Section: New Results

Syntax-Semantics Interface

Participants : Philippe de Groote, Sylvain Pogodalla, William Babonnaud.

Abstract Categorial Grammars

We have worked on implementing parsing optimization to the Abstract Categorial Grammar tool kit. These optimizations are based on Datalog program rewriting techniques, in particular a general version of Magic Sets [27], [36]. Theses optimizations rely on the tree isomorphism between derivation trees resulting from parsing with a given abstract categorial grammar, and proofs of facts in a corresponding Datalog program. Because magic rewriting breaks the isomorphism, a transformation of proofs back to derivation trees has been proposed.

Lexical Semantics

The lexicon model underlying Montague semantics is an enumerative model that would assign a meaning to each atomic expression. This model does not exhibit any interesting strucuture. In particular, polysemy problems are considered as homonymy phenomena: a word has as many lexical entries as it has senses, and the semantic relations that might exist between the different meanings of a same word are ignored. To overcome these problems, models of generative lexicons have been proposed in the literature. Implementing these generative models in the realm of the typed $\lambda$-calculus necessitates a calculus with notions of subtyping and type coercion. In this context, we have investigated several ways of expressing coercion using record types, and intersection types. In addition, William Babonnaud has shown how the structure of a generative lexicon may be formalized in type theory, using the categorical notion of a topos [10].