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Regular version of the site

Book chapter

A Polynomial-Time Algorithm for the Lambek Calculus with Brackets of Bounded Order

P. 22:1-22:17.
Kanovich M., Kuznetsov S., Morrill G., Scedrov A.

Lambek calculus is a logical foundation of categorial grammar, a linguistic paradigm of grammar as logic and parsing as deduction. Pentus (2010) gave a polynomial-time algorithm for determining provability of bounded depth formulas in L* , the Lambek calculus with empty antecedents allowed. Pentus’ algorithm is based on tabularisation of proof nets. Lambek calculus with brackets is a conservative extension of Lambek calculus with bracket modalities, suitable for the modeling of syntactical domains. In this paper we give an algorithm for provability in Lb* , the Lambek calculus with brackets allowing empty antecedents. Our algorithm runs in polynomial time when both the formula depth and the bracket nesting depth are bounded. It combines a Pentus-style tabularisation of proof nets with an automata-theoretic treatment of bracketing.

In book

Vol. 84: 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). 2017.