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Generation in the Lambek Calculus Framework: an Approach with Semantic Proof Nets

Sylvain Pogodalla
Categorial grammars and Lambek calculus found a nice embedding in Linear Logic, and many works have presented proof nets uses for linguistic purposes, with a special look at proof nets for Lambek calculus. But they have mainly explored the syntactic capabilities of proof nets, describing parsing processes. This paper presents our vision of the generation process based on semantic proof nets. These latter already took place in semantic analysis thanks to their relation with lambda-terms and Montague's semantics when attached to lexical items. Their advantages, when reversing the process to generate, consists in avoiding lambda-term unification (a former solution, but a really harder problem than generation itself) which is quickly undecidable (from second order). We can then express the process as a proof search procedure in linear logic based on a graph calculus. So that the solutions appear as a matrix computation preserving the decidability properties.
Proc. ANLP-NAACL 2000


pogodalla-naacl00.pdf (102.67 kB)