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Regular version of the site

Book chapter

On Lambek’s Restriction in the Presence of Exponential Modalities

P. 146-158.
Kanovich M., Kuznetsov S., Scedrov A.

The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called “Lambek’s restriction,” that is, the antecedent of any provable sequent should be non-empty. In this paper we discuss ways of extending the Lambek calculus with the linear logic exponential modality while keeping Lambek’s restriction. We present several versions of the Lambek calculus extended with exponential modalities and prove that those extensions are undecidable, even if we take only one of the two divisions provided by the Lambek calculus.

In book

Edited by: S. Artemov, A. Nerode. Vol. 9537: Logical Foundations of Computer Science. Springer, 2016.