LC graphs for the Lambek calculus with product

Authors:
Timothy A. D. Fowler
Affiliations:
Department of Computer Science, University of Toronto, Toronto, ON, Canada
Venue:
MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language
Year:
2007

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Abstract

This paper introduces a novel graph representation of proof nets for the Lambek calculus that extends the LC graph representation of [13] to include the product connective. This graph representation more clearly specifies the difference between the Lambek calculus with and without product than other proof net representations, which is important to the search for polynomial time among Lambek calculus fragments. We use LC graphs to further the efforts to characterize the boundary between polynomial time and NP-complete sequent derivability by analyzing the NP-completeness proof of [14] and discussing a sequent derivability algorithm.