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Symmetric Categorial Grammar

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Abstract

The Lambek-Grishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of type-forming operations (product and residual left and right division) with a dual family: coproduct, left and right difference. Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance properties: stability of interpretations for the Curry-Howard derivational semantics, and structure-preservation at the syntactic end. The move to symmetry thus offers novel ways of reconciling the demands of natural language form and meaning.

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Authors and Affiliations

  1. Utrecht University, OTS, Trans 10, 3512 JK, Utrecht, Netherlands

    Michael Moortgat

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  1. Michael Moortgat
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Correspondence to Michael Moortgat.

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In the early 1980s, Johan van Benthem’s work on the Lambek calculus lured me into categorial temptations: I have never regretted this. As for the symmetric developments, it was a pleasure to collaborate with Raffaella Bernardi, Natasha Kurtonina, and Mati Pentus on some of the results reported on here; Richard Moot and Philippe de Groote provided valuable feedback at different stages of the project. For comments on an earlier draft I thank Arno Bastenhof, Sylvain Pogodalla, Sylvain Salvati, and two anonymous reviewers. Remaining errors are my own.

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Moortgat, M. Symmetric Categorial Grammar. J Philos Logic 38, 681–710 (2009). https://doi.org/10.1007/s10992-009-9118-6

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