Réseaux de preuve et génération pour les grammaires de types logiques

Sylvain Pogodalla 1, 2
1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The study of the connection between syntax and semantics that type logical grammars set has given priority to parsing-from syntax to semantics. This thesis underlines how generation-from semantics to syntax-can also benefit from this close connection.

It relies on the logical study of these grammatical models and points out the use of linear logic and its proofnets. Around Lambek calculus, an intuitionistic non-commutative fragment of linear logic, we study the behavior of the extensions of this calculus as syntactic models, in particular with pomset calculus. For instance, we show that a fragment of this latter generates the same language class as tree adjoining grammars.

On the other hand, the appropriateness of syntax, with the notion of proof, to Montague's semantics, with lambda-terms, appears in the Curry-Howard correspondence. Using proofnets enables us to show that for Lambek calculus and linear semantic representations, with at least one constant, the generation problem is decidable and that these grammars are intrinsically reversible. We characterize the semantic forms that enable polynomial syntactic realization, so that we can propose a full generation method in this framework.

These results, and their implementation as well, use the underlying proof theory, in particular the graph presentation of proofnets. Thus, we get a uniform framework for parsing and generation. For the objective of taking non-linear semantic terms into account thanks to exponential connectives of linear logic, we give a new syntax and a new correctness criterion for proofnets with exponentials as graphs.
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Sylvain Pogodalla. Réseaux de preuve et génération pour les grammaires de types logiques. Interface homme-machine [cs.HC]. Institut National Polytechnique de Lorraine - INPL, 2001. Français. ⟨tel-00112982⟩

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