chierchia, G. {1995), Dynamics of Meaning: journal of Semantics, 12, 1, 61J-I08. Anaphora, Presupposition, and the Theory of Asher, N. & Lascarides, A. (in press), Grammar, University of Chicago Press, 'Questions in dialogue', to appear in Chicago. Linguistics and Philosophy. Asher, N. & Lascarides, A. (1998), 'The Clark, H. {1977), 'Bridging', in P. N.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
9 RE FERE NCES
I I 2 Bridging !.ascarides, A. & Copestake, A. ( 1997), 'The pragmatics of word meaning', to appear in journal of Linguistics. !.ascarides, A. & Oberlander, J. ( 1993), Temporal connectives in a discourse context', in Proceedings of the European Chapter of the Association for Computa tional Linguistics (EACL93), Utrecht, The Netherlands, 26o-68. · !.ascarides, A., Copestake; A., & Briscoe, E. J. ( 1996), 'Ambiguity and coherence', journal of Semantics, 1 3, 1, 41-65. Lewis, D. ( 1979), 'Scorekeeping in a lan guage game', journal of Philosophical Logic, 8, 3 39-59. Matsui, T. ( 1995), 'Bridging and relevance', Ph.D. thesis, University of London. Poesio, M. ( I 99 3 ), 'A situation -theoretic formalization of definite description interpretation in plan elaboration dialogues', in P. Aczel, D. Israel, Y. Katagiri, & S. Peters (eds), Situation Theory and its Applications, Vol. J, 339-74· Poesio, M. ( 1994), 'Definite descriptions, focus shift and a theory of discourse interpretation', in Proceedings of the Conference in Focus on Natural Language, June 1994. Poesio, M., Vieira, R, & Teufel, S. ( 1997), 'Resolving bridging descriptions in unrestricted text', in Proceedings of the ACL97 Workshop on Operational Factors in Robust .(lnaphora Resolution, also HCRC Technical Report Number 87, HCRC, University of Edinburgh. Polanyi, L. ( 1985), 'A theory of discourse structure and discourse coherence', in Papers from the General Session at the Twenty-First Regional Meeting of the Chicago Linguistics Society, 25-7. Pustejovsky, J. ( 1991 ), 'The generative lexicon', Computational Linguistics, 17, 4, 409-41. Pustejovsky, J. ( 1995), The Generative Lexicon, MIT Press, Cambridge, MA. Russell, B. ( 1905), 'On denoting', Mind, 14, 479-93· van der Sandt, R ( 1992), 'Presupposition ·
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Johnson-Laird, P. C. Wason (eds), Thinking: Readings in Cognitive Science, Cambridge University Press, Cambridge, 4 1 1-20. Fernando, T. ( 1 994), 'What is a DRS?', in R Cooper & J. Groenendijk (eds), Integrating Semantic Theories II, Dyana Deliverable R2.1.B, 1994, also in Pro ceedings of the First International Workshop on Computational Semantics, Tilburg, 1994. von Fintel, K. ( 1994), 'Restrictions on quantifier domains', Ph.D. thesis, Uni versity of Massachusetts, Amherst, MA. Grosz, B. & Sidner, C. ( 1986), 'Attention, intentions and the structure ofdiscourse', Computational Linguistics, 12, 175-204. Grover, C., Brew, C., Moens, M, & Manandhar, s: ( 1994), 'Priority union and generalisation in discourse grammar', Proceedings of the 32nd Annual Meeting of the Associationfor Comp utational Linguistics (ACL94), Las Cruces, USA, 1 7-24. Heim, I. ( 1 992), 'Presupposition projection and the semantics of attitude verbs', journal of Semantics, 9, 3· Hobbs,]. ( r 979), 'Coherence and coreference', Cognitive Science, 3, 67-90. Hobbs, J. ( 198 5), 'On the coherence and structure of discourse', Report No. CSLI-85-37, Center for the Study of Language and Information, October 198 5. Hobbs, J. R , Stickel, M E., Appelt, D. E., & Martin, P. ( 1993 ), 'Interpretation as abduction', Artificial Intelligence, 63, 69- 1 42. Kamp, H. & Reyle, U. ( 1993), From Discourse to Logic: Introduction to Model heoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory, Kluwer Academic Publishers, Dordrecht Karttunen, L. ( 1974), 'Presupposition and linguistic context', Theoretical Linguistics, I, 18 1-94· !.ascarides, A. & Asher, N. ( 1993), 'Temporal interpretation, discourse rela tions and commonsense entailment', in Linguistics and Philosophy, 16, 437-93.
Nicholas Asher and Alex Lascarides I I 3 projection as anaphora resolution', journal of Semantics, 9, 4· Sanfilippo, A. (I992), 'Grammatical relations in unification categorical grammar', Lingua and Stile, Fall issue. Sperber, D. & Wilson, D. (I986), Relevance, Blackwell, Oxford. Stalnaker, R (I978), 'Assertion', in P. Cole (ed.), Syntax and 'Semantics, Vol. 9: Pragmatics, Academic Press, New York.
Thompson, S. & Mann, W. (I987), 'Rhetorical structure theory: a frame work for the analysis of texts', in IPRA Papers in Pragmatics, I, 79-I05. Verspoor, C. {I996), 'Lexical limits on the influence of context', in G. W. Cottrell (ed.), Proceedings of the 18th Annual Conference of the Cognitive Science Society, Lawrence Erlbaum Associates, New York, 1 1 6-20.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
