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APPLICATIVE AND COMBINATORY CATEGORIAL GRAMMAR AND SUBORDINATE CONSTRUCTIONS IN FRENCH

ISMA¨ıL BISKRI

D´epartement de Math´ematiques & Informatique, Universit´e du Qu´ebec `a Trois-Rivi`eres CP500 Trois-Rivi`eres, Qu´ebec, Canada, G9A 5H7

Ismail Biskri@uqtr.ca Received (18 07 2004) Revised (Day Month Year) Accepted (Day Month Year)

In this article we will present a classification and an analysis, by means of Applicative and Combinatory Categorial Grammar (ACCG), of relative, completive and indirect interrogative propositions in French introduced by ”que” and ”qui”. Applicative and Combinatory Categorial Grammar is a generalization of standard Categorial Grammar. It is represented by a canonical association between Steedman’s Combinatory Catego-rial rules and Curry’s combinators. This model is included in the general framework of Applicative and Cognitive Grammar with three levels of representation: (i) phenotype (concatened expressions); (ii) genotype (applicative expressions) ; (iii) the cognitive rep-resentations (meaning of linguistic predicates). We are interested only in phenotype and genotype levels.

Keywords: Combinatory logics; Applicative and Combinatory Categorial Grammar; Sub-ordinate Construction in French.

1. The general framework

According to the framework of Applicative and Cognitive Grammar (Descl´es 1990, 1996) and Applicative Universal Grammar (Shaumyan 1998), the language analysis has to postulate three levels of representation:

(i)The phenotype level, where the particularly characteristics of natural lan-guages are expressed (for example order of words, morphological cases, etc...). The linguistic expressions of this level are concatenated linguistic units according to the language syntagmatic rules. We note the concatenation of the linguistic units u1, u2, u3 by ”u1 - u2 - u3”

(ii)The genotype level, where grammatical invariants and structures that are underlying to sentences of phenotype level are expressed. The genotype level uses a variable-free formal language, called Genotype Calculus, as its formal framework. Genotype Calculus is an applicative semiotic system used as a formal metalanguage

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for describing natural languages. In this level functional semantic interpretations are expressed by means of combinators of typed combinatory logic (Curry and Feys 1958) (Shaumyan 1998).

(iii)The cognitive level, where the meanings of lexical predicates are represented by semantic cognitive schemes expressed by means of combinators of typed com-binatory logic. We will not describe more this level. It will not interest us for this paper.

As we mentioned previously representations of levels two and three are expressions of typed combinatory logic (Curry and Feys 1958) (Shaumyan 1998). The combina-tory logic was developed to logically analyze Russell’s paradoxes and the concept of substitution. It is also in connection with Church’s lambda-calculus. These two logical systems are currently used by the computer science specialists to analyze the semantic properties of the high-level programming languages. The main difference between these two logics lies in the fact that the combinatory logic is without vari-able. what, contrary to the lambda calculation, makes it possible to eliminate the problem of variables telescoping (two different variables with the same identifier). Combinators are abstract operators who allow to build more complex operators from more elementary operators. Each combinator is associated with elimination and introduction inference rule like in ”Gentzen calculus”. For instance, we present combinators B, C* a, with the following rules (U1, U2, U3 are typed applicative expressions) :

Table 1. Combinators introduction and elimination rules

introduction rules elimination rules BU1 U2 U3 U1 (U2 U3) —————–(i-B) —————–(e-B) U1 (U2 U3) BU1 U2 U3 U1 U2 C*U2 U1 —————(i-C*) —————(e-C*) C*U2 U1 U1 U2

These rules lead to the followingβ-reduction rules : ((BU1 U2) U3)⇒(U1 (U2 U3))

((C*U1) U2)⇒(U2 U1)

aThere are many other combinators. Here we are interested only toBandC*. For more details the reader might have a look on (Descl´es, 1990)

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The combinator Ballows the composition of two typed applicative expressions U1 and U2 (U1 and U2 function as operators). The result (B U1 U2) would be then the complex operator of the typed applicative expression U3 (U3 functions as an operand).

The combinator C*is applied on a typed applicative expression U1 (U1 functions as the operand of U2). It allows to built the complex operator (C*U1) in order to apply it to the typed applicative expression U2.

These rules establish a relation, independently of the meaning of the arguments, between an expression with a combinator and an expression without combinator equivalent to the first one (from a certain point of view).

In addition to the elementary combinators, there are complex combinators built from the elementary ones. We have for example the complex combinator:B B C*. The action of the complex combinators is determined by the application of the ele-mentary combinators starting from the one on the left.

1 B B C*x y z

2 B(C*x) y z β-reduction of B 3 (C*x) (y z) β-reduction of B 4 y z x β-reduction of C*

The expression obtained in the step 4 is the normal form of the combinatory ex-pression in 1. According to Church-Rosser theorem the normal form, if it exists, is unique.

2. Applicative and Combinatory Categorial Grammar

The model of Applicative and Combinatory Categorial Grammar (ACCG)(Biskri and Descl´es 1997), as most of Categorial Grammar models (Morrill 1994) (Moorgat 1997) (Steedman 2000) (Dowty 2000), falls under a paradigm of language analysis that allows a complete abstraction of grammatical structure from its linear rep-resentation due to the linearity of the linguistic signs and a complete abstraction of grammar from the lexicon. Applicative and Combinatory Categorial Grammar conceptualizes then the languages like systems of fitting of linguistic units (words, morphemes, lexical items...) of which some function as of operators whereas others function like operands. Concretely, ACCG assigns syntactical categories to each lin-guistic unit. Syntactical categories are orientated types developed from basic types and from two constructive operators ’/’ and ’\’. The set of all types is recursively obtained by the following rules :

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(ii) If X and Y are orientated types then X/Y and X\Y are orientated types. According to Steedman’s notation (2000), X/Y and X\Y are functional orientated types. A linguistic unit ’u’ with the type X/Y (respectively X\Y is considered as operator (or function) whose typed operand Y is positioned on the right (respec-tively on the left) of operator.

In our paper, a linguistic unit u with orientated type X will be designed by0[X :u]0. According to our postulate of the three levels of representations of the languages, Applicative and Combinatory Categorial Grammar explicitly connects phenotype expressions to its underlain representations in the genotype (functional semantic interpretation).

Let us provide now ACCG rules used in this paper. To see the whole of the rules the reader might have a look on (Biskri and Descl`es, 1997) :

Table 2. Some ACCG rules

Forward Applicative rule (>) [X/Y[X::(u1]u1u[2)]Y:u2] Backward Applicative rule (<) [Y:u[X1]:(u[X\Y2u1)]:u2] Forward Type-raising rule (> T) [Y /(Y[\XX:):(u]C∗u)]

Forward Functional Composition rule (> B) [X/Y[X/Z:u1]:(Bu−[Y /Z1u2)]:u2]

The premises in each rule are concatenations of linguistic units with orientated types considered as being operators or operands, the consequence of each rule is an applicative typed expression with an eventual introduction of one combinator. The type-raising of an unit u introduces the combinatorC*; the composition of two concatened units introduces the combinatorB.

Let us deal with a simple example:

La libert´e renforce la d´emocratie (Freedom reinforces democracy)

1. [N/N :la]-[N :liberte]-[(S\N)/N :renforce]-[N/N :la]-[N :democratie] 2. [N : (la liberte)]-[(S\N)/N :renforce]-[N/N :la]-[N :democratie] (>)

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3. [S/(S\N:(C*(la liberte))]-[(S\N)/N:renforce]-[N/N:la]-[N:democratie] (> T) 4. [S/N : (B(C*(la liberte)) renforce)]-[N/N :la]-[N :democratie] (> B) 5. [S/N : (B(B(C*(la liberte))renforce)la)]-[N :democratie] (> B) 6. [S : ((B(B (C*(la liberte))renforce)la)democratie)] (>) 7. ((B(B(C*(la liberte))renforce)la)democratie)

8. ((B(C*(la liberte))renforce) (la democratie)) B 9. ((C*(la liberte)) (renforce (la democratie))) B

10.((renforce (la democratie)) (la liberte))) C*

11.renforce (la democratie) (la liberte)

The first step consists in assigning syntactic types to the lexical units. Those are entries of a dictionary where each unit is associated to one or more types. Steps 2 to 6 consist in operating the rules of the ACCG in the way to check the syntactic correctness on the one hand and progressively to build the predicative structures by the introduction of combinators with the syntactic process. Thus, step 2 consists in applying the rule (>) to the linguistic units:la andlibert´e. The subjectla libert´eis then built. The third step sees the introduction of the combinatorC*. Applied to the operandla libert´e, C*makes it possible to build an operator (C* (la libert´e)) that we compose at step 4 with the operatorrenforcewith using the rule (> B) the result is a more complex operator (B(C*(la libert´e))renforce). This last operator is composed in step 5 withla. Step 6 is the application of the operator (B(B(C* (la libert´e))renforce)la) to the operandd´emocratie. Steps 1 to 6 occur in the phe-notype. Obtaining the type S at step 6 guarantees the syntactic correctness of the statement. Steps 7 to 11 are a natural deduction in the genotype, which consists in eliminating the combinators according to the β-reduction rules shown previously. The predicative structure of the genotype level obtained at the step 11 : renforce

(la d´emocratie) (la libert´e), represents the functional semantic interpretation of the given sentence :la libert´e renforce la d´emocratie.

With such a model, we have analyzed in previous works many complex construc-tions in French like coordination (Biskri, Descl´es, 1997), sentences with backward modifiers(Biskri, Descl´es, 1997), etc. We also showed that it is possible to adapt ACCG to other languages like Arabic without involving large modifications to the model (Biskri, Delisle, 2000).

In this paper we will present the analysis of relative, completive and indirect inter-rogative constructions in French.

3. The relative, completive and indirect interrogative constructions in French and the ACCG

The concept of relation between two sentences is significant in the case of the French subordinate clauses, since subordination is a syntactic relation of dependence

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be-tween linguistic unitsb. The subordinate clause always depends from another

propo-sition. It should be noted that the category of the subordinate clauses is not well defined in French, since certain propositions which do not have any syntactic depen-dence relation with another proposition are classified as subordinate clauses. The problem of our research is formulated as follows: How are the subordinate relative, completive and indirect interrogative clauses categorised in order to support the automatic processing of the natural languages? We wanted to analyze at the same time relative, completive and indirect interrogative propositions because their cat-egories share the same syntactic structures and occupy sometimes similar syntactic functions in speech. The analysis was made on a corpus which gathers more than one hundred of different propositions. However, in our article, we will limit ourselves for practical reasons to the following propositions:

i)Qui m’aime me suive (who loves me has to follow me) :relative proposition ii)Que tu m’aimes me r´ejouit(that you love me, delights me) :completive propo-sition

iii) J’aime la personne qui m’aime (i love the person who loves me) : relative proposition

iv)J’aime qui tu aimes (i love whom you love) :relative proposition v)J’aime que tu viennes (i love that you come):completive proposition vi)Pierre aime qui l’aime (Pierre loves who loves him) :relative proposition vii)Pierre se demande qui l’aime (Pierre wonders who loves him) : indirect in-terrogative proposition

viii) La femme que tu vois est ma sœur (the woman that you see is my sister) :relative proposition

ix) La femme qui vient est ma sœur (the woman who comes is my sister) : rel-ative proposition

x) Le scientifique parle de l’objet que Pierre trouva (The scientist speaks about

bHarris in (Harris, 1976) affirms that subordination is obtained by the application of an operator builder of subordination to two simple propositions. Thus, the operation of pronominalization applied to the two propositionsJean a bu de l’eau (Jean drank water) andMarie a apport´e de l’eau(Marie brought water) allows the resultJean a bu l’eau que Marie a apport´ee(Jean drank water that Marie brought).

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the object which Pierre found) :relative proposition

xi) La robe que tu vends int´eresse cette cliente (The dress that you sell interests this customer) :relative proposition

xii) L’officier, qui donne les ordres, a d´epos´e son fusil (The officer, who gives the orders, deposited his rifle) : relative proposition

xiii) Heureux qui frissonne aux miracles de cette po´esie (Happy who shivers with the miracles of this poetry) :relative proposition

xiv) Il ´ecrase qui ne lui ob´eit (He crushes who does not obey to him) : relative proposition

xv) Pierre entend le voisin qui chante (Pierre hears the neighbour who sings) : relative proposition

xvi) L’espoir que tu viennes me r´ejouit (the hope that you come delights me): completive proposition

A subordinate clause is a proposition which depends on a main clause and which is often attached to it by a subordinating conjunction, a relative pronoun, a relative adjective, an interrogative pronoun or an interrogative adjective. However, certain syntagms which do not have any relation of dependence and which are thus not sub-ordinate clauses are classified in this category. The phenomenon can be observed for relative and completive syntagms which occupy, for instance, the function of grammatical subject. In the sentence i, the relative clausequi m’aime is the subject of the verbsuive. In the sentence ii,que tu viennes is the subject of the verbr´ejouit.

[Qui m’aime]N me suive [Que tu m’aimes]N me r´ejouit

The subject cannot be logically subordinate to the verb. The classification of the relative and completive clauses under the category of subordination as presented in Handbooks of Grammar like Gr´evisse (1991) is not conform to grammatical reality as it is observed in the two preceding examples. As for them, the indirect interroga-tive propositions are subordinate clauses which are introduced by a verb introducer expressing the interrogation and an interrogative word such asqui, quand, comment. There are two types of relative propositions: the propositions which are introduced by an antecedent and the propositions which do not have any antecedent (Mil-ickov`a, 1998). Thus, the relative clause qui m’aime in the sentence i do not have any antecedent, whereas, in the sentence iii, the relative clause qui m’aime, has an

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antecedent, the wordpersonne of which it is a backward modifier.

J’aime la [personne]N [qui m’aime]N\N

It is possible to propose a classification, according the ACCG model, which re-spects the structure of this study’s propositions. The analysis of various relative, completive and indirect interrogative clauses presented here shows that they often share common syntactic structures, and, different nouns were frequently used to identify similar syntactic constructions. For instance, sentences iv and v have simi-lar structures: subject + verb + object.

[J’]N [aime](S\N)/N [qui tu aimes]N [J’]N [aime](S\N)/N [que tu viennes]N

The propositions qui tu aimes and que tu viennes are classified in different cat-egories, that is to say respectively in the category of the relative clauses and the category of the completive clauses. The principal difference is that the two propo-sitions have not the same referent.

The operators being used to build the relative clauses and the completive clauses in French can be divided into two main categories: (i) ”builders” of nouns; (ii) ”builders” of modifiers. The true distribution of the relative, completive and in-direct interrogative propositions is done under these two categories. It is noticed that these propositions act in the same way that substantives or adjectives. The propositions which are built with a ”builder” of noun can be subjects, attributes, direct objects, indirect objects, whereas the propositions which are built with a ”builder” of modifiers often act like adjectives, and even sometimes like adverbs. The propositions can achieve in syntax the same functions as the linguistic units which make it possible to form the language such as the substantives and the adjec-tives. In the sentences i and ii,qui andqueare ”builders” of nouns. The difference between the propositionqui l’aimein sentences vi and vii is the meaning of the verb who introduces this proposition. Moreover generally, what distinguishes the relative clauses without antecedents (as in vi) from indirect interrogative ones (as in vii), is the context in which they are used. the indirect interrogative propositions require normally in front of them the presence of verb of opinion or stating (Milickov`a, 1998). it seems that the relative clauses without antecedent are closer to the indi-rect interrogative propositions than to the relative propositions with antecedents. Le Goffic (Le Goffic, 1993) advances two reasons with that: (i) the indirect interrog-ative ones almost always employ the third person of the singular while the relinterrog-ative ones with antecedent agree in kind and number with the antecedent; (ii) both of relative without antecedent and indirect interrogative propositions can have the function of direct object.

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Pierre aime [qui l’aime]N Pierre se demande [qui l’aime]N

In the sentences viii and ix, qui and que are ”builders” of modifiers. The syn-tagmsque tu vois andqui vient are both modifiers of the syntagm la femme.

La [femme]N [que tu vois]N\N est ma sœur La [femme]N [qui vient]N\N est ma sœur

As it is possible to note it, the difference is not relatively to a syntactic criterion, but to a semantic criterion (Girard, 2001). In addition, the classification ofqui (relative and interrogative pronoun cases) and ofque(completive cases) as ”builder” of noun is justified by the fact that the two operators allow the construction of syntagms referring a part of reality (an object entity): qui m’aime, qui vient, qui pense The difference between the two is that qui (relative and interrogative pronoun cases) makes it possible to refer people, whereasque (completive cases) references a verbal action or a state indication: que tu m’aimes, que tu viennes, que tu penses The

qui in interrogative cases can also be a ”builder” of noun: the proposition that it used to build can however be only object of the verb. The relative and completive clauses ”builders of nouns” can occupy a multitude of functions in the sentence: subject, direct object, indirect object, attribute. Their ”versatility” can easily be compared with certain noun phrases suchune pomme, une fille, un homme We can consequently easily replace propositions by linguistic units of different meanings but of the same syntactic structure. By this observation we notice that the language generalizes its behaviour to the whole of the units that constitute it, since noun phrases and propositions as complex as relative and completive clauses can occupy similar functions in speech.

It should however be mentioned that there is a principal difference between the rela-tive clauses and the complerela-tive clauses ”builders of nouns”: the concept of quantifi-cation. Thus, the sentencesQui m’aime me r´ejouit andQue tu m’aimes me r´ejouit

contain a major difference in their meaning:Qui m’aime can be interpreted by all those who like me and it becomes introducer of a universal quantification on a set containing the persons who like me, whereas Que tu m’aimes introduces only the fact that you like me.

What must retain our attention remains the fact that the pronouns que and qui

are perceived as operatorsc who attach what we will call anyway the subordinate

proposition to the main proposition. That is what assumes traditional Grammar. With Categorial Grammars, this aspect of the pronouns is included in the syntactic

cHarris considers also the equivalent in English ofqueandqui as operators, even if our type of analysis is different from that preached by Harris (for more details, see (Harris, 1976).

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categories assigned to them. Each syntactic category reflects the way in which the pronoun will operate on both of the main and the subordinate propositions to attach them. Thus, in (x) as in (xi) and in (viii) the pronounque, after being applied to a ”NP-Verb” proposition ([Pierre]NP [trouva]Verb), modifies a Noun ([objet]Noun) in order to give a complex Noun ([objet que Pierre trouva]Noun. We can assign the category (N\N)/(S/N) to the pronounque. In (xii) as in (ix) the pronounqui, after being applied to a ”Verb-NP” proposition ([donne]Verb [les ordres]NP), modifies a Noun ([officier]Noun) in order to give a complex Noun ([officier, qui donne les ordres]Noun. We can assign the category (N\N)/(S\N) to the pronoun qui. In (i) as in (xiii) and in (xiv) qui, is applied to an intransitive verbm’aime in (i), fris-sonne aux miracles de cette po´esie in (xiii),ne lui ob´eit in (xiv)) which category is S\N in order to construct a noun qui m’aime in (i),qui frissonne aux miracles de cette po´esie in (xiii),ne lui ob´eit in (xiv)). Thus, here, we can assign the category N/(S\N) to the pronounqui. This category reflects the universal quantification na-ture of the pronounqui in what we will call substantive subordinate constructions. We summarize the whole of possible categories assigned to que and qui in the following table:

Table 3. table of categories of the syntactic types of the relative clauses

Category Example

Noun builder N/(S/N) J’aime qui tu aimes N/(S\N) Qui vivra verra

Modifier builder (N\N)/(S/N) La femme que tu vois est ma sœur (N\N)/(S\N) La femme qui vient est ma soeur

Table 4. table of categories of the syntactic types of the completive clauses

Category Example

Noun builder N/S J’aime que tu viennes Modifier builder (N\N)/S L’espoir que tu viennes me r´ejouit

4. Examples

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a)L’officier, qui donne les ordres, a rendu son fusil

1. [N/N:l’] - [N:officier] - [(N\N)/(S\N):qui] - [(S\N)/N:donne] - [N: (les ordres)] -[(S\N)/(S\N):a] - [(S\N)/N:rendu] - [N: (son fusil)]

2. [N/N:l’] - [N:officier] - [(N\N)/N: (B qui donne)] - [N: (les ordres)]

-[(S\N)/(S\N):a] - [(S\N)/N:rendu] - [N: (son fusil)] (>B) 3. [N/N:l’] - [N:officier] - [N\N : ((Bqui donne) (les ordres))] - [(S\N)/(S\N):a]

-[(S\N)/N:rendu] - [N: (son fusil)] (>)

4. [N/N:l’] - [N : (((B qui donne) (les ordres))officier)]- [(S\N)/(S\N):a] - [(S\N)/N:rendu]

-[N: (son fusil)] (<)

5. [N: (l’ (((Bqui donne) (les ordres))officier))]- [(S\N)/(S\N):a] - [(S\N)/N:rendu]

-[N: (son fusil)] (>)

6. [S/(S\N) : (C*(l’ (((Bqui donne) (les ordres))officier)))]- [(S\N)/(S\N):a]

-[(S\N)/N:rendu] - [N: (son fusil)] (>T)

7. [S/(S\N) : (B (C*(l’ (((Bqui donne) (les ordres))officier)))a)] - [(S\N)/N:rendu]

-[N: (son fusil)] (>B)

8. [S/N : (B(B(C*(l’ (((Bqui donne) (les ordres))officier)))a)rendu)]

-[N: (son fusil)] (>B)

9. [S:((B(B(C*(l’ (((Bqui donne) (les ordres))officier)))a)rendu) (son fusil))] (>) 10.((B(B(C*(l’ (((Bqui donne) (les ordres))officier))) a)rendu) (son fusil)) 11.(B(C*(l’ (((Bqui donne) (les ordres))officier))) a)(rendu (son fusil)) B 12.(C*(l’ (((Bqui donne) (les ordres))officier))) (a (rendu (son fusil))) B 13.(a(rendu (son fusil))) (l’ (((Bqui donne) (les ordres))officier)) C* 14.(a(rendu (son fusil))) (l’ ((qui (donne (les ordres))) officier)) B

b)Qui vivra verra

1. [N/(S\N) :qui] - [S\N : vivra] - [S\N : verra] 2. [N : (qui vivra)] - [S\N : verra] (>) 3. [S : (verra (qui vivra))] (>) 4. (verra (qui vivra))

c)Heureux qui frissonne aux miracles de ce texte

1. [N/N:heureux] - [N/(S\N):qui] - [S\N:frissonne] - [((S\N)\(S\N))/N:aux] - [N:miracles] -[(N\N)/N:de] - [N/N:ce] - [N:texte]

2. [N/N:heureux] - [N/(S\N):qui] - [S\N:frissonne] - [((S\N)\(S\N))/N:aux] - [N:miracles]

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3. [N/N:heureux] - [N/(S\N):qui] - [S\N:frissonne] - [((S\N)\(S\N))/N:aux] - [N:miracles]

-[N\N : (de (ce texte))] (>)

4. [N/N:heureux] - [N/(S\N):qui] - [S\N:frissonne] - [((S\N)\(S\N))/N:aux]

-[N : ((de (ce texte))miracles)] (<)

5. [N/N:heureux] - [N/(S\N):qui] - [S\N:frissonne]

-[(S\N)\(S\N) : (aux ((de (ce texte))miracles))] (>) 6. [N/N:heureux] - [N/(S\N):qui] - [S\N : ((aux ((de (ce texte))miracles))frissonne)]

(<) 7. [N/(S\N) : (Bheureux qui)] - [S\N : ((aux ((de (ce texte))miracles))frissonne)]

(>B) 8. [N : ((Bheureux qui) ((aux ((de (ce texte))miracles))frissonne))] (>) 9. ((Bheureux qui) ((aux ((de(ce texte))miracles))frissonne))

10.(heureux (qui ((aux ((de(ce texte))miracles))frissonne))) B

d)Pierre entend le voisin qui chante

1. [N:pierre] - [(S\N)/N:entend] - [N/N:le] - [N:voisin] - [(N\N)/(S\N):qui] - [S\N:chante] 2. [S/(S\N) : (C*Pierre)] - [(S\N)/N:entend] - [N/N:le] - [N:voisin] - [(N\N)/(S\N):qui]

-[S\N:chante] (>T)

3. [S/N : (B(C*Pierre)entend)] - [N/N:le] - [N:voisin] - [(N\N)/(S\N):qui] - [S\N:chante] (>B) 4. [S/N : (B(B (C*Pierre)entend)le)] - [N:voisin] - [(N\N)/(S\N):qui] - [S\N:chante] (>B) 5. [S/N : (B(B(C*Pierre)entend)le)] - [N:voisin] - [(N\N) : (qui chante)] (>) 6. [S/N : (B(B(C*Pierre)entend)le)] - [N : ((qui chante)voisin)] (<)

7. [S : ((B (B (C*Pierre)entend)le) ((qui chante)voisin))] (>) 8. ((B(B(C*Pierre)entend)le) ((qui chante)voisin))

9. (B(C*Pierre)entend) (le((qui chante)voisin)) B

10.(C*Pierre) (entend (le ((qui chante)voisin))) B

11.((entend ((qui chante) (le voisin))) pierre) C*

e)J’aime que tu viennes

1. [N:Je] - [(S\N)/N:aime] - [N/S:que] - [N:tu] - [(S\N):viennes]

2. [S/(S\N):(C*Je)] - [(S\N)/N:aime] - [N/S:que] - [N:tu] - [(S\N):viennes] (>T) 3. [S/N:(B (C*Je)aime)] - [N/S:que] - [N:tu] - [(S\N):viennes] (>B) 4. [S/S:(B (B (C*Je)aime)que)] - [N:tu] - [(S\N):viennes] (>B) 5. [S/S:(B (B (C*Je)aime)que)] - [S:(viennes tu)] (<)

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6. [S:((B(B(C*Je)aime)que) (viennes tu))] (>) 7. ((B(B(C*Je)aime)que) (viennes tu))

8. (B(C*Je)aime) (que (viennes tu)) B

9. (C*Je) (aime (que (viennes tu))) B

10.((aime (que (viennes tu)))Je) C*

f)Pierre demande qui laime

1. [N :Pierre]-[(S\N)/N :demande][N/(S\N) : qui]-[(S\N)/((S\N)/N) :le][(S\N)/N :aime] 2. [S/(S\N):(C*Pierre)]-[(S\N)/N:demande][N/(S\N):qui]-[(S\N)/((S\N)/N):le]

[(S\N)/N:aime] (>T)

3. [S/N: (B(C*Pierre)demande)][N/(S\N):qui]-[(S\N)/((S\N)/N):le][(S\N)/N:aime] (>B) 4. [S/(S\N): (B (B(C* Pierre)demande)qui)]-[(S\N)/((S\N)/N):le][(S\N)/N:aime] (>B) 5. [S/((S\N)/N): (B(B(B(C*Pierre)demande)qui)le)][(S\N)/N:aime] (>B)

6. [S : ((B(B(B(C*Pierre)demande)qui)le)aime)] (>)

7. ((B(B(B(C*Pierre)demande)qui)le)aime)

8. ((B(B(C*Pierre)demande)qui) (le aime)) B

9. ((B(C*Pierre)demande) (qui (le aime))) B

10.((C*Pierre) (demande (qui (le aime)))) B

11.((demande (qui (le aime)))Pierre) C*

5. Conclusion

The classification and the analysis of relative, completive and indirect interrogative propositions in French by means of Applicative and Combinatory Categorial Gram-mar (ACCG) make it possible to simplify the models treating of the propositions and to highlight the mechanisms used in the French language such as the use of the functions. The French language applies its system of function to the system of the propositions. It can thus create the major part of the sentences with a limited set of functions: subject, direct object, indirect object, attribute... The emphasis put on that relative, completive and indirect interrogative propositions are divided, in fact, in a binary system (”builders” of nouns and ”builders” of modifiers), we highlight that the language integrates propositions as complex as relative, comple-tive and indirect interrogacomple-tive propositions in its system of the parts of speech in order to support the integration of these syntagms formed in a complex sentence. Such an analysis has the merit to simplify the syntactic model while emphasizing the common elements of the language. The traditional classification of the relative, completive and indirect interrogative propositions results from a confusion between syntax and semantics. The ACCG makes it possible to carry out a classification of the syntactic units which emphasizes the syntactic structure of the French language making it possible to work out thereafter a modeling on three levels: phenotype,

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genotype, cognitive representation. The present study was limited to the analysis of qui and que in French. The results of the analysis are however promising. Next studies on the relative, completive and indirect interrogative propositions in French could be broader and could relate to other propositions, such as those introduced by dont, auquel, comment, etc.

References

1. J. P. Descl´es, Langages applicatifs, langues naturelles et cognition, (Hermes, Paris, 1990).

2. J.P. Descl´es, Cognitive and Applicative Grammar: an Overview, inLenguajes Natu-rales y Lenguajes Formales, ed C. Martin Vide, (Universitat Rovra i Virgili, 1996), pp. 29-60.

3. S. K. Shaumyan, Two Paradigms Of Linguistics: The Semiotic Versus Non-Semiotic Paradigm,Web Journal of Formal, Computational and Cognitive Linguistics(1998). 4. B.H. Curry, and R. Feys,Combinatory logic, (North-Holland,Amsterdam, 1958). 5. I. Biskri, and J.P. Descl´es, Applicative and Combinatory Categorial Grammar (from

syntax to functional semantics), InRecent Advances in Natural Language Processing, (John Benjamins Publishing Company, 1997), pp. 71-84.

6. G. Morrill,Type-Logical Grammar, (Kluwer, Dordrecht, 1994)

7. M. Moorgat, Categorial Type Logics, inHandbook of Logic and Language, eds. J. Van Benthem and A. Ter Meulen, ( North Holland, Amsterdam, 1997). pp. 93-177. 8. M. Steedman,The Syntactic Process, (MIT Press, Bradford, 2000).

9. D. Dowty, The Dual Analysis of Adjuncts/Complements in Categorial Grammar, in

Linguistics (2000).

10. I. Biskri, and S. Delisle, Les Grammaires Cat´egorielles pour le d´eveloppement d’applications multilingues destin´ees au WEB, inRevue BULAG, Num´ero sp´ecial sur

le G´enie Linguistique et le G´enie Informatique, (PUFC, Besan¸con, 1999), pp 39-59.

Z.H. Harris,

11. L. Milickov´a, Les fonctions syntaxiques des ´el´ements introducteurs QUI et QUICONQUE dans les propositions relatives sans ant´ec´edant, in Etudes Romanes de Brno, (1998). pp. 7-15.

12. P. Le Goffic,Grammaire de la Phrase Fran¸caise, (Hachette-Sup´erieur, Paris, 1993). 13. G. Girard, Les fausses interrogatives, in Proc. ofS´emantique Syntaxe et Linguistique

Figure

Table 1. Combinators introduction and elimination rules
Table 2. Some ACCG rules
Table 4. table of categories of the syntactic types of the completive clauses

References

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