Bidirectional Functional Semantics for Pregroup Grammars

17 pages•Published: July 7, 2015

Abstract

Pregroup grammars are a recent descendant of the original categorial grammars of Bar-Hillel [1] and Lambek [10] in which types take the form of strings of basic types and left and right adjoints, as opposed to the non-commutative functional types of categorial grammars. Whereas semantic extraction is possible in other categorial grammars through the λ-calculus, this approach will not be feasible for pregroup grammars. In this paper, we show how to build a term calculus that could be used to fill this void. This system is inspired by the λ-calculus but differs in crucial aspects: it uses function composition as its main reduction strategy instead of function application and is bidirectional, i.e. the direction arguments are applied to terms matters. We show how this term calculus is one- to-one with a proper subset of pregroup types and give multiple examples to show how this system could be used to do semantic analysis in parallel to doing grammaticality checks with pregroup grammars.

Keyphrases: categorial, lambda, pregroup, proof

In: Makoto Kanazawa, Lawrence S. Moss and Valeria de Paiva (editors). NLCS'15. Third Workshop on Natural Language and Computer Science, vol 32, pages 12-28.

Links:	https://easychair.org/publications/paper/Pn6
	https://doi.org/10.29007/2s3s