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Categorial Grammars for Computing the Correspondence between Syntax and Semantics: An Example of Interplay between Mathematical Logic and Computational Linguistics
Christian Rétoré (Bordeaux I)

22 septembre 2008

Program: Ajdukiewicz (1931) introduced categorial grammars for the formal language of ordinary mathematical logic, and Bar-Hillel (1953) adapted it to word order in view of natural language formalisation. Lambek (1958) turned it into a plain logical system, a non commutative ancester of Girard’s linear logic (1986). Now that the relation of the Lambek calculus to intuitionistic logic and typed lambda-calculus is well mastered, following Church’s representation of predicate calculus (1930), from a categorial analysis one can compute, as explored by Montague in the seventies, a representation of the conveyed meaning, a lambda term encoding a logical fomula. We will discuss the possiblity to extend such a correspondence to linguistically more relevant syntax model like Stabler’s minimalist grammars, or to richer semantics (discourse, lexical semantics).
Course:
1/ September 22, 2008 at 6:30 pm.
References:
– "La théorie des langages", La Gazette des mathématiciens (Société mathématique de France), 115 (2008), 35–62.
– "Logique", La Gazette des mathématiciens (Société mathématique de France), 116 (2008), 29–63.
The logic of categorial grammars, Lecture Notes. Rapport de Recherche INRIA 5703.

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Christian Rétoré Christian Rétoré (Bordeaux I)
Christian Rétoré est professeur à l’université Bordeaux I.

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