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A categorial type logic. (English) Zbl 1285.03017
Casadio, Claudia (ed.) et al., Categories and types in logic, language, and physics. Essays dedicated to Jim Lambek on the occasion of his 90th birthday. Berlin: Springer (ISBN 978-3-642-54788-1/pbk). Lecture Notes in Computer Science 8222, 331-352 (2014).
Summary: In logical categorial grammar syntactic structures are categorial proofs and semantic structures are intuitionistic proofs, and the syntax-semantics interface comprises a homomorphism from syntactic proofs to semantic proofs. Thereby, logical categorial grammar embodies in a pure logical form the principles of compositionality, lexicalism, and parsing as deduction. Interest has focused on multimodal versions but the advent of the (dis)placement calculus of G. Morrill et al. [J. Logic Lang. Inf. 20, No. 1, 1–48 (2011; Zbl 1233.03035)] suggests that the role of structural rules can be reduced, and this facilitates computational implementation. In this paper we specify a comprehensive formalism of (dis)placement logic for the parser/theorem prover CatLog integrating categorial logic connectives proposed to date and illustrate with a cover grammar of the Montague fragment.
For the entire collection see [Zbl 1284.03016].

MSC:
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03B65 Logic of natural languages
Software:
CatLog; Grail
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References:
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