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Reports Year : 2005

The Logic of Categorial Grammars: Lecture Notes

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.

Domains

Other [cs.OH]
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Dates and versions

inria-00070313 , version 1 (19-05-2006)

Identifiers

  • HAL Id : inria-00070313 , version 1

Cite

Christian Retoré. The Logic of Categorial Grammars: Lecture Notes. RR-5703, INRIA. 2005, pp.105. ⟨inria-00070313⟩
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