Journal of Semantics, Volume 1, Issue 1, 1982

JOURNAL OF SEMANTICS Volume 1 no. 1, 1982 SWETS & ZEITLINGER BV LISSE - THE NETHERLANDS 2000 - JOURNAL OF SEMANTI...

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JOURNAL OF

SEMANTICS

Volume 1 no. 1, 1982

SWETS & ZEITLINGER BV LISSE

-

THE NETHERLANDS 2000 -

JOURNAL OF SEMANTICS AN INTERNATIONAL JOURNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE

Pieter A.M. Seuren (Nijmegen University)

MANAGING EDITOR:

Peter Bosch (Nijmegen University)

EDITORIAL BOARD:

Leo G.M. Noordman (Nijmegen University)

REVIEW EDITOR

Rob A. van der Sandt (Nijmegen University)

CONSULTING EDITORS: J. Allwood (Univ. Goteborg),

J. Lyons (Sussex Univ.),

M. Arbib (U Mass. Amherst),

W. Marslen- Wil�on

R. Bartsch (Amsterdam Univ.),

J. McCawley (Univ. Chicago),

H.H. Clark (Stanford Univ.),

H. Rieser (Univ. Bielefeld),

Th. T Ballmer (Ruhr Univ. Bochum), J. van Benthem (Groningen Univ.),

(Max Planck lnst. Nijmegen),

B. Richards (Edinburgh Univ.),

G. Fauconnier (Univ. de Vincennes),

R. Rommetveit (Oslo Univ.),

P. Gochet (Univ. de Liege),

H. Schnelle (Ruhr Univ. Bochum),

F. Heny (Groningen Univ.),

J. Searle (Univ. Cal. Berkeley),

J. Hintikka (Univ. Aorida),

R. Stalnaker (Cornell Univ.),

H. Hormann (Ruhr Univ. Bochum),

A. von Stechow (Univ. Konstanz),

G. Hoppenbrouwers (Nijmegen Univ.),

G. Sundholm (Nijmegen Univ.),

St. Jsard (Sussex Univ.),

Ch. Travis (Tilburg Univ ),

Ph. Johnson-Laird (Sussex Univ.),

B. Van Fraassen (Princeton Univ.),

A. Kasher (Tel Aviv Univ.),

E. Keenan (UCLA and Tel Aviv Univ.),

Z. Vendler (UCSDJ.

Y. Wilks {Essex Univ.),

S Kuno (Harvard Univ.),

D. Wilson (UCL).

W. Levelt (Max Planck lnst. Nijmegen),

ADDRESS:

Journal of Semantics, Nijmegen Institute of Semantics, P.O. Box 1454, NL-6501 BL Nijmegen, Holland

Published by the N.I.S.

Foundation, Nijmegen Institute of Semantics, P.O. Box 1454,

NL-6501 BL Nijmegen, Holland

ISSN 0167- 5133

C> by the N.I.S. Foundation

Printed in the Netherlands

CONTENTS page Editorial statement

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Johan van Benthum and Jan van Eijck The dynam1cs of mterpretatJOn .

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S.C. Garrod and A.J. Sanford The mental representation of discourse m a focussed memory system: Implications for the mterpretatJOn of anaphonc noun phrases . . . • . .

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S.- Y. Kuroda Indexed predicate calculus .

Susumo Kuno PnnCJples of discourse deletiOn case studies from English, Russ1an and Japanese . . . • .

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61

EDITORIAL STATEMENT

It is the central aim of the JOURNAL. .OF SEMANTICS to promote studies in the semantics of natural language. In our century, natural language semantics was, till quite recently, the property of a number of individual disciplines, especially philosophy, linguistics, psychology. What these disciplines offered, in this re�pect, hardly ever went beyond their own boundaries. This is now changing, and the change seems to be rapid. There is a growing awareness that by an interdisciplinary approach solutions are beginning to come into sight for problems that seemed to lie beyond the reach of the respective disciplines in isolation. Moreover, in this climate of cooperation, new problems, or which had resisted exact whose existence was either unknown formulation, are now coming more sharply into focus. Natural language semantics is becoming the common conc:ern of students of philosophy, linguistics, psychology, artificial intelligence, although there still are important differences in method and outlook.

One area where the recent trend toward integration in semantic studies is particularly manifest is discourse phenomena. Philosophers, psychologists, linguists , and students of ar. t ificial intelligence alike seern to feel that the structures and processes involved in the compre hension of texts as orderly accumulations of information·, against JS, vol. l , no. I

Downloaded from jos.oxfordjournals.org by guest on January 1, 2011

In a very literal sense, an autonomous field of studies is constituting itself. We wish to sti mulate this development and promote further integration of the disciplines involved in so far as they concentrate on questions of comprehension and interpretation of linguistic utter ances. We shall welcome contributions, in the form of articles, discus sions or reviews, furtheri ng this aim. This means that the JOU RN AL is intended to be a proper forum not only for more strictly disciplinary studies, as long as they can be read by wider circles of readers, but also for studies on linguistic semantics that go across disciplinary boundaries. It is in the combination of contributions and readership that we hope to cultivate a climate of fruitful interaction and integra tion.

a background of information available through perception or memory, and of mutual knowledge of a "contract" between communicative interactors, are somehow crucial for a better understanding of all kinds ·of semantic phenomena. For this reason, the N IS-Foundation, who publish the JOU RNAL, organized a Colloquium on Discourse Representation in Cleves, September 1 5 - 1 8, 1 9 8 1 .* A number of the papers presented there have resulted in articles, which are distrib uted over the first volume of the JOURNAL. As a matter of policy, we aim at an appropriate balance between the occasional thematic issue and issues containing arbitrary collections of articles and discus sions. This having been said, we can only express our hope and our confi dence that the start of the JOURNAL wtll prove to be propitious. The Editors

2

The Colloquium was made possible by a grant from the Philosophy Faculty of Nijmegen University, which is hereby gratefully acknow ledged. JS, vol. l , no. l


*

THE DYNAMICS OF INTERPRETATION*

Johan van Benthem and Jan van Eijck Abstract

1.

The logic of discourse representation

Two sources of confusion threaten the theory of discourse representa tion: the picture analogy and the careless use of 'semantic tableaus'. Both will be discussed here, in order to create room for a proper enterprise. Next, it will be shown how the current vogue of 'partial models ' (cf. Barwise ( 1 98 1 ), Humberstone ( 1 981)) is related to the first issue. Various suggestions will be made for further connecting research. 3

JS, vol. l , no.l

•


In current semantic theory compositional interpretations are assumed to go from linguistic items to their denotations in some model. This perspective still leaves room for a more dynamical account of how such interpretations are actually created. One natural idea is to assume that each sentence in a discourse is understood through some represen tation, 'mediating' between the language and its models. Thus, the old relation of interpre tation splits up into two new ones, viz. that between linguistic items and their representations, and that between these representations and actual models. Now, at the Cleves conferen ce it was clear that discourse representations are many things to many people. Some view them as syntactic constructs, some as psycho logical ones (yet others prefer to remain confused over this issue). Again, one popular me taphor is that of the partial picture of reality, another that of a procedural recipe for verification. Finally, these representations are supposed to e.rplain such diverse phenomena as anaphora and progressive discourse information. It is not obvious that one coherent notion could do all these jobs. On the other hand, it is not obvious either that one need not try. The purpose of this paper is to clarify some logical issues concerning discourse representa tions, while trying to bring together two of the main themes at the Cleves conference, viz. representation proper and the topic of partial information. General considerations will be found in section 1; section 2 contains applications and illustrations drawn from the two best-devel oped formal paradigms of discourse semantics (cf. Hintikka (1979), Hintikka &. Carlson (1979), Kamp (1981)). It is our contention that more clarity as to the nature and the purpose of discourse representa tion will unite, rather than divide the various currents in this develop ing area.·

VAN B ENTHEM & VAN EIJCK 1 .1

The danger of pictures

Despite the well-known defects of a Wittgensteinian picture theory of language, there is an almost irresistible urge to describe �he division of semantic labour as follows. Each sentence induces a discourse representation, such that truth of the sentence in a model amounts to embeddability of that 'picture' into that model. Now, the term 'embedding' may have various senses. But, even for a quite wide range of such senses, this idea is demonstrably inadequate: Let us assume that our theory assigns, to each sentence S, some discourse model DR(S) such that, for all models M, S is true in M iff DR(S) can be embedded into M. If such an account works at all, it would work for predicate-logical sentences S, one should think. But, a fundamental limitation now reveals itself. Proposition: The only predicate-logical sentences to which the embed ding account applies are (equivalent to) purely existential ones, con structed from (negations of) atomic formulas using only and, or, and there exists. ·

Before one starts protesting, let it be noticed that many of the 'scenarios' in psychological discourse experiments consist ·of such purely existential sequences. ( ' A gentleman entered a shop, and· pro duced a gun ') Another instance is provided by an apparently univer sal counter-example (put forward by Han Reichgelt): A madeus has a horse and Dorothea has a horse, and all these horses bite. A closer look reveals that an equivalent purely existential sentence exists: A madeus has horse that bites, and Dorothea has a horse that bites. •••

We may conclude that a more complex account is needed of the desired relation between discourse representations and actual models, if truth of the original sentence is to be mirrored. And indeed, e.g., Kamp ( 1 98 1 ) has a definition of 'embeddability' which contains essen tially all the machinery of the old Tarski truth definition. There may be interesting intermediate possibilities, however, for the relation between DR(S) and M. For instance, the 'picture' metaphor could also mean something like a 'blurred ' or 'coarse' image, which would be reflected more accurately in the requirement that DR(S) be a homomorphic image of M. (Again, in such cases, model-theoretic preservation results set limits to the faithful rendering of truth.)

4

•

JS, vol.l, no.l


Proof: Observe that if S is true in M and M' extends M, then S is true in M'. (For, if DR(S) is embedded into M, it is, a fortiori, embed ded into the larger M'.) In other words, 5 is 'preserved under exten sions', and by the -los-Tarski theorem of model theory, all such sen tences are logically equivalent to purely existential ones. Q ED.

THE DYNAMICS OF INTERPRETATION But, one might also want to strengthen embeddability to elementary embeddability (which would block the above preservation argument). This possibility will be explored below. Thus, the subject of suitable links between discourse representations and the usual semantic models offers a rich variety of choices to be explored, even though the most simple-minded one has been shown to fail. 1 .2

The ubiquity of semantic tableaus

Since their invention by E. W. Beth and others in 1 955, semantic tab leaus have been put to various uses in logic and philosophy. And indeed, the psychological and mathematical speculations in Beth &: Piaget ( 1 966) foreshadow the present 'discourse representation' ideas to a great extent. The analogy is compelling: tableaus represent existen tial truths by means of discourse referents just as moderno authors would have it. And the same goes for the branching storage of disjunc tions, as well as other connectives.

For example, a universal quantifier is treated differently in the two cases. It will get an abstract 'generic' representation in a struc ture tree; whereas, in a semantic tableau, it becomes a standing instruction to introduce requirements for new individuals in the tab leau. Or, to demonstrate the difference from yet another angle, for the purposes of anaphora, the following sentence is a perfectly ordinary case: Some woman loving no one is loved by all women she does not love. It is only the tableau analysis wich reveals its contradictoriness (which does not prevent it from having anaphoric relations). Nevertheless, semantic tableaus are extremely interesting in the earlier perspective of 'little models' . For one thing, open tableau branches are themselves models for the original se�tence: the analysis has been pushed through completely, while no contradictions occurred. (We are referring here to familiar completeness proofs in terms of semantic tableaus.) More precisely, each open branch in a completed tableau for a sentence S of predicate logic represents a class of JS, vol . l , no. I

.5


It is very tempting, then, to think of semantic tableaus as prime candidates for discourse representations - a tendency which is rein forced by tableau-like terminology in many expositions (cf. Kamp ( 1 98 I )). Nevertheless, one should be extremely careful here, distin guishing between various uses of discourse representations. As will be shown in section 2 of this paper, applications to topics such as anaphora usually necessitate a rather syntactic representation, close to the structure trees of sentences in a dis.course. On the other hand, analyses of discourse information require a kind of 'thinking' interpre tations, combining and comparing the requirements upon models ex pressed by various components of the sentences. This is the area of semantic tableaus proper.

VAN BENTHEM & VAN EIJCK models verifying S, whose domain equals any set of individuals i for which a discourse referent d occurs on the branch, and whose interpre tation verifies atomic form J las on the 'true' side of the branch, while falsifying those on the 'false' side. (There is usually quite some margin here, as not all atomic for_mulas need be decided on the branch.) There is a price to be p aid for this, of course: open tableau branches may be (irremediably) infinite. Are these 'branch models' for a sentence S somehow 'representative' for all models of S? In a sense, they are, and we find to our surprise that there exists a kind of 'embedding' connection after all - circum venting the proposition in section 1.1: Proposition: A predicate logical sentence S is true in a model M if and only if M is an L(S)-elementary extension of some branch model for S. Proof: (L(S) is the sublanguage of the full L consisting of S together

·

A comment is in order here. The preceding theorem is easily extend ed to cover the case where L(S) is the full sublanguage of L generated by the non-logical vocabulary of S. (One has to enrich the tableau for S in some standard fashion, alternating applications of tableau decomposition rules with introduction of Excluded Middle formulas S' or not S ' for all S ' in some fixed enumeration of L(S).) But, the simpler form given here stays closer to the idea of using nothing beyond the components of the represented sentences. Essentially, the above theorem may be found in Kreisel, M ints & Simpson ( 1 97 5), section 1, 1 , and in Pra�itz ( 1 975), section 3. What does such a formal theorem about predicate logic tell us concerning natural language in general? Well, at least we see that the 'dangerous' embedding idea is viable formally, when taken in 6

JS, vol . l , no. l


with all its subformulas.) ' If ' : S is true in all its branch models, and hence in all their L(S) elementary extensions. 'Only if': Suppose that S is true in M. We associate a tableau branch with M by choosing nodes in the complete tableau tree for S, together with an assignment of real individuals in M to d-iscourse referents in the tableau, such that M verifies all formulas on the ' true' side of these nodes, while falsifying all those on the ' false' side. (This can always be done, starting from a single true S in the topnode, by following the tableau-rules, using actual truth (or falsity) in M to make decisions at v -branchings and choices at l-representations.) Now, the set of all individuals in M assigned in this way forms a submodel M' of M which is a branch model for S. Moreover, by the above construction, M is an L(S)-elementary extension of M'. For, occurring on the true (false) side decides truth (falsity) in M, M' in the same way. Q ED.

T H E DYNAMICS OF INTERPR ETATION some appropriate sense. (The succes of quite different forms of tableau embedding, witness Rodenburg ( l 98 I ), only reinforces this point.) Thus, one has a guide-line as to which directions of thought concerning the semantic role of representations are worth exploring - while avoid ing the dead alleys closed off by our first theorem. It remains to be repeated that this result employs infinite representa tions in general. If one insists on finite discourse representations, then, e.g., instead of spelt-out V'l-dependencies, one will have to represent rules (say, as Skolem functions). Thus, the recipe metaphor will be re-instated over the picture idea; as in Hintikka's game-theoreti cal semantics (ct. section 2 of this paper). Let us summarize the kind of enterprise emerging from the previous considerations in the following picture: --

partial discourse discourse representation - model

L---�

1.3

Partial models

Possible world semantics is losing favour with the semantic community. A possible world is an idealized complete state of affairs (or a total state of information concerning such a situation). From various direc tions, 'partial' alternatives are gaining ground (cf. Barwise ( 19 8 1), Humberstone (1981) but the idea is a!rea4:ly found in the early seven ties with Kit Fine's work on relevance logics). Indeed, forcing seman tics for intuitionistic logic has always been a semantics of growing partial information sets (despite the formal analogy with complete world structures). Thus, the idea of using partial models and partial information is in the air. -

At the Cleves conference, a psychologist suggested an even more radical move, pleading for partial individuals. Again, that idea is fore-shadowed already in current interval tense logics: intervals may be thought of as partial temporal individuals, which have not yet made up their minds about the precise points they are going to be (cf. Van Benthem ( 1 982)). We will return to this example below. Now, these ideas may lead us to a road diverging somewhat from the enterprise outlined above. For, a radical representationalist might just as well forget about the 'actual models', and formulate a truth definition directly on the partial discourse models (say, in the context JS, vo!. ! , no. !

7


The first arrow may stand for an algoritmic production, the second for a tableau-like analysis, the third is the beckoning 'picturesque' link between 'representation' and 'reality ' . Whether there are more intermediate stages of representation to be distinguished will depend on intended applications.

VAN BENTHEM & VAN EIJCK of all possible such models). Various clauses are possible here, most of them with a non-classical ring. For instance, negation will probably be treated intuitionistically as 'absence of truth in all possible exten· sions'. Or, to mention a more suggestive case, disjunction need not be distributive any more over partial models: one need only require that a choice between the disjuncts be made 'eventually ' . (Let it be noticed, however, that the terms 'intuitionistic' and 'classical' are rather treacherous in this area: the above clause for disjunction has again classical effects!) For those who dislike this intUJtlOOJStlC turn, there is another road, again suggested by semantic tableaus. When showing that 'true' ( 'false') branch formulas are verified (falsified) in branch models, one is led naturally to think of both truth and falsity as complementa ry, and necessary notions. Thus, one might also start with primitive notions of 'verifying' and ' falsifying' for partial models, which leads to a classical negation. (Cf. Veltman (198 1).)

Theorem: For predicate-logical sentences S, , S21 where S2 is a. sentence in the vocabulary of S , , S, implies 52 if and only if S 2 actually occurs on the true side of each open branch of the S. -tableau.

Proof: 'Only if': Branch models of S, verify S , and hence also �. Therefore, not-S 2 cannot occur on the true side of any open branch - whence s2 does. 'If': If M is an arbitrary model in which S, is true, then - by the earlier theorem - M contains an L(S, )-elementary submodel M' which Now, S 2 occurs on the true side of the is a branch model for S, M'-branch, whence it is true in its L(S, )-elementary extension M. Q ED. •

Again, the message of this formal result is that Seuren's suggestion may at least be viable in some interesting sense for natural language - something which came as a surprise to (at least) these authors. 1 .4

Semantic reunion

The diverging picture which has arisen may now be re-united thus:

8

JS, vol. l , no. l


That these partial discourse models may indeed be all we need to know was also suggested by the colloquium organizer Pieter Seuren, who conjectured that even !ogical consequence may be captured ade quately at this level already. And as it happens, at least at the level of semantic tableaus, this is true. It is true in the trivial sense that S, implies S2 if and only if (S , and not S2 ) has a closed semantic tableau (for predicate logical sentences S, , S 2 ). But, it is also true in a more interesting sense, for tableaus in the extended form men tioned in connection with the preceding result.

THE DYNAMICS OF INTERPRETATION

discourse representation

partial discourse model

As Jaakko Hintikka urged the partiCipants to do, one should look for connections here. For example, there is the 'super-valuation' impulse of striving for connections of this kind: 'S is true in a partial model if and only if it is true in all its com· plete extensions to actual models.'

T o show that t h i s goal does not represent a n idle hope, here are two results from Van Benthem (1982) confirming this message for the case of interval tense logic. Modulo some technical background conditions, ( l ) a tense-logical sentence is (interval-)true at an integer interval if and only if it is (point-hrue at all in tegers w i t h i n that interval, (2) a tense-logical sentence is (interval-)true at an open rational interval if and only if it is (point-hrue at most r a t ionals within that in�erval (i.e., in all of them up to some finite number of exceptions). It is our hope that results like these (and the previous ones) indicate some lines along which integrative research will be done, while avoid ing some of the logical road-blocks awaiting earlier formulations of the nature and pretentions of discourse representations. 2

Two paradigms investigated

Two theories of discourse representation that have left the programma tic stage are those of Jaakko H intikka and Hans Kamp. (Henceforth, familiarity is presupposed with H intikka (1979), H intikka & Carlson (1979), and Kamp (1981).) These will now be analysed in the spirit of the preceding section. Striking formal resemblances come to light, even when empirical predictions may differ. (As both theories share a concern with anaphoric relations, this topic will be the focal exam ple.) It will be seen how this type of theory fits into the earlier meth odological chart, and some morals will be drawn from that awareness. JS, vol. l , no. I

9


Usually, the partial truth definitions and classical truth will not connect up as simply as this. But, the idea motivates a ' target equiva lence' which may well become extremely fruitful for further research: 'S is true in a partial model DM(S) if and only if the set of complete actual models M bearing a suitable 'embedding' relation R to DM(S) is suitably large . '

VAN BENTHEM & VAN EIJCK 2.1

H intikka's games

Pictures and games When it was remarked at the Cleves conference that some discourse representationalists are guided by a picture metaphor, while others view their constructs as procedural recipes for verification, Jaakko Hintikka replied that his game-theoretical semantics combines both view-points: it provides recipes for making pictures . N e v e r t heless, the connection between the rather procedural game-theoretical seman tics and a picture theory is less intimate than this reply suggests. And indeed, the discussion of W ittgenstein in Hintikka (1976) contains no more than an invitation to think of the relation between atomic s e n tences and the facts in a model a s pictural link.

In game theory proper, a strategy is a function from possible game situations to possible game situations, telling a player at every stage what to do next. These strategies are usually finitely representable in a 'game tree', since a player has only finitely many moves available, and the game has a limited length (either inherently, as in poker, or through some stipulation, as in chess). Many theorems of game theory depent vitally on this finiteness of the set of available strate gies for the participants. But, H intikka's strategies that play such a conspicuous role in his theory cannot be finite objects in general. When a language is played relative to an infinite model, the relevant 'Skolem functions' wiU have to encod� infinitely many possible moves. This observation may also explain the absence of any significant applications of game-theoretical results i n s i d e H i n t ikk a ' s theory. The preceding diagnosis does not imply that n o significant mathemat ical theory is possible about infinite strategies. For instance, there exist some deep foundational studies in logic concerning the so-called 'Axiom of Determinateness', which states that all two-person games on the natur-al numbers provide a winning strategy for one of the plavers. But of such notions and results, one finds no trace in game-

10

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Talking about analogies, the link between game-theoretical seman tics and the mathematical Theory of Games is also less intimate than Hintikka has it. H is semantic truth/falsity games are extremely simple zero-sum games of a complexity below the treshold where Von Neumann started creatin� the mathematical discipline of game theory. (E.g., the original Mmimax Theorem is already about the existence of 'equilibrium choices' of strategies for two players: a topic beyond the pale of game-theoretical semantics - at least, in its present state.) Moreover, many theorems of game theory proper belong to finite combinatorics. This fact reflects another important difference, which may be illustrated by ·considering the following key notion in any study of games.

THE DYNAMICS OF INTERPRETATION theoretical semantics either. Whichever way one looks at them, 'seman tic games' remains, at best, a suggestive metaphor. Games and truth

In game-theoretical analysis, truth means the existence of some win ning strategy for Myself (against Nature), with respect to a (total) model M. As was noted above, the nature of M may require infinite strategies. Again at the Cleves confence, it was suggested that this problem might be circumvented by withdrawing to the representational level, restricting the domains of universal quantification to already available (finite!) sets of discourse referents. But, such a way-out amounts to doing away with universal quantification altogether. Sen tences with only such pseudo-universal quantifiers reduce to purely existential ones, as was noticed in section 1. I. Hintikka-trees and discourse representations

not A·

•

!A A and B A.

A!

s.

•

•

M / \ ·A B·

JS, vol.l, no.l

.A and B

•

N / \

i f A, then B

not A

/M\ A .s •

i f A, then B

/\ N

A

B

11


Fortunately, no concrete strategies with respect to some actual model need occur in completely informative representations o� the above semantic games. The gist of the game rules can be captured in the following finite tree-format. Put sentences defended by Myself (M) (i.e., attacked by Nature) to the left of a node, sentences defended by Nature (N) (i.e., attacked by Myself) to the right. Mark choices with the name of the player that is to make them. Then, the game instructions build trees according to the scheme

VAN BENTHEM

&

VAN

E IJCK

every X that Y's Z's if a is an X and a Y's, then a Z's some X that Y's Z's

N

M

I

I

M

N

I

a is an X, a Y's and a Z's

I

every X that Y's Z's if a is

an

X and a Y's,

then a Z's-

some X that Y's Z's

a is an X, a Y's and a Z's

Trees and tableaus

The above instructions for negation, as well as those for the quanti fiers bear a close resemblance to Beth-type tableau rules. This goes a long way to explain the almost universal feeling that there must be a close connection between the two. Nonetheless, the above 'Hintik ka-trees' (H-trees, henceforth) that were associated with natural language sentences behave very differently from serT)antic tableaus, as the following example will show. One possible reading of the sentence

Everyone loves himself, and not everyone loves someone.

has the following H-tree:

everyone loves himself, and not everyone loves som everyone loves himself a loves a

� •

•

7� � not everyone loves someone

I

•

M everyone loves someone I N b loves someone I •

12

b loves c

JS, vol.l, no. I


The atomic sentences A arrived at eventually are then to be checked, with the winning convention that: M wins if A occurs to the left (right) and it turns out true (false), N wins if A occurs to the left (right) and it turns out false (true).

THE DYNAMICS OF INTERPRETATION Notice that no strategies are indicated for the players (after all, no specific model M is present). The tree only indicates which player has to move and what his options are. As such; it does not provide the information that this sentence happens to have a winning strategy for Nature in all models. But a Beth tableau for this sentence will 'close', revealing its inconsistency as follows. everyone loves himself, and not everyone loves someone everyone loves himself, not everyone loves someone everyone loves himself

•

I

•

I •

a loves someone

I ! a loves a

.

Thus, in a sense, 'Beth tableaus reflect upon Hintikka trees': they reason about strategies. In this particular example, the tableau teJJs us that the assumption that Myself has a winning strategy would lead to a contradiction: it follows that Nature has a winning strategy in all cases. More concretely, the above H-tree ·opened with two options for her. The Beth tableau tells N that at least one of these will be a winning one (although it does not say which one: that will depend on the particular model M). Nevertheless, why then the persistent tendency to also view Beth tableaus themselves as a kind of game? The reason is that they amount indeed to games of a rather different kind (closer to those envisaged in game theory), studied in the logical 'dialogue theory' of Lorenzen & lorenz ( 1978). This connection will not be pursued here. Summing up, the H-trees are syntactic analysis trees, doing the usual jobs such as determining relative scopes of operators, whilst also providing some information concerning verification of the sen tence. It is the latter feature which makes for their interest in the following application. Anaphora

Hintikka sees a wide range of applications for his game-theoretical semantics: this many-purpose tool treats scope-phenomena in the JS, vol.l, no.l

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a loves a

everyone loves someone

VAN BENTHEM

&

VAN EIJCK

behaviour of 'any' just as easily as issues in the meaning of knowledge and belief. For purposes of comparison with Kamp's theory, we demon strate its way of handling anaphoric phenomena. Linguists usually distinguish between anaphora at sentence level and anaphora crossing sentence boundaries. Concerning the first kind, Hintikka has not all that much to say: as in most logical seman tics, the !-{..:tree-rules for the quantifiers introduce ordinary bindings. (If anything, an account of the relevant anaphoric possibilities is presupposed here.) In order to account for anaphora in if-then sentences, or across sentences, the H-tree instructions are to be read according to the 'Progression Principle' (Hintikka & Carlson ( 1979)), p�escribing an order of playing from left to right. For instance, the qrdinary propositional rule for if-then, amounting to my choice of attacking the antecedent or defending the consequent, now assumes the following form if A, then B

If a soldier owns a gun, he cleans it.

The succesful N-strategy consisted in producing an example of a soldier with his gun, and these are now available for backward refer ence. Even more spectacularly, If every soldier owns a gun, some soldier cleans it.

may be explained likewise. Nature's strategy produces a gun for every soldier, and this function is triggered by the phrase 'some soldier' to provide a referent for 'it'. This simple story is very attractive, but also very implausible. If the Progression Principle means that one 'subgame' is played for A, after which the players (may) move to B, then Nature's winning strategy cannot be known. For, such a strategy involves typically all N's responses to moves of Myself, which cannot be divulged in a single play. (One would have to play all possible games concerning· A.) Thus, there is a dilemma: either we have a natural course of the game, without full strategies available, or we have the latter without the former. Our point remains the same as before. Having the full strategies 14

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The semantic story accompanying the tree now goes as follows. First, we play the A-game. Either M can win, and the game is over, or M ·cannot win. In the latter case, N has divulged a winning strategy for A, which M can use now to his advantage in the second round, when he defends B. This story explains the anaphora in

THE DYNAMICS OF INTERPRETATION available is unrealistic, but also unnecessary. All predictions concern ing anaphoric possibilities in connection with the Progression Principle can be formulated entirely at the level of H-trees: it is enough to know which positions on the left branch are available as anteced ents to which positions on the right branch. More precisely, the rule mi�ht be that an individual in the left branch of the H-tree for an if-then sentence that results from an N-choice after a certain (possibly empty) number of M-choices of individuals, can s e r v e a s a n least antecedent for anaphora occurring i n the right branch after a t that number of M-choices. (This is for purposes o f illustration only. As it stands, the rule is certainly not correct - even discounting pragmatic disturbances.) The strategy story then remains, in the background, as a semantic motivation for these predictions. This is a mere methodical point, of course. The vagueness of the above strategy account is not removed. (E.g., what are suitable triggers? Can a triggered occurrence still exhibit an anaphoric ambiguity?) But then, this is not a paper about anaphora. 2.2

Kamp's discourse structures

Kamp (1981) opens with the promise that his theory may yet provide the missing link between formal semantics and the psychology of linguistic competence: "(. . . ) discourse representations can be regarded as the mental representations which speakers form in response to the verbal inputs they receive. " (p. 282)

Moreqver, a 'radical departure from existing frameworks' is needed, giving rise to the following attractive notion of truth:

"A sentence S, or discourse D, with representation m is tn.te in a model M if and only if M is, compatible with m; and compatibility of M with m, we shall see, can be defined as the existence of a proper embedding of m into M, where a proper embedding is a map from the universe of m into that of M which, roughly speaking, preserves all the properties and relations which m speci fies of its domain. " (p. 278)

We are not qualified to pass judgment upon the psychological ·connection; though it should be remarked that procedural models (as opposed to pictural embedding metaphors) seem to enjoy the ascendancy in current psychology. About the account of truth, more can be said straight-away. Embedding and tn.tth

'Roughly speaking ... '. Upon closer inspection, Kamp's formal defini tion of a 'proper' (or 'verifying') embedding turns out to depend recursively on the complexity of the sentence, introducing quantificaJS, vol.J, no. I

1.5


Model theory and psychology

VAN BENTHEM &: VAN EIJCK tion over such embeddings for each layer of universal quantifiers or if-then constructs. For instance, the following sentente (from Kamp's fragment) If a soldier loves Mary, every widow hates him

will be interpreted eventually as follows. - There exists an embedding f of 'Mary' into the model such that - for every embedding g extending f by assigning a soldier that loves f ('Mary') to 'a soldier' it holds that - every embedding h compatible with g and assigning any widow to 'every widow' will result in that widow hating g ('a soldier'). · Anyone who has taken the trouble of writing out the successive clauses of a Tarski-type truth definition with the full paraphernalia of a s s i g n ments will recognize essentially the same complexity in both cases.

Discourse tableaus

Kamp's 'discourse representation structures' (DRS's) are presented in the familiar tableau-terminology of introducing 'discourse referents'. (Even some of the didactic recommendations are reminiscent of intro ductory logic courses using semantic tableaus.) Still, a DRS is more like a structure tree: as in the Hintikka case, no analysis takes place of the information in the constituents. This point is brought out more clearly by a comparison between Kamp tableaus and Hintikka trees. Instead of losing ourselves in the dreary formalistic details attaching to any explie:it tableau method, let us consider an example, viz. the above soldier-senten��. Its H-tree and its DRS (modulo some technical ities) are given below. The similarities are so obvious that they hardly need spelling out. A technical comparison (not displayed in this paper) will show the following correspondences: to each DRS, there corresponds an H-tree such that the DRS is successfully embeddable in a model M if and only if the H-tree allows for a winning M-strategy with respect to M. not every H-tree is thus derivable from a DRS. The reason behind the second observation is simply that Kamp's frag16

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This is not to say that Kamp's truth definition via embeddings is not original. It handles nasty cases of anaphora which Tarski's account does not cover. But the main point here is that 'compatibility' and 'embedding' turn out to introduce essentially the same complexity into the link between discourse representations and actual models that one had in ordinary logical semantics. Admitte�ly, there is a borderline case where the above embedding idea does work out precisely as promised in the introductory quotation. That case occurs when the discourse contains no universal phrases or if-then s e n t e n c e s; i . e . , when it consists of a sequence of purely existential sentences. And we are back at the theorem of section 1 .1.

THE DYNAMICS OF INTERPRETATION ment does not treat negation and disjunction, which allows him to get by with 'one-sided' tableaus, where H-trees are essentially 'two sided' (containing M- and N-roles). If Hintikka's fragment were restrict ed in a similar manner, H-trees could be simplified so as to leave M-defensive-actions only.

?��

if a soldier loves Mary, eveove type of sen tence. (The formal analogy between Kamp's 'up-left' rule fo� admissible antecedents and Reinhart's choice of a domain through the c - c o m m a n d relation appears to be accidental, on closer inspection.) Still, an illuminating contrast comes to light between H intikka and the linguists on the one hand, and Kamp on the other. Kamp claims that his theory provides a uniform treatment of aJJ kinds of anaphoric relations. This runs counter to the accepted linguistic division, implicit ly acknowledged by H i ntikka, into ( l ) pronouns that permit a bound variable interpretation, and (2) those that have to be interpreted refer entially (cf. Evans (1980)). Thus, e.g., most linguists consider the follow ing example (in Kamp's fragment) structurally ambiguous: Every soldier who loves a widow who loves him is happy. Either 'him' is bound by 'every soldier ' , or the pronoun refers to an individual mentioned previously in discourse; note that we cannot tell what the H-tree for the sentence looks like before this ambiguity is removed. Kamp, however, leaves it to the DRS to settle the differ ence. So, while Hintikka and Kamp both need an autonomous level of sentence syntax as input for their 'discourse syntax ' , they disagree on the whereabouts of the dividing line between the two.

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· The above 'rapprochement ' between the theories of Hintikka and Kamp has passed by some obvious differences in their over-all approach. Notably, H intikka only gives some discursive examples of how games are to be associated with surface (but then again, not quite surface) sen tences; whereas Kamp' s achievement resides to a great extent in an al�orithmic production of DRS's for sentences in a certain well defined fragment. On the whole, the greater credit must go to Kamp here; because it remains exceedingly difficult to establish just what is the scope of the game analysis. Nevertheless, Hintikka's looseness may be more natural in the sense that only the order of playing deter mines scope relations, not some pre-given syntactiC analysis. So, one sentence can get several H-trees. But then, such a modification is easily introduced into the Kamp approach as well, say through some Montagovian relation R.

THE DYNAMICS OF INTERPRETAT ION These considerations suggest the following way to fit a Hintikka/ Kamp enterprise into the methodological scheme of section 1 .2 : discourse

discourse representation

consisting of sentences f-structured by 'sentence syntax'

a supplementary structure provided by 'discourse syntax' ('enlightened H-trees' or 'Kamp DRS's')

actual models

'winning M-strategy' 'truthful embedding'

Rijksuniversiteit Groningen Filosofisch Instituut . Westersing�l 1 9 97 1 8 CA GRONINGEN

Note

This paper arose out of a paper read at the Cleves colloquium on Discourse Representation and the ensuing discussions. We would like to thank in particular Barry Richards and Goran Sundholm for their helpful comments. Part of the research for this paper was sponsored by the Netherlands Organisation for the Advancement of Pure Research (ZWO), �rant no. 22-65. *

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Sceptics might argue that, since all the action seems to occur at the middle level, the semantical part is just a ritual addition. But, as we have seen, this misses a vital point: semantic interpretation procedures turned out to motivate the workings of our discourse repre sentations. What is true, however, is that the semantical part remains rather traditional, in that the usual total models are assumed in the background. Apart from a sympathetic, but cryptic reference by Kamp to Veltman ( 1 98 1 ), there are no signs of a more radical break with traditions by having a partial semantics, closer to the discpurse represen tations themselves. So, the next task for the proponents of a rigorous, but radical theory of discourse representation lies straight ahead.

VAN BENTH E M & VAN EIJCK References

·

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of Philosophy. Barwise, J., 198 1 : Scenes and other situations. Journal 78.7; .:69-397. Beth, E.W. & Piaget, J., 1966: Mathematical Epistemology and Psychology, Reidel, Dordrecht. . Evans, G., 1 980: Pronouns. L inguistic Inquiry, II; 337-362. H intikka, J., 1 976: Language-games. In: Essays on Wittgimstein in Honour of G. H. von Wright, North-Holland, Amsterdam. Pp. 105- 1 25. Hintikka, J., 1979: Quantifiers in natural languages: some logical prob lems. In: H intikka et al. (eds.), Essays on Ma the m a t ical and Philosophical Logic, Reidel, Dordrecht. Pp. 295-314. Hintikka, J . & Carlson, L., 1979: Conditionals, generic quantifiers, and other applications of subgames. In: Avishai Margalit (ed.), Meaning and Use, Reidel, Dordrecht. Pp. 57-92. Humberstone, L, 1 9 8 1 : From worlds to possibilities, Journal of Philosoph ical Logic, 1 0; 3 1 3-340. Kamp, H . , 1 9 8 1 : A theory of truth and semantic representation. In: J. Groenendijk et al. (eds.), Formal Methods in the Study of Language, Mat hematical Centre, Amsterdam, vol. I. Pp. 277-322. Kreisel, G., M ints G.E. & Simpson, S.G., 1 975: The use of abstract language in elementary Metamathematics: some pedagogic examples. In: A. Dold & B. Eckmann (eds.), Logic Colloquium, Springer, Lecture Notes in Mathematics 453, Berlin. Pp. 38- 1 3 1 . Lorenzen, P . & Lorenz, K., 1978: Dialogische Logik, W i s s e n s c h�f t l i c h e Buchgesellschaft, Darmstadt. Prawitz, D., 1 975: Comments on Gentzen-type procedures and the classical notion of truth. In: A. Dold & B. Eckmann (eds.), Proof Theory Symposium, Kiel 1974, Springer, Lectures Notes in Mathematics 500, Berlin. Pp. 290-3 1 9. Reinhart, T., 1976: The Syntactic Domain of Anaphora. Unp u b l i shed Ph. D. disser�ation, M.I.T. Reinhart, T ., 1980: Coreference and bound anaphora: a restatement of the anaphora questions. Un�ublished typescript, Max Pianck-Institut, Nijmegen. Rodenburg, P.; 1 9 8 1 : Intuitionistic correspondence theory. Report, Mathematlsch Instituut, U niversity of Amsterdam. Van Benthem, J .F .A.K., 1 982: The Logic of Time, R e i d e l , D o rdrech t . Veltman, F . , 1 9 8 1 : Data semantics. In: J . Groenendijk et al. ( e d s . ) . , P p . 541-566.

THE MENTAL REPRESENTATION OF DISCOURSE IN A FOCUSSED MEMORY SYSTEM: IMPLICATIONS FOR THE INTERPRETATION OF ANAPHORIC NOUN PHRASES

S.C. Garrod and A.J. Sanford Abstract

1974).

While any attempt at producing a process-model for comprehension

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To a cognitive psychologist discourse comprehension poses a number of interesting problems both in terms of mental representation and mental operations. In this paper we suggest tha t certain of these prob lems can be brought into clear focus by employing a procedural ap proach to discourse description. In line with this approach a general framework for the mental represe . ntation of discourse is discussed in which distinctions between different types of memory partitions are proposed. It is argued tha t one needs to distinguish both between focussed representations available in immediate working memory and nonfocussed representations available in long-term memory and a lso between representations arising from the asserted information in the discourse and those arising from what is presupposed by it. In the second half of the paper a particular problem of anaphoric reference is discussed within the context of this framework. A general memory search procedure is outlined which contains three parameters for deter mining the search operation. We then attempt to describe certain anaphoric expressions such as personal pronouns and full definite noun phrases in terms of the execution of this search procedure, where distinctions arise from the parameter specification derived from the expressions. The cognitive psychology of discourse is concerned with the nature of the mental processes entailed in understanding what is written or spoken, and the problem of how these processes might be realised in the mind of the understander given the psychological constraints of limited attention and memory which w'e know to obtain. One very attractive li1Je of attack is to view the many and various aspects of a discourse as having an instructional component, in the sense that the reader or listener is being instructed to assemble representations of the elements of discourse in a particular way. An e.rample of this is to be found in a treatment of topic marking within the topic/com ment distinction (Halliday, 1976): topic identification may be thOught of as an instruction to implement a procedure in which the topic con tent is construed as an address in memory to which new (comment) information is to be affixed (e.g. Broadbent, 1973; Haviland &. Clark,

GARROD &: SANFORD inevitably makes use of such a procedural view, it is also sensible to consider a text as having a content, which is more directly interpret able as a set of statements. In the present paper, we shall first consider the question of text content. This immediately raises the problem of how to treat anaphoric reference, which is one of the key contribu tors to text cohesion. Finally, we shall attempt to illustrate how the instructional or procedural aspect of discourse interacts with the con tent aspect by reference to a specific problem of anaphoric reference. Discourse Content

The principal differences between these two approaches lie in the extent to which the mental representation of a discourse matches the form of words making up the discourse, and as a corollary the extent to which 'inferences' in discourse comprehension are made immediately and automatically on encountering each element of it. In fac;t, the second view assigns the establishment of the s i g n i f i c a n c e of a piece of discourse to a very early stage in its processing. We shall ·now illustrate some of the consequences of this. Thus, while the propositional structures of the following two sentences are very similar, they differ quite markedly in their significance: ( 1) The policeman held up his hand and stopped the bus. (2) The wicket-keeper held up his hand and stopped the ball. Thus following (2) with (2') forms a perfectly acceptable piece of discourse, but adding (2') to ( 1 ) does not: (2')

The score was still the same.

This would not be of any consequence if the continuity problem arose from the fact that (2') identified some particular element in (2) which was not present in ( 1), but this does not seem to be the case. The problem comes from the definite NP 'The score' in (2') but this does not identify any single phrase in the prior sentence, and is pretty remote from our understanding of 'wicket-keeper', 'hand ', 22

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It is possible to translate a discourse into a set of propositions, concate nated into a connected hierarchical structure (Kintsch, 1 914; Kintsch and Van Dijk, 1 978; Rumelhart, 1 975), and some theorists have assumed that such structures correspond to the mental (memory)representation of the discourse. A somewhat different orientation would start out from the assumption that a discourse is generally organised around settings, arguments, or situations which are already known about to some extent by a person who can read and understand it. Looked at in this way, an important function of the early part of any discourse will be to enable a successful search for a referent situation in the memory of the reader. Sanford and Garrod ( 1 9 8 1 ) have termed such a referent situation a scenario.

THE MENTAL R EPRESENTATION OF DISCOURSE 'stop' or 'ball' in isolation. The origin of the continuity problem seems to be that the NP 'The score' fails to identify anything which has a place in our .knowledge of traffic control while it succeeds in identify.,. ing a necessary component of a game of cricket. This would suggest that any mental · representation arising from the first sentence must in some way incorporate information to the effect that the sentence is 'about' an event in a game of cricket. In other words the sentence functions as a partial description of some situation in which the event being referred to has significance, and the cohesion between the two sentences does not arise from the entities being mentioned in them selves but rather from the situation being described. Let us therefore describe such phrases as 'the score' in (2') as functioning as s i t u a t i ona l anaphors in that they carry back reference to elements which are a necessary part of the previously instantiated situation.

In fact there is a certain amount of evidence which seems to support the view that interpreting situational anaphors does not impose any great load on the processig system. This evidence comes from 'experi ments in which overall sentence comprehension time is used as a meas ure of processing difficulty for that sentence . . In 1 97 4 Haviland and Clark published a paper in which they demomstrated that comprehension time for a sentence containing an anaphoric noun phrase was in part a function of the contextual availability of its antecedent . They com pared contexts like (3) and (4) below for a target sentence such as (5): (3) Mary unpacked the picnic supplies. (4) Mary took some beer from the trunk. (5) The beer was .warm. using a range of such materials they were able to demonstrate that comprehension time for sentences such a� (5) was increased in the case where there was no directly stated antecedent in the context (as in (3)) as compared to cases where the antecedent was directly stated (e.g. (4)). More recently Garrod and Sanford ( 1 98 1 ; in press) have demonstrated JS, vol. l , no. l

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What is particulary interesting about such situational anaphors is that they might give us a clue as to the nature and availability of the mental representation set up by any antecedent piece of discourse. For instance if it can be shown that interpreting sentences containing such anaphors imposes no greater load on the processing system than the interpretation of sentences containing more straightforward direct antecedent anaphors, then. it must be assumed that unstated information about the situation under discussion is as readily available in the reader or listener's mental representation as information arising directly from the stated discourse. In this way interpretation of anaphoric expressions constitutes a kind of naturalistic exercise in memory retrieval.

GARROD &: SANFORD that such increases in comprehension time do not necessarily occur in the absence of stated antecedents. For instance Garrod and Sanford (in press) showed that sentences containing appropriate situat ! o�al anaphors did not require any more processing than sentences contammg anaphors with directly stated antecedents. The appropriateness of the context was manipulated by using different titles to the passages that a subject would read. As an illustration consider the two passages below: In Court (6) Harry was being questioned (by a lawyer). (7) He had been accused of murder. (8) The la wyer was trying to prove his innocence. Telling a Lie (9) Harry was being questioned (by a lawyer). ( 1 0) He couldn't tell the truth. ( I I ) The lawyer was trying to prove his innocence.

Comparable results can be obtained when contrasting contexts like the following: ( 1 2) Keith drove to London last night. ( 13) Keith took his car to London last night. are followed by a sentence containing an anaphoric reference to a car, i.e. (14) The car kept breaking down.

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In the passage 6 - 8 a title is used which should indicate· that the passage as a whole is about something happening in court and given such a title a high proportion of subjects expect the presence of a lawyer in this situation. Thus we might predict that a reference to the lawyer in sentence (8) should cause no problems whether or not an antecedent mention occurs in sentence. (6). On the other hand with the second similar passage entitled 'Telling a Lie' no such presuppo sition exists and hence we might expect sentence ( I I) to cause problems for the reader in the absence of an explicitly mentioned antecedent in sentence (9). In fact when the comprehension times were measured for the critical sentences in the two contexts it was found that in the appropriate context (e.g. with the title 'In Court') it made no difference whether the initial sentence contained an antecedent mention (e.g. the phrase 'a lawyer') or not. However, with the inappropriate context (e.g. with title ' Telling a Lie') a subsequent difference in reading time emerged for the critical sentence when no antecedent mention occurred in the text. In other words under certain conditions interpreting 'situational anaphors' imposes no extra load on the process ing system.

THE MENTAL REPRESENTATION OF DISCOURSE In circumstances where the verb severely restricts its instrument, as with drive and vehicle, situational anaphors which refer to this instrument do not seem to require any extra processing over the direct antecedent cases (see Garrod & Sanford, 1 98 1 for a more detailed discussion). Evidence of the sort cited above leads us to conclude that if some element is considered by a high proportion of readers in that community as a necessary component of the situation being portrayed in the prior discourse then it is possible to make direct reference to it in the subsequent discourse without producing any measurable effect in com prehension difficulty for the sentence containing the reference. Memory organisa tion and procedures

In psychology, there is a well-established distinction between two types of memory. The first is a dynamic system of limited capacity which 'holds information pertinent to whatever task is at hand, and which is readily availabl� to the processing system. It has been referred to as short-term working memory (e.g. Baddel�y and Hitch, 1 974). The second corresponds to a more usual use of ' memory' ,.. and is a relatively static store of effectively limitless capacity, in which resides our wealth of knowledge both specific and general. Such a distinction may be seen to have a relevance to discourse processing, in that as a discourse unfolds, we seem to be most aware of the current topic of the discourse and information relevant to it, rather than being equally aware of earlier parts of the discourse. In terms of anaphora, this means that references to entities which are part of the current aspect of a text should be more easily (or quickly) accessed than references to parts which do not correspond to the current topic of discussion. Indeed, experimental work suggests that this is the case (Sanford & Garrod, 1 9 8 1 ; Sanford, Henderson & Garrod, 1 980). Apart from a distinction of this kind, which we shall now call the current focus vs. static memory distinction, it is also necessary to accommodate representations of information not specifically mentioned in a discourse but directly relevant to it, such as the scenarios alluded to in the previous section. To do this, let us first distinguish between asserted information, which is actually given by the text itself, and conceptual information, which corJS; vol. l , no. !

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Just as anaphoric reference serves as an important basis for text cohesion, so ease or difficulty of reference resolution provides a means for investigating the availability of structures in memory which result from reading discourse. In this section we shall briefly outline a system of memory organisation which reflects differences in availability and provides a framework for considering the more procedural aspects of discourse.

GARROD &: SANFORD responds to the scenario. Now either we could assume a unitary working memory, in which both types of information were intermingled , or we could assume that the two types of information were sufficiently different to correspond to different partitions of working memory. Certainly the two must be distinguished in some way. For instance, it is an easy matter to distinguish between 'Mary dressed the baby' and ' Mary put clothes on the baby ' . Although memory experiments have shown that people are confused to a degree about which of two statements of similar meaning occurred in a text of some length (e.g. Sachs, 1 967), in the short-term such confusions are not so common. So what is said and what is meant can be kept separate. However, another distinction can be made, and that is that a reference can be made to a dependent of an entity which is -explicit (asserted) more easily than it can to an entity whose existence depends upon interpreta tion; consider for instance the following set of sentences ( 1 5) Mary put the clothes on the baby. ( 1 5 ') The material was made of pink wool.

( 1 6) Mary dressed the baby. If ( 1 5) and ( 1 6) led to the same mental representation, then this would not be expected. It is interesting to note that a similar distinction to the one between asserted and conceptual information is also recognised by some of those modelling human memory, and is expressed as the difference between episodic and semantic memory (Tulving, 1 972). Thus while semantic memory is supposed to reflect general knowledge, dissociated from any specific situation in which it was acquired, episodic memory contains knowledge of particular episodes. In the present case, the asserted/conceptual and focused/static distinction yields four memory types, summarised in Table 1 . There are various distinctions now to be made between representa tions in explitit and implicit focus. First of all consider the kind of representations of entities which might be suitable for implicit focus, bearing in mind that it is nothing more than a currently accessible part of semantic memory. If the sentence being represented is Keith was driving down to London, then anaphoric probe experiments show that car is an 'available entity'. However, the implied 'car' is not a specific one on the present' account. It is simply a representation of the fact that part of the definition of drive in this sense is to travel by car. In fact, car in this representation can be thought of as a variable, which can take as a value any specific instance of a car, or even any 'vehicle-like entity'. Thi s is difficult to envisage from the point

_

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In a reading-time study, ( 1 5' ) was read more rapidly than it was when the antecedent was changed to:

Nature of Memory

Origins of representation

Asserted

Conceptual

Focused

Static

Explicit Focus

Long term Text Memory

Implicit Focus

Long Term Semantic Memory

Table 1 A schematic characterisation of the four memory partitions

In complete contrast, explicit focus seems best represented as tokens for entities which are introduced into the discourse. For instance, introducing 'a car' or 'the car (de novo)' would set up a token for that entity. In this way, Keith drove to London and Keith went to London by car would have different structures, as illustrated in Figure 1 . The main point here is that although i t is possible to find a representa- . tion corresponding to car in both (a) and (b), in (a) it is a variable, , and in (b) it is a token. If it is useful to ·make these distinctions, as we have argued, then one would expect the information in the different partitions to be differentially addressed by various search directives. The force of the present paper is to suggest that such differential addressing finds its linguistic counterpart in the nature of referring expressions. In particular, we shall concentrate on the distinction between Explicit and Implicit focus, and shall begin with the contention that full definite noun phrases (FDNP) and pronouns can be viewed as triggers to imple ment searches of memory, and that they differ in the partitions which they address.

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of view of declarative representations, but can be readily appreciated from a procedural point of view: the variable car can be looked at as a series of tests which might be applied to any definite noun-phrase in subsequent discourse. If the noun-phrase passes the tests, then i t will stand as an instantiating value for the variable. Such arguments form the centre of most schema-based explanations of comprehension (see, for instance, Norman &: Rumelhart, 197 5).

GARROD &. SANFORD Figure 1 (a) 'Keith drove to London' eith

s

EX PLICIT FOCUS Scenario 1

�

Role l

IMPL ICIT FOCUS Scenario 1 : Driving Role I : Driver : Destination Role 2 etc

� il1s

� Role 2 �

Action

ondon

Role I travels to Role 2 by< Car>

(b) 'Keith went to London by car' eith

''

Role

�� 1

� � �

Role 2

London

Role )

is

IMPL ICIT FOCUS Scenario 2: Human goes Somewhere Traveller Role I Destination Role 2 Mode of travel Role 3 etc Role I travels to Action Role 2 by means of Role 3

Car Anaphoric e:rpressions as processing directives Let us begin by defining a specification for any language string which is to serve as a memory search directive. Such a specification would comprise (a) the domain (s) of memory over which the search i s to take place, (b) the information available in the string which may be used to guide the search, and (c) the type of information being searched for , together with any restrictions on the type. So, if we wanted to define the procedure behind representing a F DN P as a search directive, then our task is to specify (a), (b) and (c). If our specifications are adequate, then all examples of usage in a language should be accommo dated, and a psychological test of the account should yield a positive result. Consider a personal pronoun in this light. One particularly striking thing about pronouns is that they appear strange when used to refer to an implicit antecedent. Thus, 07') is a natural continuation o f 28

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t

EXPL ICIT FOCUS Scenario 2

THE MENTAL REPRESENTATION OF DISCOU RSE (17) while (17 ) is not: "

( 1 7) Mary dressed the baby. (17') The clothes were made of pink wool. (17") They were made of pink wool. At first sight, it may appear that one possible problem with 07") is that they could refer to Mary and the baby, although the pragmatics of the rest of the sentence would ultimately rule this out. H o wever, it seems equally odd to use a pronoun to refer to an implied entity of which there will only be one: ( 1 8) Mary won the first round of the mixed tennis championship. ( 1 8') *He was not a very good opponent. ( 1 8") The man was not a very good opponent.

In terms of specifying the retrieve procedure for the personal pro noun it therefore seems sensible to restrict the search domain to that of explicit focus, which would mean that the pronoun 'he' might trigger a procedure of the following kind: RETRIEVE

(a) DOMAIN: Explicit focus. ( b) PARTIAL DESCRIPTION: Singular, Male, ( Human) . (c) RETURN: Matching token identity in explicit focus. But is it possible to formulate a comparable procedure for handling the FDNP? It may be helpful to start by considering certain other contrasts between use of the pronoun and the F DNP. When considering the contrasts between pronouns and FDNPs with respect to situational antecedents we employed a simple substitution procedure and then asked the question, whether the two forms of expression were equivalent under substitution. This method can be extended to look at a number of other cases which would indicate that pronouns behave differently form FDN Ps as anaphoric devices and consideration of these cases suggests that under certain circum stances the two forms of expression take on quite different interpreta tions in the same context. For instance when the antecedent mention is interpreted generically an anaphoric pronoun may be used in circumstances where the equiva lent FDNP is ruled out ( see 19-22 below ) . JS, vol . l , no. l

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Not only is 'he' unambiguous in this context, but it is also no less specific than the alternative 'the man' in 1 8" , so there is no ambiguity whatsoever, and no new information is being introduced. Considerations such as these lead to the hypothesis that pronouns can only be used anaphorically to refer to explicit representations - i.e. they are not suitable for situational anaphora.

GARROD &: SAN FORD

( 19) (20) (2 1 ) (22)

An animal needs oxygen. It cannot live without water either. *The animal cannot live without water either. An animal cannot live without water either.

In this case the pronoun seems to naturally substitute for the generic indefinite 'an animal' in (22) rather than the definite 'the animal' in (2 1). A somewhat different example of the failure of pronoun/FDNP substitution occurs when the FDNP serves to establish a generic inter pretation of something which has previously been introduced into the context as a specific referent. As with:

(23) Once upon a time there was a cat. (24) Now the cat is renowned to be the laziest of animals. it

Once upon a time there was a cat. Now, they are renowned to be the laziest of animals. but In this case the pronoun is probably cataphoric on the general expression animals at the end of the sentence. Examples such as these and the ones constdered in rela�on to pro nouns and situational anaphora all support the view that the pronoun is very much constrained in its interpretation by the original interpreta tion of the antecedent, yet may take on almost any such original interpretation. With the FDNP on the other hand the interpretation seems to depend more upon the nature of the noun phrase itself and its sentential context than the original interpretation of its potential antecedent. Thus when an antecedent receives a generic interpretation as w i th ( 19) then the pronoun takes on such a generic reading whereas the FDNP cannot in these cases. However when the antecedent is interpreted specifically as in (23) the pronoun seems to require a similar specific interpretation, yet the FDNP may take on a different generic reading if this is forced by the rest of the sentence in which it occurs. At the most general level the pronoun serves primarily as a device for maintaining previous references, while the FDNP may have an additional attributive function allowing it to establish meaning but within the constraints of the current domain of discourse. In this way its interpretation need not rely exclusively on that already established for the antecedent. The distinction between a purely reference mainte nance function versus an establishment of meaning function is in our view reflected in part in the distinction between searching explicit

30

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Again it is of course possible for the pronoun to take on a generic reading as with:

THE MENTAL REPRESENTATION OF DISCOURSE focus which contains token representations and implicit focus which represents pragmatic information derived from the prior interpretation of the text, but largely only implied by the text itself.

A more detailed discussion of the nature of construct procedure is beyond the scope of the present paper (but see Sanford & Garrod, 1 98 1 ). However, what we intend to do in the remainder of the paper is to explore the more subtle stylistic distinction between pronouns and the· F DN Ps and see what light these might throw on the details of explicit focus representation. One of the conclusions which we will reach is that explicit focus may be thought of as the repository for structural information arising from both the text as a whole and the sentence under interpretation. Explicit text.

focus and information deriVing from the structure of the

Evidence for the importance of the reference maintenance function of personal pronouns emerges also from studies of the distribution of pronouns or other noun phrases in spontaneous speech. For instance in a recent paper Marslen-Wilson, Levy and Tyler ( 1 982) carried out a very detailed analysis of the circumstances of usage of personal pronouns, zero anaphors and fuller noun phrases in a task where the subject retold a simple comic book story which centred on two main characters. The principle analysis depended upon a breakdown of the story into an �ierarchical structure of distinct events embedded within episodes embedded within the story. This breakdown emerges very JS, vol . l , no. J

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In terms of formulating an appropriate procedural characterisation for the F DNP this would suggest that it needs to recover a wider range of information from memory than the pronoun and so trigger a more general retrieve procedure operating over the whole focus domain, both explicit and implicit, with the aim of recovering informa tion not only about token representations but more importantly about the pragmatic restriction in implicit focus which may or may not be directly linked to the tokens. At the same time it must be possible for FDNPs to trigger additional procedures whose goal is to construct new elements in the representation on the basis of the information already retrieved. This is necessary both to account for the fact that F DN Ps when used as 'situational anaphors' must enable construction of information in explicit focus to represent the newly established referent, and may also be required when the F DNP is employed to establish a new interpretation of an already introduced referent as with examples like ( 24). The procedural characteristic of pronouns and FDNPs may therefore be distinguished in two main ways ( I) in terms of the differences in restriction of search domain in memory and (2) in terms of the additional construction procedures associated with the interpretation of the F DN P, which are not available for the pronoun.

GARROD &: SANFORD clearly from the nature of the story itself, and turned out to be an exceptionally good predictor of the choice of anaphoric device. For instance if the reference occurred within an utterance which related to the same story, episode and event as one containing t!le antecedent mention then a pronoun or zero anaphor was chosen on 46 occasions out of the 50 observed. Thus in the vast majority of cases when the pronoun was used, it occurred at the most embedded levels of the narrative and functioned to maintain reference within an action sequence. On the other hand in a context which only related to the same overall story as that containing the previous mention there were only 2 out of 8 occasions when the pronoun was used and the incidence of these two could be accounted for in terms of local structural constraints on the utterance in which they occurred.

There is also some recent experimental evidence (Purkiss, unpublished, see Sanford &: Garrod, 1 98 1 ) using the reading time procedure which has a direct bearing on the claim that pronouns . and F DN Ps serve rather different functions in discourse. The materials used in the study have the general form shown in Table 2. In the first sentence of each set, two entities are introduced (e.g. The engineer and the television set). During subsequent sentences, in the 'subject position' materials, reference is made only to the entity desig nated by the object noun phrase. When the final (target) sentence is reached, anaphoric reference is made to the subject position noun phrase in the first sentence. Furthermore, the referring expression can be either a repeat noun-phrase or a pronoun. For the 'object posi tion ' materials, this pattern is changed so that the intermediate sen tences are about the subject of the opening sentence, and the final sentence refers back to the object, again either by a FDNP or a pronoun. The second major variable in the design is · the number of sentences w!lich intervene between antecedent and anaphor. In one condition, the sentences marked with asterisks were included, and in another, excluded. The two major variables correspond to two factors which appear to influence the choice of a pronoun as an anaphor. The first, the 'topicalisation' principle, is exemplified by the apparent ease with which a logically ambiguous pronominal anaphoric reference can be used to refer to an entity introduced as a subject noun phrase in an active sentence - the following illustration is taken from Broadbent 32

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This pattern of observation is consistent with the view that the speaker is employing pronouns and zero anaphors simply in order to maintain reference with a minimum of new interpretation, while lexical ly more specific expressions (mainly proper names in Marslen-Wilson et al. 's monologues) are reserved either to introduce characters at the beginning of a narrative or to re-establish them as central actors in a new episode.

THE MENTAL REPRESENT AT ION OF DISCO U RSE Key noWl-phrase in subject positon The engineer repaired the television set. It had been out of order for two weeks. *It was only a few months old. *It was the latest model. He/the engineer took only five minutes to repair it. (TARGET) Had the television set been out of order for five weeks? Key noWl-phrase in object position The mother picked up the baby. She had been ironing all afternoon. *She would not be finished for some time. *She was very tired. The baby/it had been crying nearly all day. (TARGET) Had the mother been sleeping all afternoon? Table 2 Sample of materials used in the pronominal reference study (Purkiss 1978)

(27) The feedpipe lubricates the chain, and it shou ld be adjusted to leave a gap half an inch between itself and the sprocket. Broadbent's study indicated that most people interpret it a s anaphor of the feedpipe and not the chain.

being an

The second major variable corresponds to the principle that pronouns are used to refer to things which have been mentioned recently i n a d i s:.. course. This is exemplified in linguistics by Chafe's ( 1 972) concept of foregroWlding. Subjects read through materials of this type in the self-paced re&ding situation described earlier, and in the analysis attention was paid to the time subjects spent inspecting the final {'target') sentences. The results are shown in Figure 2. Of particular interest here are the results for the object position materials, which clearly demonstrate an ' interac tion between number of intervening sentences and pronoun/FDNP reference form. ·

Provided there is only one intermediate sentence, sentences with a pronoun anaphor are actually read slightly more quickly than those using an FDNP. Indeed, this trend holds over both subject-position conditions. However, when the number of intermediate sentences is larger, the trend is reversed for object-position antecedents: F DNPs are apparently handled more rapidly than pronouns.

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( 1 97 3).:

GARROD & SANFORD Figure 2 TOPIC

1.7 -; 0 •

� w

:I ;:

i

c w a::

COMMENT

, I

I

/

1.5

/

/ �

1.3

1.1

��

� ,�

1

3

NUMBER OF INTERVENING SENTENCES

3

Mean reading time for target sentences with sentence F D N Ps ; length difference neutralised. So l i d l i n e s : dotted lines: pronoWlS.

A further experiment, the first in a series on plural pronouns (San ford & Garrod, in preparation), supports the dissociation of function viewpoint. Typical mC�.terials are shown in Table 3. It was a fine Saturday morning. John and Mary went into town. She/they/Mary wanted some new clothes. (b) The library was quite fulJ. Linda and Jim could not sit down anywhere. The librarian told hirn/them/Jim to wait.

(a)

Table 3 Sample of materials used in the plural antecedent experiment. 34

JS, vol. l , no. J


These results seem to show that pronominal mappings are most readily made when the antecedent is in the subject position and/or recent. Now it is possible to argue that when a noun phrase is in the subject position, or has been mentioned recently, then it has a 'stronger' representation in explicit focus, and is more readily available as a potential antecedent. However, such an argument cannot explain how pronouns are handled more rapidly than FDNPs in one condition and more slowly in another. To accommodate this, Sanford & Garrod ( 1 98 1 ) suggested that a pronoun m ay search only explicit focus, and that object-position F DN Ps are not represented in explicit focus after a number of intervening sentences, while subject-position ones are. However, as we will see below, this simple strength of representation explanation will need to be modified somewhat if we are to account for certain additi9nal phenomena.

THE MENTAL REPRESENTATION OF DISCOU RSE In this study, a plural topic FDNP in the second sentence is referred to by an anaphor in the third. The pronoun could either be plural, b e i n g codesignative with the entire topic FDNP, singular, being codesignative with one element of the FDN P, or a singular FDNP, being codesignative with the same element of the topic . · A further contrast in conditions is indicated in the materials: the anaphor could be either in the topic or in the comment position of the sentence in which it appears. Now there are many good reasons to suppose that a plural FDNP would be represented as a group in explicit focus, and so would be more readily mapped to a plural pronoun than to a singular one. How ever, Figure 3 shows the situation to be more complex in fact. Figure 3 2.2 'U 2.1 •

!

a:

1.7

�

NAll£

PRO

PLUPRO

Mean reading time for target sentences. Square points: anaphors in the object position of the target' sentence; round points: imaphors in the subject posi tion. Points are joined by lines. {or clarity only. In the figure are shown the reading times for the target sentences containing the various forms of anaphoric expression. The top curve refers to the reading times for those target sentences in which the expression is in syntactic object position while the bottom curve shows the times for the subject position sentences. Of interest here is the interaction between form of expression and its syntactic position in the sentence. For instance, for the plural pronouns it makes no signifi cant difference whether they appear as subject or object of the target sentence but in the case of the singular pronoun there is a considerable and reliable difference in reading time associated with the positioning. It seems that the singular pronoun is only effective in identifying one of the members of the plural antecedent when it occurs in subject position, while the plural pronoun works very well, and the lexically more specific name works moderately well in either position of the sentence. How can we account for this rather extraordinary finding? It may be helpful at this point to consider in a little more detail JS, vol. l , no. l

35


"' 2.0 :I � f:l 1.11 z E c 1.8 "'

GARROD & SANFORD some of the work on usage of pronouns occurring in different syntactic positions of the sentence. In a recent paper Karmiloff-Smith ( I 980) observed that older children always reserved sentence initial pronouns for reference to what she called the thematic subject of the narrative that they were telling where thematic subject corresponded to the central actor in the story. This led her to conclude that pronouns in subject position could possibly be thought of as default expressions for maintenance of thematic subject. A similar conclusion is of course suggested in Marslen-Wilson et al. ( 1 982) observations in which pronouns were employed to maintain the characters in central roles within an already established action sequence whereas more specific lexical items such as proper names were reserved for re-establishing the antece dent in the central role. Given these observations it would seem appro priate to make some additional assumptions about the mechanisms of pronoun resolution and the sort of antecedent information which must be available in the focus memory system.

RETRIEVE (a) DOMAIN: Explicit focus. (b) PARTIAL DESCRIPTION: Male, Singular, H uman (Subject). (c) RETU RN: Matching token identity from the set defined by the variable thematic subject. F rom a processing point of view having retrieve procedures of this sort allows the system to capitalise on the fact that the subject of a sentence in a narrative is usually taken to refer to the thematic subject of the discourse. Thus when a purely reference maintenance device, such as a pronoun, is encountered it is assumf!d that the identity 36

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In the first place we might speculate that in addition to the tokens held in explicit focus there might also be certain types of structural information derived from the prior discourse which is also represented. Thus we could find information about the identity of the current thema tic subject or subjects. Since such information can be derived directly from the structure of the previous text it does not seem unreasonable to assume that it is represented in the explicit part of the text represen tation. Furthermore we must assume that the retrieve procedures triggered by pronouns in different syntactic positions within a sentence may be augmented with structural information which would allow them to identify structural variables in explicit focus. Given such assumptions it is possible to differentiate between the kind of search procedure associated with a sentence initial subject pronoun and a pronoun encoun tered somewhere in the rest of the sentence, which is clearly necessary if we are to accommodate Karmiloff-Smith's observation and the results of the reading time experiment reported above. So Jet us assume for the moment that a search procedure triggered by a sentence ir�itial pronoun such as 'he' might be described in term s of the following specifications:

THE MENTAl REPRESEN TATION OF DISCOURSE of the thematic subject is being maintained. The corollary to this is that when a fuller noun phrase is encountered which is primarily not a reference maintenance device but one for establishing reference it would be assumed that a new thematic subject is being established. As a result of this we would expect to find that sentence initial pro nouns were particularly effective in just those circumstances when they identified referents from among the set of things which could be considered as thematic subjects.

let us now return to the specificat ion of the retrieve procedures for the two types of pronoun encountered in the target sentence. When the pronouns were in subject position (See Table ( 3a)) they would both trigger searches for current thematic subject and come up with the two tokens currently allocated. In this way either search would succeed in recovering a matching antecedent. On tl'le other hand when the pronouns were not in subject position the retrieve procedure would not have access to the content of the thematic subject variable since the search would not be directed to this set. The retrieve for the plural pronouns would therefore succeed in finding the token assigned to the group agent whereas with the singular pronoun there would appear to be no syntactically matching singular token readily available, and further time consuming search operations would be needed in order to recover a matching antecedent. Finally, since we have not assumed that structural information should have any effect on the process of interpreting proper names or FDNPs, use of these expressions should not lead to any reading time effects associated with their syntac tic position in the sentence. Clearly this explanation is would need to carry out a results do suggest that we between the types of search noun according to both the that of the pronoun itself.

post hoc and in order to verify it we number of control experiments, yet the need to be able to somehow distinguish procedures employed for resolving a pro structural context of its antecedent and

Finally, it is worth mentioning that the sort of structural augmentaJS, voi. J , no. l

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This might allow us to put forward a tentative explanation for the rather extraordinary reading time result observed in the experiment reported above. If we first consider how the sentences containing the antecedents might be represented in focus, two types of information would result; first, information relating to the discourse structure to the effect that the two actors (e.g. John and Mary in Table (3a) or linda and Jim in Table (3b)) were both potential thematic subjects, in which case the thematic subject variable would be assigned the two tokens and secondly, that the two actors as a group serve as joint agents in the action being portrayed in the sentence in which they occur, so the tokens as a group would also be mapped into some variable in implicit focus.

GARROD & SANFORD tion of the retrieve procedure which we have been entertaining for pronouns in sentence initial position in discourse may also have its counterpart in the sentence domain itself. It has often been pointed out that pronouns in the subject of a co-ordinate or subordinate clause tend to pick the sentence subject as antecedent. For instance in a sentence like the following:

(25) John hit Bill and then he ran away. the pronoun is usually interpreted as codesignative with John, whereas in a sentence such as (26)

(26) John hit Bill and then Mary shouted at him.

So let us now attempt to summarise the arguments. In the first plac·e we have suggested that it is helpful to characterise the interpreta tion of anaphoric expressions in terms of search procedures which operates on restricted domains corresponding to distinct focus partitions in working memory. On the basis of both previous work in. the general field of cognitive psychology and clarity in describing the representation we have proposed a partition in the focus memory system into two components: one, explicit focus, functioning as a repository for asserted information which may consist in both token representations correspond ing to the various individuals mentioned and structural information arising from the discourse itself; the other, which we termed i m p l i c i t focus, serving to represent i mplicit knowledge-derived information needed to give the discourse significance. Given this distinction in the memory system it was then suggested pronoun resolution could best be described in terms of the execution of retrieval procedures restricted to the explicit partition whereas interpretation of full definite noun phrases could be described as in part arising from the execution of retrieve procedures operating . on both partitions and, in addition, construct procedures. In this way anaphoric pronouns derive their interpretation directly from the previous discourse, whereas F DNPs are interpreted within the broader constraints of our interpretation of the previous discourse and the particular sen tence in which they occur. This reflects the basic distinction between the reference maintenance function of the pronoun and the reference establishment function of the fuller noun phrase. 38

JS, vo!. l , no l


the pronoun seems to select the most recently mentioned antecedent (i.e. Bill). Examples such as these led Caramazza & Gupta ( 1 979) to put forward what they term the parallel function hypothesis for pronoun resolution. Yet again we might assume that these preferences emerge from a restriction on the retrieve procedure triggered by subject posi tion pronouns but in this case within the more local domain of the current sentence.

THE MENTAL R EPRESENTATION OF DISCOURSE General Discussion We have tried to show how a psychologically-based account of reference resolution might be constructed. In natural language, a wide variety of referring expressions are used in a wide variety of circumstances. Even the small number of examples considered in the present paper attests to this variety. The psychological approach to the problem aims to provide a description of the admissible possibilities within the constraints of mental operations. These constraints are presumed to operate in all situations demanding language comprehension, and are presumed to originate in limitations on man as a processor of symbolic information.

One major outcome of the approach is to emphasize the procedural aspects of discourse fragments. Thus it is not sufficient to say that a pronoun and an antecedent noun phrase refer to the same thing in a given case. What is required is a description of the mental opera tions which that pronoun brings about, and which uitimately results in the establishment of coreference. In the present paper we have indicated some of the problems which one encounters in trying to do this, while at the same time hopefully suggesting some solutions. The procedural approach is not merely attractive because it lends itself naturally to computer implementation, but also because it bestows other advantages. For instance, although two different forms of refer ence might be used in a particular situation, the final representation (meaning and significance) may be exactly the same; however, the process leading to that representation would be quite different. An example of this might be the way in which both definite and indefinite FNPs can be interpreted generically. JS, voi. J , no. l

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The main constraints considered here are those characterising the structure of memory. Almost without exception, psychologists distin guish between working memory (a system oi lim ited capacity, sharing short-term storage and data-manipulation duties) and long-term memo ry. In the first part of the paper, we described how such a distinction gives rise to a major criterion for separating aspects of memory used in text comprehension. Not only psychologists, but also workers in artificial intelligence have found a similar distinction to be useful. Thus Grosz ( 1 977) distinguishes between 'focused' and 'unfocused' information in her discussion of understanding systems which might be implemented in computers. In this case, the utility of the distinction is computational: if references are made to entities, then it is necessa ry to restrict the search domain to manageable proportions. There is also another good reason for supposing that the reference domain must be limited, and that is that many sentences in language are elliptical. It is only possible to use ellipsis if the range of possible referents. is very limited. Indeed, a fully psychological approach would maintain that the possibility of ellipsis only arises because of the constraints which characterise human working memory.

GARROD &: SANFORD Finally, although the discussion here has been restricted in the main to pronouns, the framework put forward is well suited to the N Ps, analysis of other referring expressions, such as indefinite restricted relative clauses, and guantifiers in general. University of Glasgow Adam Smith Building Glasgow, Scotland

References

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Baddeley, A. &: Hitch, G., 1 974: Working memory. In: G.H. Bower (Ed.), The Psychology of Learning and Motivation. 8; 6 6 7 - 6 7 9 . Broadbent, D.E., 1 973: In Defence o f Empirical Psychology, M e t h u e n , London. Caramazza, A. &: Gupta, S., 1 979: The roles of topicalisation, parallel function and verb semantics in the interpretation of pro nouns. Linguistics, 17; 497-5 1 8. Chafe, W ., 1 972: Discourse structure and human knowledge. In: J .B. Carrol and R.O. Freedle (Eds.), L a n guage Comprehension and Acquisition of Knowledge, W inston, Washington. Pp. 4 1 -70. Garrod, S. &: Sanford, A.J., 198 1 : Bridging inferences and the extended domain of reference. In: J. Long &: A. B a d d eley ( Eds.) H i l l s d a le, N .J. A t tention and Performance IX. L . E . A . , Pp. 3 3 1 -346. Garrod, S. & Sanford, A.J., in press: Topic dependent effects i n language understanding. G.B. Flores d'Arcais, R. Jarvella (Eds.), The Processes of Language Understanding, J . Wiley &: S o n s , Chichester. Grosz, B., 1 977: The · representation and use of focus in dialogue under standing. Technical note 15, SRI International Artificial Intelligence Center. Halliday, M.A.K., 1 967: Notes on transitivity and theme in English, Part 1. Journal of L inguistics 3; 37-8 1 . Haviland, S.E. &: Clark, H.H., 1 974: What 's new? Acquiring new information as a process in comprehension. J o u r n a l of V e r ba l Learning and Verbal Behavior, 13; 5 1 2-52 1 . Karmiloff-Smith, A., 1 980: Psychological processes underlying pro n o m i n a l i sation and non-pronominalisation in children's connected discourse. In: J . Kreiman &: A.E. Ojeda (Eds.), Papers fro'!! the Parasession on Pronouns and Anaphora. Chicago Linguistic Society, Chicago. Pp. 23 1 -250. Kintsch, W., 1 974: The Representation of Meaning in Memory, E r l b a u m , Potomac. Kintsch, W ., &: van Dijk, T.A., 1 978: Toward a model of text comprehen sion and production. Psychological Review, 85; 3 6 3 - 3 9 4 .

THE MENTAL R EPRESENTATION OF DISCOU RSE

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Marslen-Wilson, W., Levy, E. &: Tyler, L.K., 1 982: Producing inter pretable discourse: the establishment and maintenance of reference. In: R. Jarvella & W. Klein (Eds.), S p e e c h , Place and Action; Studies in Dei:ris and Related Topics. J. Wiley &: Sons, Chichester. Pp. 339-378. Norman, D., Rumelhart, D.E. &: L.N.R., 1 97 5: Explorations in Cognition, Freeman, San Francisco. Rumelhart, D. E., 1 97 5: Notes on a schema for stories. In: D.G. Bobrow & A. Collins (Eds.), Representing and Understanding Studies in Cognitive Science. Academic Press, New York. Pp.2 1 1 -236. Sachs, J.D.S., 1 967: Recognition memory for syntactic and semantic aspects of connected discourse. Perception & Psychophysics, 2, 437-442. Sanford, A.J. &: Garrod, S., 1 9 8 1 : Und e rs tanding Wri t ten Language; Explorations in Comprehension Beyond the Sentence. J. W iley &: Sons, Chichester. Sanford, A.J., Henderson, R. &: Garrod, S., 1 980: Scenario-shift as a variable in text cohesion. U npublished Report, University of Glasgow. Tulving, E.A., 1972: Episodic and semantic memory. In: E. Tulving & W. Donaldson (Eds.), Organization of Memory, A c a d e m i c Press, New York. Pp. 3 8 1 -403.

INDEXED PREDICATE CALCULUS

S.- Y. Kuroda

Abstract A programme to construct an extension of predicate calculus is pro posed in which predicates and constants are indexed and interpreted with respect to different (mini-)worlds reffered to by . indices. From another perspective the proposed system is an extension of the idea of indexing noun phrases in syntactic representations in generative grammar. Some applications are given. In particular, it is applied to the description of ambiguities in intensional contexts, and a com parison is made with a description recently given by Saarinen.

This view is in a certain obvious sense unrealistic for explicating actual language use in discourse or in conversation as a cognitive activity. In everyday situations, we deal only with a very small chunk of the whole real world. Even if we talk about world politics, our background understanding of the world is fragmented and minuscule. Thus, we might say, at least as a first idealization, that we use the same uninterpreted language (logical representations) in different occasions of discourse and conversation, i.e. a formal system with the same meaning postulates and axioms etc. on different occasions of discourse, but models with respect to which such a formal system is interpreted vary from an occasion of use to another. But, however more realistic this view may sound, this change of view is, one might say, really immaterial, so far as generalities of semantic theory are concerned. For, even though one talks as if logical representations are interpreted with respect to the real world (and JS, vol. I, no. I

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When the conception of logic is applied to natural language, it seems generally to have been tacitly assumed that logical formulae are inter preted with respect to the 'real ' world; that is, the whole real world is the model w.r.t. which each predicate is evaluated unless it is within intensional contexts. The recent influence of Montague grammar might f urther enhance such a perspective. In fact, each predicate is ihterpre ted not just by the whole real world, but with reference to all possible worlds. Each use of a sentence in discourse is, so to speak, backed up with all possible worlds, if we take what Montague grammarians say literally. 1

S. -Y. KURODA all possible worlds) in general semantic theory, the theory is not made dependent on any particular specific properties of the real 'real world'. The reference made by the theoretical semanticians to the real world would be much like the reference made by logicians to an unspecified set as a model when they formulate general truth conditions. When formal logic is applied on specific occasions, it is applied to various specific sets; but such variability is of no concern to a general theory of logic. L ikewise, reference to the real world and all possible worlds in general semantics, one might say, is only a far;on de parler, a n d w e don't have to be concerned with these concepts in a general theory.

H aving formulated a problem for the theory of discourse, however, will not be engaged in empirical analyses of discourse in a proper sense, in this paper. My present concern is rather this: once one sees the need for such a multiple model discourse theory, the door is open to explore extreme consequences of such an approach. For, one might ask, how small can discourse be, or how small must we assume discourse can be? There cannot really be any natural lower bound of the number of sentences in discourse, just as, conversely, there cannot be any natural upper bound for the length of a sentence. This observation might suggest the following: given the kind of problem we are concern ed with, we cannot separate the sentence from the discourse; i.e. we may not be able' to shield sentence semantics in a fixed-model framework, while we develop a multiple-model discourse theory. Then, we may be. thrown back on the general theory of sentence semantics. W ith this background, I would like to illustrate the usefulness of 44

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This comparison, however, is not appropriate in at least two respects. For one thing, the assumption that the fixed world is the' real world has customarily been taken as entailing a specific type of ontological presupposition. Only very recently has this point begun to be subjected to serious criticism. (cf. Saarinen, 1 978; 1 98 1 .) Let me put aside this point for now, however. We shall for the moment be concerned with the other point. Natural discourse or conversation does not proceed like a formal application of logic to mathematics; in natural discourse, as speaker and hearer, we are constantly adjusting ourselves to changing 'contexts', shifts of 'topics ', from one moment to another. Our daily language activity is not made of a sequence of separate chunks of discourse, each with a well-defined universe of topics that can be simulated by a 'mode l ' . If such were the case, in order to simulate natural discourse, we would have to deal with 'model changes' during a stretch of discourse, and a f ixed-model theory of semantics would at least have to be supplemented by a multiple-model discourse theory ' that can deal with the interaction of contexts, or, formally, of models. This means that the theory of discourse in natural language would involve a nontrivial aspect of discourse structure, an aspect which a theory dealing with discourse in formal logic in the standard sense (say, proof theory) does not have to be concerned with.

INDEXED PREDICATE CALCULUS a multiple-model approach in sentence semantics, without motivating it on the study of discourse structures in a proper sense. I shall first present rather simple-minded examples and then later move on to an attempt to relate this approach to descriptive problems of intension al contexts of a familiar type.

•

I agree with Fauconnier that the understanding of sentences involves. mental constructs in terms of which the semantic function of the sentences, at least so far as their extensional aspects are concerned, are to be accounted for. However, Fauconnier's emphatic advocacy of a processing-oriented approach, I believe, is misguided. In my view, processing presupposes structure. According to this view, one might expect that a new approach advocated in the name of 'processing approach' would be significant and interesting just to the extent that it rightly leads to recognize structures of an as yet unrevealed charac ter. If that should be the case one might then investigate all the impli cations of this revelation and endeavour to obtain an adequate structur al account. The initial proposal for a processing approach could then be re-evaluated as a proposal for a processing model. Here is not the place for me to present details of Fauconnier 's approach and direct ly comment on it. However, I will freely borrow examples from his paper. It might also be stated at the outset that the present paper is intend ed only to set out a programme, not as a summary of an accomplished work. In particular, this point may need to be emphasized if the propoJS, vol. l , no. l

4.5


Before proceeding, however, let me just insert a remark on the background of the origin of this paper. Initially, this work was under taken as a sort of respons to G illes Fauconnier 's paper 'Mental spaces In a certain - a discourse-processing approach to natural logic'. 2 perspective we share the same concern. We are both challenging the view apparently prevalent among contemporary philosophers of language and linguistic semanticians under their influence. According to this view, sentences are associated with formal representations of a logical system of some sort such that the meaning of each sentence, at least to the extent that meaning in the extensional sense is concerned (and in recent times even more strongly, as a matter of intensional meaning) is accounted for in terms of referential interpretation (in the sense of formal logic) of the formal system with respect to the whole real world (or in an even more grand scheme, with respect to the class of all possible worlds), which is somehow metaphysically set transcen dentally and absolutely, independent of cognitive structures and psychcr logical processes. Counteracting this standard view, in the above men tioned unpublished paper, Fauconnier advocates a p�rspective in which "there will be no such thing as an abstract discourse-independent seman tic representation, or logical form for a sentence: rather, the sentence is a set of instructions for setting up and referring to the mental constructs which supports the organization of discourse." (p .5)

5.-Y. KU RODA sal is taken to be one for a system of formal logic. No semantic rule in the strict sense of formal logic is formulated. Only plausible indica tions are given to suggest how the proposed system might be formalized as an extension of standard (non-modal and modal) predicate calculus. Let me first consider the following sentence: ( 1 ) Since it was so stuffy in the house, Mary went up to the attic and opened the window.

In contrast ; in indexed predicate calculus (!PC), the relevant aspects of ( l ) can be represented, essentially, as (2)

W ENT-UP

i

(Mary, the attic) & OPEN

j

( Mary, the window)

where i refers to a m ini-subworld around the house and j to a mini subworld of this subworld, say, the attic. J Formally, indexed predicate calculus is an extension of predicate calculus. In addition to the usual vocabulary of predicate calculus, it contains the set I of indices. Each predicate symbol is indexed by an element of I. Instead of having a one-place predicate BLUE, for example, we have an array of indexed one-place predicate symbols, BLUE ; , BLUE ; , Semantically, a model to interpret !PC is a class of 'worlds' , or 'mini-worlds' , W ; , identified by elements of another index set J. !PC resembles possible world semantics in this multi world feature. But the intended function of this multi-world feature in !PC is quite different from that in possible world semantics. A valuation (an interpretation) of !PC determines a function k from I to J . In other words, an index i refers to a world W k ( i ) . •.•

46

JS, vol. l , no. l


If one applies ordinary predicate calculus to definite descriptions in natural language, it may be implicitly understood that the universe of discourse, i .e., the model with which logical expressions are assigned a valuation, is appropriately delimited. The president of France may be referred to as "the president of France" without delimiting the real world as a model for an interpretation of predicate calculus, but this is not generally the case with the use of singular definite nouns. The phrase "the attic" in ( 1 ) is understood to be the attic of a particular house in the context of the discourse in which ( l ) is inter preted with an appropriate mini-subworld of the real world, in which the house referred to by the house in ( I ) is the one and only house to refer to. But this proviso cannot save the direct application of the theory of definite descriptions to ( 1 ). For, the definite descrip tion the window here is most likely understood to be the one and only window of the attic, and obviously not of the house. The house most likely has more windows than just the one in the attic. Hence, we would have to paraphrase the window in ( 1 ) as the window of the attic, syntactically restoring a more abstract represe·ntation.

INDEXED PREDICATE CALCULUS What are 'worlds' ? In the simplest cases, they may simply be consid ered sets. Then, a predicate symbol indexed with i is interpreted in to which i refers; the familiar way with respect to the set W k { i ) under if, for example, P is a one-place predicate, the value of P i We later need a given interpretation is a subset of the set W k { i ) a more elaborate account when we use indexed predicates in intensional contexts and let them be evaluated with respect to a 'world' in our sense. But for the moment, this simple suggestion would suffice for the discussion of the next few examples. •

As another example, consider the following sentence, adapted from Jackendoff ( 1 975), through Fauconnier ( 1 979): (3) A girl with blue eyes has brown eyes.

(4) (Ex) (GIRL(x) & BLUE(x) & BROWN(x)). But (3) is 'factually' contradictory insomuch as no one can have blue eyes and brown eyes simultaneously. In IPC (3) may be rendered as (5) (Ex) (GIRLi (x) & BLUEi (x) & BROWN j (x)) where i and j are intended to be interpreted as referring to different worlds, (the real world, or a mini-subworld of the real world) and the world of the picture in question, respectively. An existential quanti fier binds three occurrences of variable x, two of which serve as argu ments of a one-place predicate indexed by i and the remaining one as the argument of a one-place predicate indexed by j. A natural convention for interpreting such an instance of the existential quantifier would be to assume that the domain of the variable bound by the But i n the ordina quantifier is the 'intersection' of W k{ i ) and W k { j ) As and W k { j ) • ry sense, there is no intersection between W k { i ) in certain versions of modal logic, however, · we assume that cross world identification functions are defined among worlds, without specify ing any metaphysical nature of such functions. Then, ( 5) asserts the existence of an individual who is a girl with blue eyes in the real world (in the relevant mini-subworld) who has an image in the world of the picture with brown eyes. •

Let me formulate the convention indicated above (and an obvious dual of it) for the convenience of later reference: JS, vol. l , no. l

47


In a context in which the speaker is looking at a picture, this sentence may be understood to mean that some girl with blue eyes in the real world is painted as a girl with brown eyes in the picture. Let BLUE and BROWN be one-place predicates to which we assign the meanings 'having blue eyes' and 'having brown eyes' , respectively. If (3) is trans lated directly into ordinary predicate calculus, using these predicates, one would get a form something like

S.-Y. KU RODA (C- 1 ) If an individual variable x occupies a pos1t1on in predicates P i 's, where i ranges over a subset I' of I, and x i s bound by the existen tial (universal) quantifier, the domain of the variable x is the intersection (the union) of W k(i ) , i ranging over I ' . ' Intersection' and 'union' must be determined relative to cross-world identification functions. 4 I will now borrow another example from Fauconnier to indicate that individual constants, in addition to predicates, may be indexed� Consider a movie in which Caesar played by Richard Burton seduces Cleopatra played by Elisabeth Taylor. One might say: (6) In this movie, Richard Burton seduces Cleopatra. Let us represent Richard Burton and Cleopatra by b and c, respectively, and consider the formula where they indicate SEDUCE and the two constants b and c are freely indexed:

Now, the natural convention would be that if a constant a i indexed with j fills a place of a predicate indexed with i, the referent belongs to the 'intersection' of the worlds indicated by i and j. In our example, the seduction takes place in the world of the movie; i indicates the world of movie. Richard Burton is a name for a person in this real 5 As Richard Burton has a role in world; j indicates this real world. the movie, the referent of b i may be found in the 'intersection' of the world of movie and this real world. Likewise, the name Cleopatra belongs . to a historical world, and hence t�e index k of ck indicates this historical world. But since Cleopatra is represented in the movie, the referent of c k may be thought as belonging to the 'intersection' of the world of movie and the historical world. Altogether, then, the above formula is interpretable as true in the desired way. In contrast, if we interpret index i as indicating the present real world (thus, the same as j), the formula is not interpretable 6 , because Cleopatra does not belong to the 'intersection' of the present real world and the historical world. Consider, next, the following Japanese sentence: (8) subete no kyoozyu-ga gakusei-o minna rakudai-saseta. all professor-SUBJ student-OBJ all flunked Given an appropriate context, this sentence may be ambiguous. One reading may be translated as (9) All the professors flunked all the students. 48

JS, vol. l , no. l


(7) SEDUCEi (b i , c k ).

INDEXED PREDICATE CALCULUS and the other as ( 1 0) Every professor f lunked all of his/her students. If one wants to give a sem antic account of this ambiguity of (8) within the ordinary framework of logical representation, one would have to set up two abstract logical representations for (8), essentially encoding the structure of (9) and ( 1 0), respectively. In IPC the ambigui ty is essentially captured as a matter of scope difference, a familiar situation. To see this let an index i refer to a mini-world of the institu tion in question. The reading (9) may be formalized as: (1 I)

(yY) ( S i (y) ::::> (Yx) (P i (x) ::::> Fi (x,y)))

where S, P, and F stand for 'student', 'professor' , and 'flunk', respective ly. Next, consider the reading ( 1 0). For each professor x, we need to specify all the students in a mini-world of this professor. Assume that the index j refers to this mini-world. Then, we might have:

depends to represent this reading. But note that the mini-world W k ( " ) on each professor x. In order to accommodate this dep�ndency, we allow a quantifier to bind a variable at an index position. Instead of ( 1 2), we introduce: (y) :::> lj (x,y ))) ( 1 3) (Vx) (Pi (x) ::::> (Vy) (S f(x) where the intended interpretation of f(x) is the mini-world of each professor x. If we use the notation of restricted quantifiers, ( I I ) and ( 1 3) are replaced by: 0 4)

�Y>s. (Yx\>.

1

1

( 1 5) (� )

P

i

5

F (x,y) i

f(x)

F.

1

(x,y).

Even though the two quantifiers involved in ( 1 5) are both universal, the order of the two quantifiers is relevant, because the first quantifier binds the index of the predicate restricting the second quantifier. In contrast, the order of the two occurrences of the universal quantifier in ( 1 4) is i r relevant. ·

The syntax of indexed predicate calculus, then, must contain one variable function symbols, like f in the above example. The variable position is filled by an individual variable, like x in the above example. JS, vol. l , no. l

49


( 1 2) (\fx) (Pi (x) ::::> ( yy) (Sj (y) :::> F i(x,y)))

S.- Y. KURODA The interpretation given to f(x) is a function from the domain of the variable x (in the above example, W k ( i ) ) to the index set I; that is, for each value of x, f(x) determines a world W k ( f { x ) )" The syntax must also stipulate that if a predicate is in the scope of a quantifier, it may be indexed by a functional index bound by the quantifier. Let me now turn to sentences with an intensional context of a familiar type. Consider: ( 1 6)

Magnus believes that a witch blighted the mare.

Tne familiar technique of scope is customarily used to distinguish different readings of ( 16) in the usual formal logic representation. Thus ,compare ( 1 7)

( !x) (WITCH (x) & (BELIEVE (MAGNUS, BLIGHT (x, the mare)))

( 1 8)

(BELIEVE (MAGNUS, (]x} (WITCH (x) & BLIGHT (x, the mare)))

( 1 9)

(! x) ( WITCH. (x) & BELIEVE. (Magnus, BLIGHT. (x, the mare)))

(20)

BELIEVE. (Magnus, ( h) ( WITCH . (x) & BLIGHT. (x, the mare))).

1

1

l

1

l

l

In (20), the existential quantifier binds two occurrences of variable x, which are both in predicates indexed with j. Hence the domain of the variable is the world indicated by index j. The semantic rule associated with the predicate BELIEVE must stipulate that it is the belief world of the subject of the verb believe, in this case, Magnus, o r perhaps a subworld within it. In contrast, i n ( 1 9) the existential quanti fier binds two occurrences of variable x, one of which is in a predicate indexed with i and the other in a predicate indexed with j. The world indicated by i is pragmatically chosen; an unmarked choice is the real world - or a mini-subworld of it - conceived by the speaker. The domain of variable x is then the 'intersection' of the worlds indicated by indices i and j, i.e., those individuals in the real world who also exist in Magnus' belief world. Before proceeding further let me insert a remark on the formal semantics of indexed predicates. We say that index j indicates Magnus' 'belief world' and predicates indexed with j are interpreted with respect to this world. But in standard logic predicates in intensional contexts are not given a semantic interpretation simply by a set, but by a class of sets, or 'possible wor Ids' , in the technical sense of modal lo�ic. 50

JS, vol. l , no. I


( 1 7) and ( 1 8) are usually taken to represent the so-called specific and the nonspecific readings of ( 1 6), respectively. There is no novelty in indexed logic for the representation of these readings. Different indices, i and j , are assigned to predicates inside and outside the scope of BELIEVE:

INDEXED PREDICATE CALCULUS Incidentally, I am inclined to believe that it would be more appropriate to assume . that predicates in contexts usually taken as nonintensional should be generally interpreted as if they were in intensional contexts; then, indexed predicates are to be interpreted always by means of a class of sets as in epistemic modal logic, and what we here call a (mini-)world is always a class of sets (possible worlds in epistemic modal logic). But this is just a hint and irrelevant to the following discussion. Now consider (21)

( 3 x ) BELIEVE . (MAGNUS, WITCH . (x) & BLIGHT . ( x , the mare)) I

I

I

Both occurrences of variable x are in a predicate indexed with j. Hence, following the general convention introduced earlier, the domain of x is the world indicated by j, i.e. (perhaps, a mini-subworld of) Magnus's belief world. In contrast with (J 9), ( 2 1 ) does not have the existential entailment w.r.t. the real world, as (20) does not. The difference be tween (20) and ( 2 1 ) , in turn, relates to the de-dicto/de-re d i c h o t o m y .

(22)

Magnus believes that Barbara is a witch and that she blighted the mare.

is true. In contrast, this does not follow from de dicto (20); it may be that for no individual x, 'Magnus believes that x is a witcn and that she blighted the mare' is true. Compare ( 2 1 ) with the formula in ordinary predicate calculus obtained by dropping indices from it: (23)

( 3 x) BELIEVE (MAGNUS, WITCH (x)

&

BLIGHT (x, the mare)).

As mentioned earlier, the customary convention associated with logical representations interprets terms in a nonintensional context with respect to the real world (as conceived by the speaker). (23), thus, claims the existence of an individual in the real world, which, according to Magnus's belief, but perhaps not the speaker 's, is a witch. The existence of this individual is 'transparent'; only is her characterization as a witch 'opaque ' . (23) does not represent the reading (2 1 ) of ( 1 6). Ordinary· logic with the customary convention cannot represent this opaque reading (2 1). How can we represent the meaning assigned to (23) by the customary practice in the framework of indexed logic? I do not know whether the English sentence ( 1 6) has a natural reading corresponding to this customary logical form, but I leave this factual question open. If the JS, vol. l , no. !

51


· Thus, ( 2 1 ) is subject to existential instantiation; for some individual, say Barbara, though perhaps unbeknownst to the speaker, the proposition

S.-Y. KU RODA meaning of (23) is not represented by ( 2 1 ), how can it be represented in the indexed logic? We have to bind x in a predicate indexed with i outside BELIEVE, but unlike the representation in ( 1 9) the predicate WITCH cannot serve this purpose in this case. The required predicate can have no conceptual conteut except for the mere existential import w.r.t. the world indicated by index i. A natural solution would be to introduce a 'universal' predicate U, such that for any x, U(x) is true. Such a predicate is redundant in customary logic, but it would be natural and useful for our purpose. Thus, we have (24)

( 3: x) (U. (x) & BELIEVE (MAGNUS, WITCH. (x ) & BLIG H T. (x, the I I l l mare))

to represent the meaning that would customarily be assigned to (23). The domain of x is now again the 'intersection' of the worlds indicated by i and j. Let us now consider the sentence obtained by replacing the proper name Magnus in ( 1 6) by the universally quantified term everyone: Everyone believes that a witch blighted the mare.

a type of sentence discussed by loup ( 1 977) and Fauconnier, following her. We now have two de re opaque readings, one with narrow and the other with wide scope of the existential quantifier w.r.t. the univer sal quantifier: (x) & BL IGHT.

(26)

( Vy) ( ] x) BELIEVE. (y, WITCH .

(27)

( ] x) ( V y) BELIEVE . (y, WITCH . (x) & BLIGH T . (x, the mare)) . I J ( Y) J (Y )

I

J(Y)

J (Y )

(x, the mare))

In ( 26) the existential quantifier is in the scope of the universal quanti fier and the domain of x is dependent on y , i.e., the belief world of y. For each y , x ranges over the belief world of y indicated by the index j(y). In contrast, in (27) the variable x is bound inside the predi cates indexed by j(y), where y ranges over the domain of everyone; hence the domain of x is the 'intersection' of the worlds indicated by j(y)'s, i.e., the common belief of everyone's concerned. If we drop indices from (26) and (27), we get formulae in ordinary logic: (28) ( V y) ( ]x) BELIEVE (y, W ITCH (x) & BLIGHT (x, the mare)) (29) ( ]x) ( Vy) BELIEVE (y, W ITCH (x) & BLIGHT (x, the mare)) How would they be interpreted according to customary convention? Since the existential quantifier outside of the scope of BELIEVE is assumed to carry the existential entailment, these formulae are taken as entailing the existence of an entity x (possibly depending on y for (29)) in the real world, which 'everyone ' believes is a witch and which 52

JS, vol. l , no. l


(25)

INDEXED PREDICATE CALCULUS 'everyone ' believes blighted the mare, although the speaker does not necessarily believe in this characterization of x. These meanings can be represented in indexed logic by means of the universal predicate U introduced earlier: (30) (31)

(x) & BLIGHT (x, ( V y ) ( :!x) (U (x) & BELIEVE (y, WITCH i i j(y) j(y) the mare))) (x) & BLIGHT (x, ( 3 x ) ( V y ) (U (x) & BELIEVE (y, WITCH i i j(y) j(y) the mare))).

In contrast, ordinary logic with the customary convention has no natural way of representing the readings (26) and (27). In comparison with the 'opa q ue' reading (30) and ( 3 1 ) , the correspon ding 'transparent ' readings are represented by (32) (33)

( V y) ( Sx) (WITCH . (x) & BELIEVE . (y, BLIGHT.

In (32) x depends on y and it ranges over the intersection of the worlds indicated by index i and index j(y), i.e. (some subdomain in) the intersec tion of the (speaker's) real world and y's belief world. In (33), in contrast, x does not depend on y and it ranges over (some subdomain in) the common beliefs of the speaker and of the everyone 's concerned. The de dicto reading of (25) is represented by (34)

( V y) BELIEVE. (y, ( 3 x) (WITCH . I

I( y )

(x) & BLIGHT. .

J ( y)

(x, the mare))).

This is the same reading as represented by the ordinary logical form obtained by dropping all the indices from (34): (35)

( V y) BELIEVE (y, ( S x) (WITCH (x) & BLIGHT (x, the mare))).

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