Journal of Semantics 13: 139-1 Ko

O Oxford University Press 1996

The Definite Article: Code and Context FRANCIS RENAUD CRLAO/EHESS, Paris

Abstract Numerous grammatical items can only be understood if the context is taken into account. In order to provide a formal treatment of this problem, we introduce the nonon of knowledge base into linguistics. After having worked out a hard core system of rules for analysing numerals, definite articles, and indefinite articles, we give a thorough study of the French singular definite article le. This grammatical item has the particularity of not encoding a fixed information stored in the lexicon, but of running a program ofinformation processing We show that the referential computation can be made by a precise algorithm working on a definite stratum of the reader's knowledge base. In this framework, the uniqueness hypothesis of Russell becomes a guideline to retrieve memorized information. The algorithm accounts for deictic as well as anaphoric referential identifications. Our analysis proposes a unitary account for a large part of empirical data and reconciles the logical approach of Russell-Montague with the pragmatic approach of Hawkins.

o INTRODUCTION What is the difference between grammatical items and other words of the language? Is the semantic value of the article the in the noun phrase the table of the same nature as that of the noun table? To answer this question, we shall not take the point of view of linguists who consider that the essential job of linguistics is only to build logical representations of sentences. This is because we believe that the meaning of an expression cannot only be in its logical representation. It seems more likely to be the product of a dynamic processing ofinformation.This is why we attribute two

complementary tasks to semantics: (i) building semantic representations of a logical nature; (2) handling these representations in specific cognitive contexts. In the recognition stage, the parser builds the semantic representations with the support of the syntactical structures. This relation between syntax and logic was first established on formal grounds by Montague, and remains an ideal for us to reach in semantics, as the beautiful book of Kamp & Reyle (1993) testifies. But to narrow semantics to this construction stage has always seemed insufficient to us. Why should we construct formulas ifwe then have no use for them? We would like to avoid producing formulas without any operational force. To be effective, these representations have to be brought into play to

140 The Definite Article: Code and Context

account for inferences and dialogues. Moreover, they must be able to be subjected to empirical tests. All the empirical data we can gather on any linguistic problem (such as time, quantification, etc.) do not determine in a unique fashion what the best representations are. Semantic theory is undetermined by observation. To overcome these insufficiencies, we thought it necessary to borrow the notion of a knowledge base from artificial intelligence. It is a memory where not only the representations of the sentences analysed are recorded but also extralinguistic knowledge (whether accepted or tacitly possessed by the hearer at speech time). The model also contains a reasonable module which makes it possible to draw inferences and compute answers to questions by using the techniques of resolution by unification. We thus have the means to distinguish clearly between the semantic representation of an expression and its meaning. We understand the meaning of an utterance as the whole set ofinferences one can obtain after entering its semantic representation into the knowledge base.

Once an implementation of this model has been devised, it becomes possible to simulate dialogues. We enter a small text into the computer and we ask questions: who does what? when? etc. Then, since to understand a text is to be able to answer questions on that text, it becomes possible to test semantic hypotheses empirically: the best hypothesis is the one that gives the best simulation of a dialogue. We used this model to give linguistic analyses of spatio-temporal expressions in Chinese (Renaud 1988) and in French (Renaud, forthcoming). And when we began to study nominal determiners in French some years ago, we discovered that here, too, the notion of a knowledge base has a leading part to play in their semantic interpretation. It is a truism in linguistics to consider that meaning depends on context. There are countless examples of starred (inacceptable) sentences which, when provided with an adequate context, become perfectly acceptable. This banal observation is wholly inexplicable in the traditional semantic frameworks (a la Montague or Kamp), since the computation of semantic representations consists in retrieving information stored in the lexicon and combining them according to the syntactic structures. A detailed study of the French definite article convincd us that they involve instructions to process contextual information. They trigger off a search in the knowledge base, the purpose of which is to identify a referent. If the procedure succeeds and returns a constant, definite articles acquire a logical representation in the spirit of Russell. Thus we have the means of reconciling the logical approach of Russell and the pragmatic approach of Hawkins (1977). This article1 consists of three parts: first, we introduce our linguistic model; second, we give a sketch of a system of rules to parse some of the French determiners; third, we give a thorough study of the definite article le.

Francis Renaud 141

1 FOR AN OPERATIONAL SEMANTICS We are trying to model how speakers understand sentences—how they encode the information into semantic representations and how diey process this information. We are only dealing with recognition. For the sake of concreteness, we will present our model in the shape of its computer implementation. It is composed of four modules: (1) a grammar module, consisting of rules for die construction of syntactic and semantic representations; (2) a knowledge base, KB, where die semantic representations of the sentences are stored; (3) a parser, which employs the grammatical knowledge to build a semantic representation SR of the sentence; and (4) an automatic reasoning module, which computes the answers to questions. Sentence

auto, reasoning — •

Answer

When the computer/listener is given an assertive sentence, he parses it and builds a semantic representation which is stored in the knowledge base. Thus we can enter a small text and then ask questions on it. The representations of the questions are sent to the automatic reasoning module, which computes answers. 1.1 The grammatical module This module is based on a linguistic theory that we can only sketch out here. The syntactic analysis is made by an unification grammar (Smolka 1992; Carpenter 1992). Within the li mi ted needs of this article, we will often content ourselves with rewriting rules of context-free grammar. Each syntactic structure is associated with a rule of semantic construction. We have chosen to use a very powerful tool to build semantic representations: the lambda-calculus. It has the advantage over the DRS-construction rules (Kamp & Reyle 1993) of allowing an integrated analysis of syntax and

The Definite Article: Code and Context

semantics. A simultaneous syntactic and semantic analysis is psychologically more plausible dian a sequential one.2 Let us suppose we want to represent (i) Mary came by come{m), where m is a logical constant representing Mary. If we take XP.P(m) (all the properties of m) as the SR (semantic representation) of the noun phrase N2, the computation will be made by S - N2 V2 So:— S1.S2 where So, Si, and S2 are die semantic representations of the sentence S, die noun phrase N2 and die verb phrase V2 respectively. The dot between Si and S2 represents the application according to lambda-calculus. The rule tells us that if the V2 came has the representation S2 — come and the N2 Mary has the representation Si — XP.P(m), then the sentence S will have the representation So : - Si£2 - (XP.P(m)).come by which ^-reduction gives come(m). Let us also take a rule of construction of N2 from a proper name NM N2-NM So:- XP.P(Si) where So and Si are the semantic representations of N2 and NM. With these two rules, we can sketch a derivation oiMary came S, come(m) N2, A. P.P(m) I

V2, come came

NM, m Mary

1.2 The parser For each sentence, the parser uses the knowledge of die grammatical module to build a formal representation. The grammatical module, as previously presented, could lead us to believe that it works in a compositional manner. But that is not entirely die case. The reason for this is that die management of spatio-temporal reference requires us to process information that has been previously recorded by memory. When we analyse die tenses of the French sentences: (2) Max entra. II vit Anne. [Max came in. He saw Anne]

Francis Renaud 143

we must be able to represent the succession of the events came in and saw Anne. To do that, at the same time as we parse the event ei vitAnne we must be able to search in the-memory for the previous event entrer[eo, max), indexed by eo, in order to note the succession end(eo) < beg(ei) (end of eo before beginning of ei).

In this same example, the analysis of the pronoun il (he) also supposes a processing of contextual information. In previous work (Renaud, forthcoming), we dealt with the management of the temporal reference point Here we will consider the nominal reference of the French definite article le in its specific, countable uses. We will see that it cannot be represented by a predefined semantic representation recorded in the lexicon but by a program of processing the contextual

information. The running of this program will possibly return an identifying referent which will then be used to build the semantic representation SR of the noun phrase. Thus the SR contains some pragmatic information.

1.3 The knowledge base As soon as the sentences of a text have been analysed by the parser, their semantic representations are recorded in the knowledge base (KB). The knowledge base permanently contains the necessary information to give an 'intensional depth' to the predicates introduced from the lexicon (definition of properties of transitive relations, links between process and state, etc.) and some general or episodic knowlege of the world. We shall define the Knowledge Base KB as the set ofinformation (knowledge, beliefs, assumptions, etc.) accepted or tacitly possessed by the hearer at the speech time.

As we have seen, the SR associated with a sentence contains a lot of pragmatic information linked to the utterance situation: knowledge about the speaker and the addressee, of the speech time, of the referent point, etc. Nevertheless, we do not consider that the whole meaning of the utterance is contained in its SK Numerous contextual effects can only be obtained by plugging this SR into the KB. The predicates appearing in the SR obtain their meaning only if they are linked to other predicates of the language by a rich network of relationships and if they are instantiated in general knowledge schemas. It is more or less deep activation of the relations between the SR and the KB that defines the depth of the understanding. In a verbal interaction, not everything is said. To understand is to be able to restore all the missing information in order to build a coherent and complete representation of a 'world model' (Enjalbert & Victorri 1994). The meaning ofan utterance is always defined relative to a knowledge base. It is not

frozen in a representation but is obtained by a dynamic processing of the whole information contained in the SR of the utterance and in relevant parts of the

144 The Definite Article: Code and Context

KB. This dependency on the parts of the whole produces a holistic effect,3 making semantic analysis particularly difficult. 14 The reasoning module This module is a mechanical theorem-proving system used to compute the answers to questions. Whenever the parser receives a sentence in the interrogative form, it first computes its SR according to the rules of grammar and then dispatches the SR to the reasoning module. The answer is then computed by resolution, a theorem-proving technique using unification (as in Prolog). Finally, an answer generator translates the logical answer into a natural language answer. To make resolution proofs, it is necessary to eliminate existential quantifiers. Consider, for example, the following (3) Paul a epouse une Chinoise. Elle est jeune et johe. [Paul married a Chinese woman. She is young and pretty] If the indefinite article introduces an existential quantifier, as is traditionally assumed, the first sentence will be represented by: (sr3) 3e3x(epouser(e, paul, x) A chinoise(x)) e is an index which specifies the uniqueness character of the event At the nme of storing the SR into the KB, each existential quantifier triggers off the creation ofa

new constant4 (up till now not used). With eM, c37, these new skolem constants, the clauses I epouser(e36, paul, c37) I chinoise(c37) will be added to the KB. When the second sentence is parsed, the analysis of the pronoun elle (she) will run a procedure of anaphor resolution. In die rule which introduces pronoun PRO JN2-PRO I S o : - XP.P(srch_ant(Ui)) the algorithm searching for antecedents srch ant uses the features of gender and number (transmitted by die feature structure Ui of PRO) to extract a possible class of candidates from a particular register refer-disc where the constants and die heads of noun phrases are stored. In the present case, it will search for a singular feminine noun and will find a possible candidate Chinoise in refer-disc. Then by unification in die KB, it will return die skolem constant c37. Thus die second sentence will be represented by age(c37, jeune) A aspect(c37, joli)

(we do not consider die time).

Francis Renaud 145

Without skolemization, we would have come up against the serious problem of performing modifications on a previously built SR: if the representation sr3 had been put into KB, we would have to put the SR of the second sentence age(x, jeune) A aspect(x, joli) (with a free variable!) inside die scope of the existential quantifier 3x of sr3. Thanks to skolemization, we do not liave to modify structures built previously; we only have to add new information into die KB. Knowledge bases for non-linguistic knowledge and dieorem proving are still not regarded as centrally relevant to die study of natural language by many pure linguists. However, diese traditional tools of artificial intelligence are essential if we want to study functional words such as die definite article, whose purpose is to process context Contrary to HPSG (Pollard & Sag 1994) and to most contemporary linguistic theories, we do not believe tJiat die ultimate goal of semantics is to build formal representations. For us, SRs are not ends in themselves but means to account for

observed inferences. This is why this model has been designed to account for dialogues. It gives us a precious means of testing semantic hypodieses: the best hypodiesis is die one diat simulates dialogues better. This conception of an operational semantics has also been defended by many psychologists (Johnson-Laird & Garnham 1980, for example) and AI computer scientists (die theory closest to ours is diat of Enjalbert 1989; Enjalbert & Victorri 1994).

2 THE HARD CORE OF NP RULES It is quite obvious that die introduction of formal representations allows a full clarification of hypodieses and makes discussions easier. But, for us, die importance of formalization also lies in the fact that it makes it possible to build step by step a complex formal system integrating a large number of language properties. This is die reason why, before launching into a diorough study of the definite article, we begin by sketching a system of representations for most of the determiners. We plan to devise a hard core of rules which should not need reshuffling even when faced with the slightest difficulty. It would have been possible to expound the formal properties of die singular definite article widi the help of predicates with individual arguments. But such a representational scheme could not be extended to account for die properties of plural determiners. The system which we are about to present is backed up by a sufficient number of properties to be able to stand up to various extensions. It is based on set type arguments. Although necessary, diis typing is not sufficient to account for some properties. To prevent an oversimplified opposition of collective and distriburive interpretations, we shall also introduce die notion of

146 The Definite Article: Code and Context

cover. Unfortunately, it will not be possible within the scope of this article to give appropriate justifications for the notion in question. First, let us see why we need set type arguments. Our problem is with the representation of verbs with collective subject, such as se reunir [to meet): (4) Tous les eleves se sont reunis. [All the students met] (5) *Max s'est reuni. [Max met] An SR of (4.) with individual type can be Vx(stud(x) ^ meet(x)) But from this formula and 'Max is a student' stud(m), we can deduce the formula meet(m) (which will be the SR of the agrammatical sentence (5)). Consequently, we must introduce a set type argument meet(stud) which means that the meeting involves the whole set of students stud — Xxjtud{x) (restricted to a given group in situation). We choose set typing instead of the semilatnce typing of Link (1983). The latter sort of typing seems to create complications without any explanatory advantages.5 Let us now consider the following example: (6) (Taisez-vous), les eleves travaillent [(Be quiet,) the students are working] This sentence is true in each of the following situations: — either each student works by himself, — or all the students work together, — or in any other intermediate situation, as when the students work in small groups. Rather than proposing three representations, we prefer to introduce the notion of cover that enables us to give only one representation, true in all possible situations. A cover of the set of students eleve is a family of sets & — [C], C 2 ,.. • Cn} whose union covers the whole set eleve: eleve - C, u C 2 «-»... v C n Thus, sentence (6) will be represented by 3 ^ cover(^ , eleve) A VX(X e & => travailler(X)) The distributive reading is obtained by taking a family of sets with one element C1-{a1}...Cn-[an}

i . e . ^ - {{a,}... (an)}

whereas the collective reading is obtained by a family of one set of all students n — 1,

C, — eleve,

& 3 {eleve}

Francis Rcnaud 147

This notation makes it possible to give only one representation for both the distributive and the collective readings as well as the intermediate readings, generally neglected by linguists. For a cover Si — (C,, C 2 , . . . Cn} of the set C, we will note the union of its elements . Si - C, u C2 u . . . u Cn - C We take an individual type argument for a noun such as 'eleve' and set type arguments for a verbal predicate. A subset of 'eleve' will be noted such as: X C eleve whose meaning is Vx(X(x) 3 eleve(x)). For a verbal predicate p and a set of individuals X, the formula p(X) will mean that the whole set X takes part in die event p at a definite place and a definite time. Now we add a few words on the problem of quantification. Consider cases like the following: (7) Les eleves ont deplace trois armoires. [The students moved three cupboards] This sentence can be true in numerous situations. But is it necessary to translate this multiplicity of values in a multiplicity of representations? Shall we, like Kempson & Cormak (1981), give four different representations of Two examiners marked six scripts or, like Davies (1989), give no less dian eight representations? Generally, disambiguating such sentences without context causes a lot of trouble for speakers. It seems psychologically implausible that they should first methodically build four or eight representations, then proceed to eliminate the representations which are incompatible with the context. This is why we choose here to take only one formula to cover the whole set of possibilities. To account for the scope problem in (7), instead of representing the plural the students by XP.(Pjtudent), the set of properties of students, we prefer to take the set of properties of a cover of students: X& 3SI (student — v.Sl A &>.Sl). For the singular relational noun phrase 'lafillede Sophie' (Sophie's daughter) we must take a singleton Si — Q^QJC) (for {{x})) as a cover X^.3ly(fille.(Q.s).y) A 3x(fille.(Q.s).x A ^.(Q.(QJC))) For more details, see the rules in the Appendix. 2.1 Type theory notation Type theory is a generalization of predicate logic which makes it possible to introduce arguments of any type. One thus obtains a language well suited to dealing with quantification and plurality in natural languages. We do not give here even a cursory introduction to type theory but refer the reader to the excellent book of Andrews (1986).

148 The Definite Article: Code and Context

Type theory is, as we have said, a generalization of predicate logic based on typed lambda-calculus. The two basic operations are application and abstraction. The application of a function for a predicate p to an argument x will be notedfoeand pjc, instead of the f(x) and p(x) of logic. If x is of type a (noted xxx), and f of a type a -•• P (noted f.a —• P), then f.x is of type p. The abstraction is used to construct functions from terms. By the t|-reduction principle, we shall consider that the set of girls is represented byfille as well as by Axifdle*). If one takes ind to stand for the type of individuals and prop to stand for the type of (Boolean) propositions, then Xxifille*) is of type ind —• prop. Any term of type a -* prop will be interpreted as a set of elements of type a, and any term of type a, -* (a2 -" prop) will be interpreted as a binary relation over elements of types a, and a2.

To represent the singleton {a}, a set with only one element, one has to take the term Xx(x — a). With Andrews, we shall note equality with the prefixed symbol Q: a — x will be represented by Q^x and Xx(x — a) by XX(Q^JC), i.e. Q.a by ^-reduction. Consequently (Q.a) corresponds to the singleton {a}.

If we now want a predicate with set type arguments, as in se-reunir.eleve, we shall have to take the following types: eleve:(ind — prop)

se-reunin((ind — prop) -* prop).

and with a two-argument predicate, we shall have aimer.X. Y where X and Y are of type ind -»prop. We shall adopt the convention of association to the left of parentheses; for instance: aimerXY - ((aimerX).Y). Let us also see how to represent the intersection and the union of two sets. Let us consider the set of girls and the set of students. Their intersection is composed by each x which is both girl and student: hc{girl* A student*). Their union is composed by each x which is either a girl or a student: kx{girl* V student*). These terms will be noted directly by girl n student and girlv student. So, we can adopt the following definitions: for X and Y of type a -» prop, we define the new sets of the same type: XnY- def Xx(X.xAY.x) XuY- def Xx(X.xVY.x) (with infixed operators as and *~\ we shall omit the dot which notates application, so that X n y must be understood as 1 A Vy (fils.(Q.s).y 3 3E(etaLE.(Q.y).malade A m £ intE)) We can sum up this first sketch of the properties of le, les, and un (with the value un des) by the following lexical entries: (Li) le, Det, \Nk#> (3,x N.x A 3X(NJC A les, Det, XNI& (card.N > i A 3 J ( N - v.& A 9>.&)) un (des), Det, \Nk#> (card.N > A 3,x(N.x A This first outline of the representation of le N is taken from Russell's formula for definite description. Let us remember that his formula, within the form given by Montague, is: 3yVx((N(x)*(x-y))AP(y)) Although it is different from our formula (Li): 3,xN(x) A 3x(N(x) A P(x)) (after having taken the same typing on individuals) one can show that the two formulas are equivalent. The purpose of (Li) is to bring to the fore the distinctive feature of the uniqueness presupposition. Still, the parts asserted and presupposed of the representation, inherited from the lexicon, are put on an identical footing. But we are going to have the uniqueness condition play an essential part in the dynamic construction of the SR on the basis of the context. So we will depart radically from Kamp & Reyle (1993), who give the same static representation to the definite and the indefinite (cf. pp. 122 and 254) i.e. XNXP3x(N(x) A P(x)) by rendering their DRS in logic.8 We thus see that the difference between le and un mainly originate in the uniqueness hypothesis 3,x N.X. What is more, for the time being, formula (Li) accounts for the fact that presupposition is preserved under negation, since the negation will be introduced through the variable 9>, in the 'asserted' subformula, without affecting the 'presupposed' subformula.

Francis Rcnaud 15 3

3.2 The role ofthe context Is all the information we draw just from examples (1) and (2) representative of the properties of le and un! A first survey of the difficulties met by the representations of (Li) will give us the opportunity to introduce the problem of the contexts of interpretation. In section 3.3, we shall try to present an inventory of these contexts. Let us take at random a concrete, nonrelational, count noun without any determination, such as Tie (island) in: (6) L'lle a ete detruite le 27 aout 1883 par une sene d'eruprions volcaniques. [On August 27th 1883, the island was destroyed by a series of volcanic eruptions] We want to ask first, 'what island are you talking about?' When we are faced with the first mention of an island, sentence (6) is infelicitous, unless one appeals to a stylistic device commonly found in novels and in the press, by which a badly identified object is introduced immediately by definite article and whose characteristics are disclosed later. We shall study this device in section 3.3.3.1, but for the time being we shall look at the device used to introduce a new object by means of an indefinite article ('Le 27 aout 1883, une ile a ete detruite par une sene d'eruptions volcaniques. [On die 27th of August 1883, an island was destroyed ...']) or by means of a definite article, as in this text adapted from Wilson (1993: p. 27): (7) L'lle de Krakatau a ete detruite un lundi matin, le 27 aout 1883, P a r u n s e r ie de puissantes eruptions volcaniques . . . Tandis que Hie s'effondrait dans la chambre souterraine videe par l'eruption, la mer s'engouffrait dans la caldeira ainsi creee. [On Monday morning of the 27th of August 1883, the island of Krakatoa was destroyed by a series of volcanic eruptions... As the island collapsed in the underground space emptied out by the eruptions, the sea rushed into the caldera thus created] If we apply our rules (Li) to the first sentence, we obtain, with some simplifications: 3,x(ile.x A name.(Q.x).kra) A 3x(ile.x A name^Qjc).kra A 3X3E(X C eruption A detruire^.X^Qjc) A int£ Q [1883,8,27])) (name.(Qjc).kra is a predicate which gives the name 'kra' to the entity x) which after skolemizarion gives ile.c,0 A name^Q.clo).kra A Vx((ilejc A name.(Q.x).kra) => x — c10) A d12 Q eruption A ile.c,, A name.(Q.c,,).kra A detruire.eu.d^Q.c,,) A int.e u Q [1883,8,27]

15+ The Definite Article: Code and Context

Thus, thefirstmention of an island, even made with a definite article, introduces a new constant c,0 into the knowledge base, which will be assumed to be, by default, different from all other constants (except for c,,). Empirically, we observe that the second mention of an island in the second sentence obviously refers to this same object. So, we cannot, in this last case, use the representation (Li) of la which will produce a new constant, different from c,0 (and c n ). But we shall see that if we use the uniqueness constraint 3,x ilex to search m the knowledge base, we will be able to bring back the right constant c10. Then all that remains is to instantiate the existential variable of the 'assert' part of le Ni to transmit the right information to the right place. We shall set out the exact procedure to search for the antecedent later on, but we can for the moment say that the 'presupposition' 3,X(NJC) will be changed into a search algorithm Srchinfo which will return a constant c, identifying the antecedent This will then be assigned to the variable x of 3X(NJC A &> .(Q.(QJC)) as: le Ni - \? ((Xx(N.x A 9> .(Q.(Qjt))))5rch-info) Example (7) provides us with four first mentions of definite noun phrases: 'le 27 aoiit 1883', 'la chambre souterraine', 'la mer' and 'la caldeira'. We can disregard the interpretation problem for nouns of dates and mass nouns, since our study only deals with count nouns. The two other nouns are cases of associative anaphora: they belong to the special terminology and they should be understood as 'la chambre souterraine de volcan (the underground space of the volcano)' and 'la caldeira produite par le volcan (the caldera of the volcano)'. In his knowledge base, the reader can come across the existence of a volcano through the mention of the volcanic eruption d12 introduced in the first sentence and through general knowledge about volcanoes: volcanoes usually develop in an underground space and their explosion may produce a caldera. On this basis, it becomes possible for an algorithm to prove the uniqueness of the space and of the caldera in the restrictive discourse universe. We shall later propose a rule for the treatment of this problem. We shall deal later with the case of nouns with a unique referrent ('monoreferring' nouns, such as 'la volcanologie', vulcanology) and that of deictic uses (such as 'ferme la porte', shut the door) which can all appear in a first mention (cf. section 3.3.3). The two kinds of anaphora illustrated in (7), the direct anaphora ('lile') and the associative anaphora ('la chambre souterraine'), can be taken into account if the article 'le' does not translate directly into a logical representation taken from the lexicon (as does rule Li) but into a representation built on the basis of contextual information supplied by the knowledge base. It has frequently been observed that the starred (unacceptable) context-free linguistic examples could become 'acceptable', when some appropriate context has been supplied. This very common phenomenon in natural language comes

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from the fact that one part of the information is encoded and that the other has to be constructed from the context. The methods of taxonomic description, which have allowed linguists to make progress, seem utterly ineffectual in the face of the fantastic profusion of possible contexts. We assume that to account for the contexts we will not have to give a description of all the possible contexts, but only that of the algorithm ofcontextual information processing. 3.3 Contextual restrictions We shall try to classify the specific uses of the definite article le (with count noun). We propose three kinds of use: 1. either the lexicon guarantees the uniqueness (monoreferring nouns); 2. or the information stored in the memory makes it possible to check the uniqueness; 3. or all these search processes fail but the use of a noun complement or of a deverbal head is enough to guarantee that the uniqueness hypothesis will be compatible with the basis. We study these three processes of analysis in the following three paragraphs.

3.3.1 Encoded information is enough to guarantee uniqueness of reference: monoreferring nouns Monoreferring noun phrases are noun phrases with a definite article but with a rigid referent; such is, for instance, the case of proper names. Thus, 'la Seine' and 'Paris' both only refer to one item. We usually choose to represent them by their minimal forms: k#>&.{Qj(Qs))

and

X ^^.(Q^Q.p))

where s and p are constants identifying the river Seine and Paris. Of course, to be more precise we should accompany these lexical entries with additional information as 'a French river that flows through Paris ...' or 'Paris, the capital of France ...' (8) X^(fleuve.s A ds.(Q.s).(l.(fr)) A name.(Q.s).'La Seine' A . . . A (9) \& (capitale.(Q.fr).) A name.(Q.p).'Paris' A & .(Q.(Q.s))) ds is a predicate of localization such that ds.(Qjc)^l.y) requires that the individual x is in the place of the individual y (1 is a function referring to a place; one can also have functions corresponding to on, under, south, etc.). Into this category of monoreferrings, we put: • toponyms such as: la (Loire/Seine, etc.), le Massif Central, la Chine, la Mecque, etc'

156 The Definite Article: Code and Context

• time nouns locating periods on the absolute time axis: le cretace, le Moyen Age, etc.; • well-known people or historical events: le Roi Soleil, la Revolution Francaise, la Restauration, etc.; • names of works (le Ramayana, le Coran, la Joconde, etc.), names of newspapers (Le Monde), trade names, company names, names of stars (la lune, le soleil), etc. 'Le pape' [the pope] or 'le dalai' lama' are not included in this category since they refer to different people at different times. They are count nouns depending on time. One can speak of 'deux papes' [two popes] or of 'Phistoire des papes' [the history of the popes], but 'deux Chines' [two Chinas] will have a different value and Thistoire des Chines' would be very odd. Also classified among the monorefernng nouns are a class of nouns (such as 'la campagne' [the countryside], 'la paleontologie, la realite virtuelle') which are neither stricdy countable: trois (*campagnes/tables) [three (*countrysides/tables)] nor strictly mass nouns: (de la/un kilo de) (*campagne/confiture) [(some/one kilo of)(*countryside/

J am )] Many of them are deverbal or deadjecnval nouns ('la construction, l'intelligence') and will not be studied because of lack of space. As all these terms refer to unique entities, they should be characterized by unique identifying constants, possibly accompanied by some prototypical properties (a foreigner or a robot coming across the term 'la CGT in a text would certainly be very disappointed if the lexicon just told him it is the only entity of its kind). Thus, if we look at the representation (8) of'la Seine', we see that the uniquenss is mechanically imposed by the introduction of the constant s and that the definite article plays no essential part So syntactic rules just bring up the uniqueness already encoded in the lexicon. But, on syntactical grounds, it is

necessary to protect the autonomy of such nouns as 'Seine', 'France', or 'lune' because of such uses as 'une Seine endormie', 'en France', 'la pleine lune'. Later (at the end of Section 3.3.2.1a), we shall give the rule of interpretation of the monorefernng nouns. But for the time being, let us emphasize the fact that the system of identification of world objects works correctly only if we subject the knowledge base to some constraints. It will be assumed that, by default, all the predefined constants are unique and distinctfrom one another. For most

speakers, the lexicon will attribute the same identifying constant to 'la Corse' and 'l*ile de Beaute'. But we can also have speakers for whom these constants are different and who are subject to opacity effects in certain contexts.'

Francis Rcnaud 157

It is only a posteriori and by default that this uniqueness of constant constraint is imposed on the knowledge base. If, for example, a text mentions a river for the first time without naming it ('Nankin est situe sur les bords d'un grand fleuve', Nankin is on the bank of a large river, etc.) and then subsequently gives its name, *Le Yangzi', we will have to identify the constant coming from the Skolem constant generator (for ex. c101 for a large river) with the constant identifying the monorefernng phrase (for ex.g for the Yangzi): c101 — g. That is to say, as the analysis of the text proceeds, the umqueness of constant condition can always be called into question. Thus it can only be dynamically managed by the theorem prover which in real time and by default guarantees the uniqueness of each constant, unless the contrary is explicitly specified. Cj / Cj

for

i/j.

3.3.2 There is not enough encoded information to guarantee uniqueness of reference but the search for contextual specifications succeeds We will consider successively the process of searching for information about the speech situation, the previous context, and the general knowledge. We shall call tliese restrictions respectively deictic, anaphoric, and cognitive (or general) restrictions. 3.3.2.1 Deictic restrictions (a) Direct deictic identification Consider the request: (10) Pourrais-tu fermer la porte. [Could you shut the door] Let us suppose that this order is given to a robot equipped with the visual captors and algorithms enabling it to recognize the objects in situation. Moreover, let us suppose that it stands in a room with two doors: one open and one closed: our robot will be able to identify and to represent in its memory one open door C|, one closed door c2, one open window c3, one human interlocutor c4, etc. This information is all stored in a particular stratum of its knowledge base KBrit, the situational (orpragmatic) stratum (coming from the sensory store in human beings). Disregarding temporal phenomena, KBrit would contain, among other things: porte.c, A ouvert(Q.c,) porte.c2 A ferme.(Q.c2) fenetre.Cj A ouverL(Q.c3) etc.

158 The Definite Article: Code and Context

Each of these objects c, is associated with a picture and is referred to a spatial coordinate system bound to the room. Moreover, the base will have the general properties of the predicates used: thus we shall have 'si une porte est ouverte elle n'est pas fermee' (if a door is open it is not closed) vx((porte.x A ouvert.(Q.x)) => ->ferme.(Qjc)) or in conjunctive normal form: -•portcx V -.ouvert(Qjc) V -.ferme.(Qjc)

(OF)

Finally, each stratum of the base is supposed to contain all the information on its reference domain. Thus the mention of two doors c, and c2 does not amount to saying diat the base knows the existence of two doors perfecdy but is unaware of other possible doors. On the contrary, we will have to suppose that the information is complete, that is to say no other door is involved in the situation. This property of domain closure, studied by Reiter (1984) in relational data bases, will be formulated here as: -•portcx V x - c, V x - c2

(CL)

To sum up, KBrit will contain the following information:

„-„ at

porte.c, A ouvert(Q.c,) porte.c2 A ferme^Q.c^ . fenetre.Cj A ouvert(Q.c3) ' -.portcx A -ouvert(Qjc) V -ferme.(Q.x) —"portcx V x — c, V x — c2 (CL) etc.

(OF)

If we now look at the order to shut the door ('ferme la porte'), the meaning of 'fermer' requires that before doing the action the door must be open ('ouvert'). In this case, it is empirically obvious that the uniqueness hypothesis linked to 'la porte' should not only be 3,xportejc but UNI — ^^ (porter A ouvert.(Qjc)). With the help of this restriction, it is now clear that we can prove KBrit I- 3,x(portcx A ouvert(Qjc)) The major point of interest in diis demonstration stems from the fact that if we do it by refutationl0 we can get a substitution x«- c, which will return the right identifying constant of the object. After negation and skolemizaoon of the goal 3tx(portejc A ouvert. (Q-v)), we get -•portcx V -H3Uvert.(Qjc) V (porte.(fx) A ouvert(Q.(fx)) A -{fa — x)) By resolution of this goal on porte.c, and then on ouvert.(Q.c,), we get porte.(f.c,) A ouvert(Q.(f.c,)) A --(f.c, — c,)

Francis Renaud 159

with the help of the substitution x — c,. The resolution of porte.ff.c,) on (CL) gives f.c, - c, V f.c, - c2 which by resolution on the previous —>{f.c, — ct) gives f.ct — c2 and by substitution of the last equation in ouvert.(Q.(f.c,)) we get ouvert.(Q.c2). Its resolution with the axiom (OF) gives -•porte.Cj V --fenne^Q.c^ which to our delight can be resolved withporte.c2 and ferm£.(Q.c2) in KBrit, and which in the end gives the desired contradiction (the empty clause) and the subsotuation x •*- c,. Our first intuition, according to which the uniqueness hypothesis has to play a role in the identification of the referent, is translated here by an effective computation procedure which returns the right identifying constant q (and then a spatial localization). The last stage of the analysis of the phrase 'la porte' will be to apply the substitution x «- c, to its representation. X^(Xx(portejc A ^.(Q.(Q^)))).c, -pX^(porte.c, A i?.(Q.(Q.c,))) Then the classical rules of sentence construction will give the following representation for the order (10) ordre.(fermer.e.(Q.rob).(Q.c,) A porte.q) (the robot identifying itself by the constant rob and being able to localize c,. From this example, we will remember the following three points: — the uniqueness hypothesis does not only behave as a presupposition in the traditional meaning of the term; — the uniqueness hypothesis is not a logical representation transmitted from the speaker to the hearer. On the contrary, it is an instruction used by the hearer in his program of processing contextual information to identify a particular individual; — finally, the formulation of the uniqueness hypothesis 3,{portejc) is incomplete, at least in the illocutionary frame of the given example. To be effective, the additional predicate ouvert. (Q-x), coming from a presupposition linked to the verb, must be added. In the general case, we shall note this restrictive predicate by R and thus the uniqueness hypothesis by 3,X(NJX A RJC).

We can verify that if the situation did not imply the presence of the two previous doors c, (open) and c2 (closed) but also one third door Cj open, the proof KBrit V- 3,x(porte.x A ouvert(Q.x))

i6o The Definite Article: Code and Context

would have failed. In this case, one can agree that the hearer/computer will ask 'which door?' to launch a dialogue. We shall sum up the analysis of a phrase le Ni in an identifying context (as that in (10)) as follows: — First, a procedure Srch-info.(N f~> R} which processes the situational information is run, with N being the representation of Ni and R the restrictive predicate. This procedure tries to prove by refutation KBrit I- 3,X(NJC A R.X) Two possibilities arise: (a) either the proof succeeds and then at the same time returns a substitution x «- t, where t is a ground term (variable-free) such that KBrit H N.t A Rt (b) or the proof fails. If we introduce the additional procedure TestSrch-info, one can then sum up the alternative: (a) the proof succeeds and Test-Srch-info.(Ns~> R) returns 'true'

Srch-info.(Nn R) returns the term t (b) the proof fails and Test-Srch-info.(Nn R) returns 'false' — The final representation of le will be: n . \ '

le, Det, acc(gnmasc A nbsg) \Nk& if Test-Srch-info.N then (XX(NJC A & .(Q.(Qjc)))).(Srch-info.N) else answer-by-the-question 'quel N?'

(for the time being, we are not considering the restrictive predicate R. It will be introduced later). The rule shows us that we can build general algorithmic rules applied to the contextual information. Thus, we see that semantics does not need to make a content analysis of the context. Nevertheless, we will show that if we want to avoid the appeal to ad hoc contextual information, we conceive of KB as being comprised ofsmall units (which we call stratum). Before studying odier contexts, let us see if it is possible to give a synthesis of (Li) and (L2). Let us again take example (1) 'le fils de Sophie est malade (The son of Sophie is ill)': — either no information on Sophie's children is available in the base: KB I-/- 3,x fils.(Q.s).x KB I-/— card(fils.(Q.s)) / 1

1-/— means 'one cannot prove'

Francis Renaud 161

In this case, we have to assert the uniqueness and introduce an existential variable: ,x fik(Q.s).x A 3x(fils.(Q.s)jc A ^.(Q.(QA))) — or we already know that Sophie has one and only one son, Paul: Then die proofof KB I- 3,x fils.(Q.s)jc successfully halts and returns die identifying constant p of Paul. In this way 'le fils de Sophie' becomes

— or we know Sophie has several or no sons: KB I-/- 3,sx fils.(Q.s)jc KB I- card(fils.(Q.s)) / i in this case die hearer can show his disagreement widi die presupposition of the utterance (i) (or we are in the situation depicted in section 3.3.3.1) Thus die synthesis of rules (Li) and (L2) is possible. With this aim in mind, let us introduce an additional procedure to test if KB \- card.N 7* 1 can be proved. We will call it Test-Srch-info-NU. The old procedure which tests whether uniqueness KB I- 3,xN.x can be proved will be called Test-Srch-info-UNI, and the procedure which brings back the substitution, Srch-info-UNI. With these notations, the rule appears as

(L3)

le, Det, acc:(gnmasc A nb:sg) INK& if Test-Srch-info-UNLN then ((XX.NJC A ^.(Q.(Qjc))).(Srch-info-UNI.N)) else if Test-Srch-info-NU.N then retort-by-the-quesuon 'quel N?' else 3X(NJC A

Let us label the first formula, when Srch-info-UNI returns an identifying constant c already known in the base XNk&> (N.c A ^.(Q.(Q.c))) as the identifying value and die second formula \Nk&> 3x(N.x A &>{Q{Qx))) as the existential value.

162 The Definite Article; Code and Context

In this latter formula, we choose not to keep the assertion of the uniqueness hypothesis 3,XNJC, although this choice is disputable, as we will see later. Since trie Russell uniqueness presupposition associated with the existential value is used to direct the algorithm which 'pragmatically' searches for the referent, rule (L3) thus carries out the synthesis of the logical approach of RussellMontague and the pragmatic approach of Hawkins (ig77, iggi). We recall that when

this search succeeds, the referent found is transmitted to the 'asserted' part of the Russell-Montague formula. Thus we have a precise and powerful tool which, contrary to the intuitive notion shared set (orP-set) of Hawkins, can be empirically tested. What we have is not a simple list of world objects but a knowledge base, sufficiently rich in information to enable us to define an effective procedure for processing information. Although Heim's (1988) notion of'file' is more precise than that of the shared set of Hawkins, we can apply the same kind of criticism to it Unlike the 'files', the KB, a well-defined and well-studied notion of AI, plays an essential part in our theory of meaning, and its usefulness goes far beyond the problems involved in the interpretation of nominal determiners. Furthermore, we give an effective procedure for processing the information contained in the KB and we will see that it is possible to structure that information into subunits sufficiendy well-defined to avoid the resorting to ad hoc information (see later the problem of 'accommodation'). This representation (L3) makes it possible to understand why (4.1) 'le pere de Sophie est malade (the father of Sophie is ill)' is correct, whereas (5.1) 'la portiere de ma voiture ferme mal (the door of my car shuts badly)' can pose problems. Wejust have to spur on some general knowledge of the base: 'tout humain n'a qu'un seul pere (every human only has one father)' vx3,y pere.(Q.x).y = Vx3y(pere.(Qjc).y A Vz(pere.(Qjc).z 3 z — y)) which after skolemization by the function pr appears as: (PR) VxVy(pere.(Q.x).y « (y - (prx))) Parsing 'le pere de Sophie' will make the test TestSrch-info-UNI.(pere.(Qj)): (PR)... I- 3,x pere^Q.s)jc This refutation succeeds and returns the substitution x •*- pr.s. Thus the identifying value of the noun phrase will be: \& ((Xx pere.(Q.s).x A ^Q.(Qj())).(pr^)) ~$k&> (pere.(Q.s).(pr.s) A So rale (L3) brings this satisfactory representation into sentence (4.1): pere.(Q.s).(pr.s) A etate.(Q^pr.s))jnalade A m e inter.e

Francis Renaud 163

Thus with the help of general knowledge about the world, the definite article can have an identifying value at itsfirstmention. No ad hoc information" need be added to die KB. On die other hand, in example (5.1) 'la portiere de ma voiture ferme mal', the test Test-Srch-info-Uni will fail if we know that a car has several doors. In this case, die rule (L3) correcdy allows for the listener to ask additional information: 'quelle porte? (which door?)' (other possibilities will be considered later). Let us now test (L3) on the following example: (11) Le pull de Sophie a retreci au sechage. [Sophie's sweater has shrunk during die drying] Let us suppose that diis sentence has been spoken in front of a clodies-drier. To be felicitous, there must be only one sweater belonging to Sophie present in die speech situation. Of course, die dozen or so sweaters Sophie owns as well are not to be taken into account. Even if in front of die drier there are two sweaters belonging to Sophie, only one of which has shrunk, die sentence would be infelicitous—it would be more suitable to say 'un pull de Sophie a retreci12 (one of Sophie's sweaters has shrunk)'. To account for diese properties exacdy, it is imperative, as in die robot example, to take for KB,lt only the objects which are present in the speech situation and no others.

Finally, as announced in Section 3.3.1, we are going to ensure that rule (L3) makes it possible to interpret die monorefernng noun phrases correcdy. If we take a singleton as the semantic representation of'Seine', as in die lexical entry: Seine, N, Xx(fleuve.s A ds.(Q.s).(l.fr) A name.(Q.s).Ta Seine' A x - s) we can verify that Srch-info-UNI succeeds and returns x «- s and dius gives \& ((Xx(fleuve.s A ds.(Q.s).(l.fr) A name.(Q.s).'La Seine' A x - s A i?.(Q.(Q.x)))).s) - \9> (fleuve-s A ds.(Q.s).(l.fr) A name.(Q4'La Seine' A ^.(Q.(Q.s))). as die identifying value of'la Seine' (after having taken out the tautology s — s). So it is dianks to the uniqueness ofreferent encoded in the lexicon that die definite

article of a monoreferring noun obtains its identifying value. (b) Indirect deictic identification (bi) Use of spatio-temporal localization of the situation Let us consider diis headline from Le Monde: (12) Le gouvernement accorde une aide de 1,5 milliard aux agriculteurs. [The government grants aid of 1.5 milliards to farmers] Anyone anywhere meeting this sentence in a French newspaper will understand 'le gouvernement' as 'le gouvernement francais'. The noun

164 The Definite Article: Code and Context

'governement' is relational: it is the government of a given country at a given time. If we pay no heed to the temporal localization, the uniqueness hypothesis will be: 3x3y(gouvernemenL(Q.y)jc A pays.y A Vz(gouvernement.(Q.y).z 15 z — x)) Furthermore, the notion of 'gouvemement' (as with 'pere') is associated with a functional relation: 'chaque pays a un et un seul gouvemement (each country has only one government)': (G) Vx(paysjc ^ 3y(gouvernement(Qjc).y A Vz(gouvernement(Qjc)^ 3 z — y))) To be able to make the same kind of analysis as with 'le pere de Sophie', we just have to select the right situational stratum. Knowing that the sentence (12) has been taken from a French newspaper, the reader, wherever he is, is going to activate his stratum of knowledge about France. Thus K B , , ^ will be composed of (among other things): pays.fr (France is a country) and the general knowledge (G) on governments. One can see that the proof of KB«it(fr) *~ 3x3y(gouvernement-(Q.y).x A pays.y A Vz(gouvernement.(Q.y).z D z - x)) succeeds and returns x *- gv.fr (gv skolemization function) y •*-fr.We just have to generalise the process by which we instantiate the variables of (L3) to get ^.gouvemement.(Q.fr).(gv.fr) A ^".(Q.(Q.(gv.fr))) Finally, we see that the representation of'le gouvemement' is the same as that of 'le gouvemement franfais'. Thus we are happy to see that the rule (L3), which has been constructed to account for other kinds of example, also works perfectly well with (12). (b2) Use of knowledge specifically shared between speaker and listener The knowledge used in the previous examples was general knowledge shared between most of the native speakers. But it can also happen that some episodic knowledge shared only by the speaker and his addressee is activated. If I say to my wife: (13) Ce soir, je passerai a la boulangerie. [This evening, I'll go to the baker's shop] only my wife will know which baker's shop I am speaking about Although there are three baker's shops near our home, the term 'la boulangerie' will refer to the baker's shop where we usually buy our bread. One can understand that with the help of this restrictive predicate which will guarantee the success of the first test rule (L3) will return the correct referential identifying value. But it is interesting to note that this utterance (13) will also be comprehensible to a hearer who has no

Francis Renaud 165

information on the shops near our home. In this case, the two tests of (L3) fail and the rule returns k^>3x(boulangerie^c A ^.(Q.fQ^c)))—the hearerjust has to extract any baker's shop. No shared knowledge is necessary to understand (13) (contrary to Hawkins 1991 who appeals to 'some subset of entities (P), in the discourse universe which is mutually manifest for speakers and hearer on-line'). We thus see that rule (L3) accounts for Donellan's referential and attributive readings (a very specific baker's or any baker's). For the addressee, the choice between one ofthese two readings depends on his knowledge ofthe world and not on what the speaker has in mind.

On the other hand, when we arrive at a new place on holiday, instead of (13) I would rather say: (14) Ce soir, je passerai dans une boulangerie. [This evening, I'll go to a baker's shop] since the indefinite article does not call for a process ofsearch in the base. We thus find again the observations made by Damourette & Pichon (1950) or Christopherson (1939) who respectively uphold the thesis of the 'notoriety' and 'familiarity' of the definite article (the definite article refers to the already known individuals). This familiarity effect simply comesfromthe referential identifying reading when the kowledge base is compatible. For rule (L3) to work well, it is of the greatest importance that Srch-info-UNI activate the appropriate stratum of the base: the previous examples all show that we have to take a stratum KBrit containing the information about the immediate speech situation with, if necessary, speaker-hearer shared information.13 3.3.2.2 Anaphoric restriction: the retrieval of*information from the representation of the previous text The stratum of the base we are going to study will be called the 'textual stratum' and will be noted K B ^ (a) Direct anaphora Let us consider the example: (15) Vincent Van Gough s'installa a Aries en 18 8 8.. .Ilreproduisitles sites quise trouvent aux environs de la ville [Vincent Van Gouch settled in Aries in 1888 . . . He painted the settings in the vicinity of the town] In such a simple text, it is clear that at the time when 'la ville' is parsed, the search throughout the semantic representation of the previous text will return the substitution x «- arl: KB^, I- 3,x vilkx

166 The Definite Article: Code and Context

if we represent 'Aries' by X«^(villearl A name.(Q.arl).'Arles' A and if we appeal to Reiter's domain closure hypothesis. To our great surprise, the algorithm Srch-info-UNI seems able to resolve the direct anaphora! Unfortunately, such a simple computation is seldom seen. If we look at Chapter DC of Une Vie de Van Gogh (Sweetman 1990), which describes Vincent's time in Aries, in the first five pages we find, in all, four occurrences of 'Aries', two occurrences of'Marseille' and nine occurrences of'la ville', all referring to Aries. The mention of two towns in the context forbids the rough use of the uniqueness hypothesis in order to search through the textual stratum. Let us look at an example closely: (16) (Vincent sortit de la gare d'Arles) A sa gauche, il apercevait la grand-rue qui se dirigeait vers Marseille; devant lui se dressait la porte de la ville. [(Vincent went out of the station of Aries) On his left, he saw the main street leading to Marseilles; before him, towered the gate of the town] For a human reader, it is quite obvious that 'la ville (the town)' refers to Aries, seeing that 'la porte de la ville (the gate of the town)' stood in front ofVincent who had j us t arrived at Aries and that Marseilles is one hundred kilometres from there. Thus, through this chain of reasoning, we have a tail to discover a formal proof, making it possible to identify the antecedent correcdy. However, this is on condition that we introduce a restrictive predicate in the uniqueness hypothesis: UNI — il existe une ville x et une seule telle que la porte de x se dresse devant Vincent. (there is one and only one town x such that the gate of x stands in front ofV.) Thus we again find the problem of restrictive predicates already met in 'ferme la porte (shut the door)' (needing the predicate 'ouvert (open)') or 'le pull de Sophie (Sophie's sweater)' (needing the predicate 'present en situation (present in situation)'. In actual fact, the restriction is brought by the sentence in which the noun phrase appears. Sometimes, as in (16), we just have to take the relative: 'la ville dont la porte se dresse devant lui (the town whose gate stands in front of him)', or in (13) 'la boulangerie ou je passerai (the baker's shop where I'll go). To confirm this hypothesis, let us look at this new example: (17) Pourrais-tu coller cette note sur la porte. [Could you stick this note on the door] In a situation where there are several doors, to make it possible for our dear robot to pick the right door, it would have to use the information given by the sentence

Francis Renaud 167

under parsing. For example, the robot would say to itself: ifhe wants to stick a note on a door, this is to enable everyone to read it, therefore it's better to put it on the door of the corridor. Thus, in the same speech situation, the occurrences of'la porte' in 'ferme la porte' and 'colle cette note sur la porte' may have different referentsl We thus see that the information used to identify a referent is given not only by the knowledge base but also by the sentence under analysis. We have here a beautiful example of noncompositionality.14 We do not claim to put foward the solution to the problem of anaphora resolution (of definite description). This is a very difficult question which needs huge capacities of semantic information processing but which may probably also use further syntactic notions such as the DRS of Kamp or discourse focus. To give a formal translation of our observations on the restrictive predicate, we first have to modify the rule (L3). A simple means of introducing a restrictive predicate R lies in adding an abstraction XR, which will give the R to the search algorithm but will keep N intact on the 'assert' part of the representation in order to avoid getting: 'devant lui se dressait la porte de la ville dont la porte se dressait devantlui (before him, towered the gate of the town whose gate towered in front of him)'

(U)

le, Det, acc(gnmasc A nb:sg) XNXRX^ if Test-Srch-info-UNL(N n R) then ((Xx.N.x A ^.(Q.(Qjc))).(Srch-info-UNl-(N n R))) else if Test-Srch-info-NU.(N r> R) then repliquer-par-la-question 'quel N?' ejse 3x(N.x )

Of course, the difficulty is to introduce this restrictive predicate advisedly. In order to do it at the level of the rule N2 - Det Ni, we must have SO :— ((SiS2)Jlestr). But the predicate Restr, being dependent on the sentence under analysis, cannot be introduced in a compositional manner. We shall not stop at this small technical problem while a lot of mysteries still remain about the data. To sum up, we can say that the algorithm Srch-info-UNI searches through the knowledge base in relative darkness. The only trail followed is that given by the uniqueness hypothesis with its possible restrictive predicate and by limiting the search process to the restricted frame of discourse universe defined by the situational or textual stratum (KBrit or KBttt). (b) Associative anaphora Let us remember that in (12) the interpretation of'le gouvernement' clearly needs to 'let in the clutch' on the speech situation. On the other hand, we will see that in a narrative, in which by definition the chain of events is not linked to the speech

168 The Definite Article: Code and Context

time, the interpretation of le N will be a matter for the previous text (which we call cotext).

Let us see an example with nonrelational nouns: (18) Vincent alia a Anvers. Il vit la cathedrale, l'Hotel de Ville, les rues tortueuses de la vieille ville mais c'est le port qui le frappa le plus. [Vincent went to Antwerp. He saw the cathedral, the town hall, the winding streets of the old town but it was the harbour that struck him most] To be able to locate the cathedral (and all other underlined nouns), the reader's KB must contain the following information: 'Chaque grand ville occidentale a une cathedrale (each large Western town has a cathedral)' l a Belgique est un pays d'occident (Belgium is a Western country)' Moreover, the lexical entry of'Anvers' must contain the information that 'Anvers est une grande ville de Belgique (Antwerp is a large town in Belgium)'. Let us sum up this information after removing the role of the West: Vx(ville.x 3 3y(cathe.y A ds.(Q.y).(l.x) A Vz(cathe.z A ds.(Q.z).(l.x) 3 z - y))) ville.av (av identifying constant of Anvers) After having skolemized with the function c and having applied one modus ponens, we will have in the base ville.av cathe.(cav) ds.(Q.(cav)).(lav) -'cathe.z V -xk(Q.z).(l.av) V z — (c.av) When we were working with a relational noun, it was the presence of the first argument of the noun (usually bound to a noun complement) that enabled us to retrieve the specifications from the base. Here, with a unary noun (or sortal noun, i.e. with only one argument), we must introduce a localization predicate that will be used to anchor the cathedral in a place. The uniqueness hypothesis will be 'il existe une seule cathedrale se trouvant dans un lieu (there is one single cathedral in a place)' UNI - 3x(cathejc A 3y(ds.(Q.x).(l.y) A Vz(cathe.z A ds.(Q.z).(l.y) 3 z - x))) Now all that remains for us to do is to make the proof by refutation of KB^, hUNI to obtain the substitution x «- cav, y — av. Rule (L4) then gives us the specifications we looked for \P cathe.(cav) A ds.(Q.(cav)).(l.av) A Consequently, 'la cathedrale' is 'la cathedrale d'Anvers'.

Francis Renaud 169

If the previous text now mentions the town of Brussels, we again come up against a problem such as that of choosing between Aries and Marseilles which we met in (16). In that case, we have to analyse the sequence of actions: 'A go to X', 'A see V with the help of some general principles: 'If an individual A has gone to the place X, afterwards he is in X', 'if an individual A located in X sees Y, then Y is in X'. We must also take into account the sentence under analysis •Vincent saw a cathedral' 3y cathe.y A voir.E.(Q.v).(Q.y). With the help of these items of information, which are all highly likely in the situation under consideration, it becomes possible to make the refutation which will give us Antwerp rather than Brussels. Let us also point out the central part played by the part/whole relation in the associative anaphora. (19) Jai emmene ma voiture au garage. Lecoffre ferme mal. [I took my car to the garage. The boot shuts badly] If we have available in memory the fact that 'cars have only one boot', the search algorithm will have no trouble in returning the right specification. Let us say in passing that since we are searching through logical representations we could also succeed with an indefinite antecedent: (20) J'ai emmene une voiture au garage. Le coffre ferme mal. [I took a car to the garage. The boot shuts badly] whereas a surface analysis that tried to restore the noun complement would give 'le coffre d'une voiture (the boot of a car)' and thus would introduce another car into the universe. Fradin (1984) was one of the first to observe insightfully that the knowledge used in this kind of process was stereotypic knowledge. Kleiber (1993b) found a lot of arguments to support this view. So the textual stratum is composed of the representation of the previous text and of the associated stereotypic information. This information is general knowledge, shared by most of the speakers, and which gives the necessary, prototypical or scenic (coming from a scenario) properties of

objects. (As a rule, we will represent it by the Reiter's default rules, Sombe 1989)). Lobner (1985) laid great emphasis upon the role of functionality: 'the crucial condition is that the head noun in these uses provides a general two-place functional concept'. At first sight this seems to be right, since the algorithm Test-Srch-info-UNI will succeed in its quest for uniqueness if it finds a functional axiom in the KB. But Kleiber (1993b) clearly shows that this condition on the noun is not sufficient in itself. It must necessarily be of stereotypic nature. We can rapidly illustrate this particular status of knowledge by this famous example adapted from Kleiber (1993b):

170 The Definite Article: Code and Context

(21) Nous entrames dans un petit village. L'eghse dominait les maisons. [We came into a small village. The church towered above the houses.] (22) Nous entrames dans un petit village. ??La superette etait fermee. [We came into a small village. ??The superette was closed] The prototypical relation between 'small village' and 'church' is enough to interpret 'l'eghse' as Teglise du village'. But substituting Teglise romane (the romanesque church)' for 'l'eghse (the church)' is enough to make the sentence look very strange. As for sentence (22), it seems very odd in French, although everyone knows a lot of small villages with a superette. The functionality of the head noun, which of course guarantees the uniqueness condition in rule (L4), seems to be valid for the associative anaphor only if Test-Srch-info-UNI is done upon stereotypic information. Rule (L4), contrary to Heim's accommodation,15 when working in recognition, makes it possible to account for all these effects. We thus experience a pleasant surprise when we realize that the same algorithm allows us to carry out direct and indirect specifications: direct and associative anaphora (sections 3.3.2.2a and b), as well as what we have called direct and indirect deictic identification (sections 3.3.2.1a and b). This result can be understood as a consequence of the fact that in the direct case the uniqueness hypothesis contains only one existential variable to instantiate, whereas in the indirect case it contains two: one variable instantiating the referent and the other, non referential, instantiating a noun-complement relation.1* Moreover, when one works in generation, the availability of stereotypic information is not even enough to guarantee that associative anaphora with 'le' will be possible. As a matter of fact the anaphoric link can be established by the definite article as well as with the clitic 'en' or the possessive 'son/sa/ses'. Fradin (1984) and Kleiber (1993a, b) have made detailed studies of this problem, while working mostly on the syntactic surface and from the standpoint of generation rather than recognition. By definition, we limit associative anaphora to those cases where the search for a double instantiation (of referential and non referential arguments) through the textual stratum succeeds. Although, very often, the specification can be brought by a noun complement, we prefer to avoid any syntactic definition.

3.3.2.3 Cognitive restrictions Until now we have considered the process of retrieving information stored in more or less long-term memory. The preceding analysis of deictic and anaphoric restrictions made use of information originating from the sensory store (real-time perceptions of the objects in the speech situation) or textual short-term information (immediate anterior text). On the contrary, the

Francis Renaud 171

activation of lexical memory carried out during the analysis of monoreferent is a matter of long-term memory. We are now going to see other cases of recourse to this long-term memory: episodic memory (23, 24) and general knowledge of the world (25). Let us look at the following examples: (23) (Le Monde) L'accord de libre-echange nord-americain doit etre examine par la Chambre des Representants mercredi prochain. [(Le Monde) The North-American free-trade agreement will be examined by the House of Representatives next Wednesday] (24) Un accord de libre-echange entre l'Indonesie et la Malaisie est en cours de discussion. [A free-trade agreement between Indonesia and Malaysia is under discussion] It seems to us that if the Le Monde journalist believes he is allowed to introduce an 'accord' by means of definite article in the first sentence of his article, he will also believe that his readers already know of the existence of this agreement. On the other hand, brand new information, as in (24), must be introduced by an indefinite article. The definite article in (23) seems to function here in the same manner as with direct anaphora, but instead of searching through the cotext the algorithm Srch-info-UNI searches the long-term memory KBL T . If it finds an identifying constant q, it brings it back to the sentence under analysis. But if it finds no specifying information, it introduces a new constant by means of the existential quantifier, exactly as the indefinite article does in (24). In this case, then, the 'familiarity' effect of the definite article comes from the activation of long-term memory.

As a matter of fact, regardless of whether the activated information comes from the speech situation, from a previous text or from older knowledge the analysis process will work, in every case, in the same manner. It looks as though there were only one phenomenon, with subcases whose boundaries are indeterminate, as in the following example: (25) II faut que j'emmene ma voiture (au/dans un) garage. [I have to take my car to the/a garage] The speaker will only use the indefinite article when he has an occasional garage in mind (on holiday for example), and he will use die definite article in the other cases. But from the listener's point of view, the analysis of'le garage' will resort to: (a) deictic restrictions, if he shares some very specific knowledge widi the speaker, enabling him to uniquely identify the garage; (b) anaphoric restrictions, if a garage has been introduced in the previous text; (c) general

172 The Definite Article: Code and Context

knowledge, telling him 'every car owner usually takes his car to the same garage, near his home'. Any occurrence ofthe definite article thus triggers a search procedure through the base. The search strategy we have sketched consists in reviewing the pragmatic, textual, or general strata of the base (also taking stereotypic knowledge into account) until the time when the right stratum isfound. If all the search processesfail and if no specifications are given by noun modifiers, there remains only the existential value possibly associated with a stylistic effect (as we shall see later in section 3.3.3.1) or the principle of conservation of unity of time and place (by a principle ofdiscursive coherence which requires that, in the absence of contrary information, spatio-temporal referring points are retained from one sentence to the next).

3.3.3 All the processes of search for information have failed In section 3.3.1 we saw that the uniqueness hypothesis may be guaranteed by the lexicon, and in section 3.3.2 we saw that it can be obtained by searching through short-term or long-term memory. We still have to look at the case when all these methods fail. We will distinguish two possible situations: (i) we have a stylistic effecq (11) the specifying information is given by a modifier (noun complement, relative clause).

3.3.3.1 Stylistic device and the construction of a mental model Let us consider, for example, the following sentence that began an article in the Courrier International:

(26) Six heures, le reveil sonne dans la chambre de Peggy Schneider. Elle se leve, prepare le cafe, pose le pain, le miel et la confiture sur la table de la cuisine. [At six o'clock, the alarm clock rings in the bedroom of Peggy Schneider. She gets up, makes coffee, puts the bread, the honey and the jam on the kitchen table] The article goes on by making us attend to the morning activities of Peggy. The audior uses the direct style generally used in television reports. He thus invites the reader to build a mental image of the scene for himself. One can assume that this image works as a sequence of TV pictures containing an alarm clock ringing, a woman making coffee, etc., accompanied by a commentary that we shall interpret according to the principles of deictic restrictions seen in section 3.3.2.1a. This stylistic device, which does not date only from the period of television, is also abundantly used by novelists, as in the narrative:

Francis Renaud 173

(27) Max posa la mail} sur le genou de Sophie. [Max put his hand on Sophie's knee] Although, Max has two hands, as well as Sophie's two knees, by using this direct report style the author makes us see one single hand laid on one single knee. It remains necessary to define a new test in rule (L4) to direct this case towards the existential value (since (L4) would lead us to ask the question: which hand, which knee?). Might it be that (27) could be represented by the less natural sentence: (28) Max posa une main sur un genou de Sophie. [Max laid a hand on a knee of Sophie.] Since for us semantic representations are used to control all possible inferences, we do not see from this point of view what could distinguish (27) from (28). In any case, if we had to take account of this stylistic effect, it would be better to save this kind of information in a special register. 3.3.3.2 Specifying noun modifier Since giving a general analysis of noun complements and of relatives is too complex to be taken up here, we shall content ourselves with setting out some simple cases. (a) Modification by an attributive complement Examples of attributive complements are: Tile de Krakatau', 'le port de Mombassa', 'la dynastie des Tang' (Krakatoa island, etc.). These kinds of definite noun phrases can be used without difficulty at first mention, even with a hearer supposed to know nothing about them. These complements are sometimes labelled 'attributive complements' since they can be associated with structures such as 'Krakatau est une ile (K. is an island)'. Let us again take the representation of 'Hie de Krakatau' given in section 3: \& 3x(ilejc A name.(Qjc).'Krakatau' A ^.(Q.(QJC))) We shall start by representing17 the phrase: 'ile de Krakatau' by Xjt(ile.x A name.(Qjc).'Krakatau') then by applying (L4). In general, the uniqueness hypothesis 3,x(ilejc A name^Qjc).'Krakatau') will return nothing and thus will lead to the existential value 'l*ile de Krakatau' - X^x(ilejc A name^Q^.TCrakatau' A

174 The Definite Article; Code and Context

We could seek to guarantee uniqueness by a default rule which would say that, exceptions aside, all entities with die same name are identical: VXVYVA(name.XA A name.YA 3 X - Y) But we can verify diat Srch-info-UNI still fails in this case, since this rule does not guarantee die existence of an island widi die name of Krakatoa.

(b) Modification of an extractable noun complement *Le fils de Sophie (die son of Sophie)', from which we started, but which we still have not classified, is an example of an extractable18 noun complement. As we have seen, to be identifying, a noun widiout a modifier, such as die noun in 'la porte (die door)', needs an anaphoric or a deictic context (the door about which we have spoken or die door here present in situation). On die other hand, in 'la porte de mon bureau [die door of my office]', the presence of a modifier will translate die task of finding a specification to die complement For instance, the following sentence can be uttered out of die blue: (29) La porte de mon bureau ne ferme pas a cle. [The door of my office does not lock] whereas (30) La porte ne ferme pas a cle. [The door does not lock] requires a specifying context. Or consider (31) (Cosquer a decouvert une grotte dans les Calanques) L'entree de la grotte se trouve a 3 5 m sous 1'eau. [(Cosquer has discovered a cave in die Calanques) The entrance to the cave is 3 5 m below sea level] The phrase 'la grotte (die cave)' can be analysed by anaphora according to die method seen in section 3.3.2.2. Let us suppose diat Srch-info-UNI brings back the constant c33 that has been introduced by the skolemization of 'une grotte'. In diis case, if entree [entrance] is considered as a relational noun, die set of all entries of the cave will be he entree.(Q.Cjj)jx. If die uniqueness hypodiesis is not able to bring anything back, the phrase 'l'entree de la grotte (die entrance of die cave)' will be represented by die existential value: (grotte.c33 A entree.(Q.c33).x A & .(Q.(Q.x))) It is because a cave can have one or several entrances and because we do not have any data on diat subject (Srch-info-NU.(entree.(QW.c}})) consequendy fails) that the noun specification will pass through the assertion of the uniqueness hypothesis of the noun head:

Francis Renaud 175 e.C33 A entree^Q.c 33 )jc).

So we see that the definite character of 'Pentree de la grotte' does not come here from the identifying value of (L4) but from its existential value! In this case, the two checks of rule (L4) guarantee that we can add the uniqueness condition to the KB without ending up in inconsistency (noted byD) KB u 3,x(grotte.C33 A entree.(Q.c33)jc) I-/— a On the contrary, with a functional noun such as 'pere', which by definition is constrained by the property 'tout individu n'a qu'un seul pere (every person has one single father)', the algorithm Srch-info-UNI will succeed every time and will return an identifying value as seen in section 3.3.2.1 a. But then it is this kind of uniqueness specificity which makes 'pere de Sophie' incompatible with the indefinite article 'un'. (*un/le)(pere de Sophie/nez de Sophie/regne de Koubilai/ ...) We thus see that what is sometimes called complete definite description can be obtained by the identrfyng as well as the existential value of (L4). The analysis of 'le roi de France (the king of France)' cannot be reduced to one of these cases, since 'roi' is a functional noun,19 albeit one with a temporal dimension. In the sentence 'le roi de France est malade (the king of France is ill)', the algorithm Test-Srch-info-UNI in rule (L4) would activate the knowledge that France is now a republic with no king. Then Test-Srch-info.UNI fails and TestSrch-info-NU succeeds (card N — o), so (L4) rejects the sentence by replying 'which king of France?' Modification by a relative clause gives the same type of restrictions as modification by a noun complement We shall not consider it here. We have seen in this long section that (L4) is very useful for unifying a lot of data into a single formula which were scattered until now. This rule points out that the article 'le' in all its specific uses firstly tries to identify a referent in the knowledge base. It does not transmit an assertion taken in the lexicon, but runs an algorithm that searches among items of pragmatic knowledge on speech situations ('ferme la porte, le gouvernement accorde une aide'...), contextual, general, or episodic shared knowledge (respectively, anaphora, 'le pere de Sophie', 'le boulanger1) to return an identifying constant (and more generally a ground term). The uniqueness hypothesis that guides the processing of information works well in so far as it applies to a well-delimited stratum of the knowledge base. When the search succeeds, one gets a 'familiarity' effect, an effect which has been known for a long time by traditional grammar. But when the search fails, the hearer is forced to introduce a new referent, while possibly adding the

176 The Definite Article: Code and Context

additional information given by the uniqueness hypothesis, which in such a case behaves as a specifying assertion. Furthermore, we notice with pleasure that our analysis does not stop here. We observe that when the algorithm is run with a uniqueness hypothesis containing several existential variables, it is able to extract indirect specification (deictic indirect identification and associative anaphora) from the situational or contextual stratum of the base, possibly complemented with some stereotypic knowledge. finally, we have noted that the traditional opposition between the deictic and anaphoric interpretations has been relativized a httle since in both cases we have the same kind of processing of memorized information. This unitary approach is moreover empirically corroborated by the fact that in French no linguistic expression is specialized in the anaphoric function and that all the anaphoric expressions can also have deictic uses (Kleiber 1901). Rule (L4) allows us to give a unitary presentation of anaphoric as well as deictic values with direct as well as indirect referential identification. It sheds light on the

first-mention use as well as on anaphoric recall. FRANCIS RENAUD CRLAO EHESS 54, Bd. Raspail 73270 Pans Cedex 06 France e-mail [email protected]

Received: 2 5.07.94 Revised version received: 15.03.95

APPENDIX Afirstapproximation of the rules is: N2-DetN

V2 -• Vt N2 Uo:Ul

(RGi) So:-Si.S2

(RG2)

(RG3)

N2-NPR UChUi

N2 - N2 et N2 So:g

S1.RX.Y))] PH -* N2 V2 SP :— if Ui;(accnib:pl n cln.--grp) A Ltolvxoll then Si^X,35' r 9rA plur.3^

f "

* * * * * * * r*

******

else Si^2 (RG4)

V*2 — Vi UonUi SO :— >.aTVX{3r.X3 3E(SiJLX))

In the second line of the rules, we introduce feature terms (or attribute/value lists) which enable us to make tests and to transmit

Francis Renaud 177 information over long distances (U| repreFinally, the sentence La plupart des eleves se sents the feature term at category 1 of the rule, sont reunis (Most students met), which presents starting from the left). Thus in (RGi), so many problems for Kamp & Reyle (1993) Ui^cclU2^cc tells us that the term Ui of (as they acknowledge in section 4-4-6), is the Det and U2 of the N will unify for the parsed by these rules in a simple mannen agreement feature ace (this is the notation of 3.5? 3 (X C eleve A carcLX > 1/2 Smolka 1992 but it is not essential for the cardileve A X - u.St A VY(.5? Y 3 3Eserest). The lexical entries are: reuniriLY)) LEX: In conclusion, let us point out the formal le, Det, acc(nb:sg A gnmasc), relationship between le and les. At first sight, XNkP 3,X(NJC) A 3 X ( R X A then- representations seem utterly different la, Det, acc(nbsg A grfem), Nevertheless we shall show that they are \NkS> 3,x(N.x) A 3X(NJC A ^ Q ^ Q J C ) ) ) closely related. They only differ in their les, Det, acc(nb:pl), XNk&> card.N > 1 A presuppositions: 'le N' presupposes that N is 15? (N - u.SI A S>.St) composed of only one individual, whereas 'les un, Det, acc(nb:sg A gnmasc), N" presupposes that N is composed of several XNkP 3,x(Nj£ A & ^Q^QJI))) individuals. Let us start from the following une, Det, acc(nbsg A grfem), representations: JiNX^> 3,X(NJC A 9 ^Q.QJC)))

trois, Det, accmb^l, XNkS> 3.5? 3X(X c N A card.X - 3 A X - u.St A 9>.3t)

la plupart des, Det, accnb:pl, lNk&> 3.5? 3X(X C N A carcLX > 1/ 2card.N A X - u.St K9> .St) max, NPR, acc(nb:sg A gnmasc), m Sophie, NPR, acc(nbag A gnfem), s eleve, N, acenbag, eleve

le - \NK& card.N - 1 A 3.5? (N h&Sl) les - XNX^ card.N > 1 A 33t (N A 9 .St)

v.£ (Li) u.St (L2)

The condition card N — 1 amounts to saying that N is a singleton 3x(N — QJC), so (Li) is

These rules only apply to count nouns with but we know that the cover of (x) is {(x)) their specific value. On a trial basis, let us see how our rules parse the example Les eleves se sont reunis (Thethus \NkS> 3x3.5? (N - Q.x A St students met). With (RGi), we have A.!? ..5?) les eleves - \» 3.5? (eleve - «-»StA S>.St) and by substitution And with (RG4), we get (in the first step, we XNX^> 3x(N - QJC A S> .(Q^Qjt))) disregard the auxiliary): sc sont reunis - X3TVX(9r.X 3 3E sereunirJLX)

moreover one can demonstrate that H (N - QJC) 3 NJC

As the lexical entry of se reunir has the feature so clvxoll and as the subject is plural (accnb:pl) XNX^> 3X(NJC A & ^Q^Qji))) and has no group feature, rule (RG6) will add the plurality constraint to the cover and if the uniqueness condition is reIS? (eleve -