Lambek calculus is NP-complete

Authors:
Mati Pentus
Affiliations:
Department of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
Venue:
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Year:
2006

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Abstract

We prove that for both the Lambek calculus L and the Lambek calculus allowing empty premises L* the derivability problem is NP-complete. It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NP-complete.