Contenu du sommaire : Les grammaires catégorielles, sous la direction de Béatrice Godart-Wendling

It is often said that, through Ajdukiewicz and Lesniewski, categorial grammars ultimately stem from the pure grammar Husserl spoke about in the fourth Logical Investigation. Without being false, this picture is not very unaccurate and, in order to understand adequately the history of the idea of categorial grammar, it is necessary to see it in its relationship with type theory. Montague grammar, for instance, shows very clearly that there is a systematic correspondance between categorial grammar on one hand and Church simple type theory on the other hand. As a matter of fact, we now knows that Ajdukiewicz most original idea has to do with functionality rather than with category: the system of categories - or, as linguists used to say, of parts of speech - is generated from two basic categories (n, s), and derived ones (n/s, etc.) are conceived as functions taking other categories as arguments. As there is nothing specially categorial in categorial grammars, one may wonder why they were so called. Once again, referring to Husserl doesn't suffice to answer: syntactic categories appeared first as an improved version of the syntactic genera introduced in Carnap's Logical Structure of Language. The role of Ryle, who was the first to pay due attention to the close relationship between types and categories, need to be stressed, too.

This paper has a double aim. First, in a historical and theoretical part, it shows how Ajdukiewicz's categorial grammar (1935) is directly related to Lesniewski's theory of semantic categories (1922). Secondly, it emphasizes that Ajdukiewicz's analysis of quantification constitutes a very anticipation of the contemporary categorial solutions which make use of lambda abstraction in order to deal with quantified expressions. In the absence of any published writting concerning the theory of semantic categories, the main categorial features of Lesniewski's languages are identified in analysing the two logical systems (Protothetics and Ontology) governed by the theory of semantic categories. This study points out the theoretical ideas which will be retained by later categorial grammars and which strongly constrast with Chomsky's transformational model. Furthermore, this analysis reminds that quantifiers were not categorized in Lesniewski's systems and explains this lack's reasons. After a short presentation of Ajdukiewicz's seminal categorial grammar, the paper examines Ajdukiewicz's treatment of quantification and shows how it constitutes an extension of Lesniewski's theory which foreshadows current compositional solutions.

Through a historical comparison of the first categorial models (Ajdukiewicz 1935, Bar-Hillel 1953 and Lambek 1958), this paper traces the evolution of the notion of category (or type) and analyses the different kinds of rules which govern these grammars. Finally, it considers the changes induced by the syntactic rules on structure representation.

This article is the result of a collaboration between Godart-Wendling and Lambek in the form of an interview. The former asks the latter to retrace in broad outline his interest in the application of mathematics to linguistics. Prompted by her penetrating questions, he recalls how his old formulation of categorical grammar arose from algebra, but borrowed techniques from logic. He recalls how later he turned to rewrite rules to explicate verb-conjugations and kinship terminologies in natural languages and how, more recently, he returned to a simpler version of categorial grammar, which lends itself to easy one-dimensional calculations in place of the original two-dimensional proof-trees.

The linguistic notion of meaning has suffered great modifications in the last thirty years. The works by the American logician Richard Montague have played an important role in this change of perspective. In fact, Montague Grammar (MG) is nowadays one of the main formalisms used in the actual semantic theory. His proposals are directly related to the categorial tradition, in which main subjects concerning language meaning had been studied from a logical and a computational point of view. Maybe this is the reason why the contraposition of MG and Dynamic theories of meaning was a constant in the 1990's. Indeed, the Montagovian framework of semantic analysis has been applied in many works on meaning theory and dynamic semantics during the last decade. In this paper, we have a sight on one of those theories about natural language semantics based on the MG framework.

The paper analyzes the correspondence existing between the Syntactic Calculus (Lambek 1958) and (multiplicative) non-commutative linear logic (Abrusci 1991), both in its intuitionistic and classical formulation. Particular attention is paid to the fragment of classical non-commutative linear logic (or classical bilinear logic) that is a conservative extension of the Syntactic Calculus. We present some linguistic applications of this system and propose a way to build up planar graphs for its type logical formulas.

In this paper, I compare two grammar formalisms that have their roots in the categorial type calculus of Lambek 1958: the pregroup grammars of Lambek (1999) and the multimodal type-logical grammars of Moortgat (1996, 1997). The core components of these two frameworks have the limited expressive capabilities of context-free grammars. Natural languages exhibit structural patterns that require analytical tools stronger than context-free. Pregroup grammars and multimodal type-logics follow different strategies to achieve the required extra expressivity: closing type assignment under metarules in the case of the former, and combining a base component with a module of structural postulates for the latter. Using the Dutch crossing dependencies as a benchmark test, I contrast these strategies, and evaluate how they deal with problems of undergeneration and overgeneration.