Extraction in the Lambek-Grishin calculus

Authors:
Arno Bastenhof
Affiliations:
Utrecht University
Venue:
ESSLLI'08/09 Proceedings of the 2008 international conference on Interfaces: explorations in logic, language and computation
Year:
2008

Citing 2
Cited 1

Continuation semantics for symmetric categorial grammar

WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Symmetries in natural language syntax and semantics: the Lambek-Grishin calculus

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Relational semantics for the Lambek-Grishin calculus

MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language

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Abstract

We propose an analysis of extraction in the Lambek-Grishin calculus (LG): a categorial type logic featuring subtractions A Θ B and B Θ A, with proof-theoretic behavior dual to that of the usual implications A/B, B\A. Our analysis rests on three pillars: Moortgat's discontinuous type constructors ([6]); their decomposition in LG as proposed by Bernardi and Moortgat ([1]); and the polarity-sensitive double negation translations of [3] and [5], inspiring the Montagovian semantics of our analysis. Characteristic of the latter is the use of logical constants for existential quantification and identity to identify the extracted argument with its associated gap.