The Logic of Categorial Grammars: Lecture Notes

Christian Retoré 1
1 SIGNES - Linguistic signs, grammar and meaning: computational logic for natural language
INRIA Futurs, Université Sciences et Technologies - Bordeaux 1, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Université Bordeaux Montaigne, CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : These lecture notes present categorial grammars as deductive systems, and include detailed proofs of their main properties. The first chapter deals with Ajdukiewicz and Bar-Hillel categorial grammars (AB grammars), their relation to context-free grammars and their learning algorithms. The second chapter is devoted to the Lambek calculus as a deductive system; the weak equivalence with context free grammars is proved; we also define the mapping from a syntactic analysis to a higher-order logical formula, which describes the semantics of the parsed sentence. The third and last chapter is about proof-nets as parse structures for Lambek grammars; we show the linguistic relevance of these graphs in particular through the study of a performance question. Although definitions, theorems and proofs have been reformulated for pedagogical reasons, these notes contain no personnal result but in the proofnet chapter.
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Christian Retoré. The Logic of Categorial Grammars: Lecture Notes. RR-5703, INRIA. 2005, pp.105. ⟨inria-00070313⟩

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