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Publication Detail
On Lambek’s restriction in the presence of exponential modalities
  • Publication Type:
    Conference
  • Authors:
    Kanovich M, Kuznetsov S, Scedrov A
  • Publication date:
    01/01/2016
  • Pagination:
    146, 158
  • Published proceedings:
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
  • Volume:
    9537
  • ISBN-13:
    9783319276823
  • Status:
    Published
  • Print ISSN:
    0302-9743
Abstract
© Springer International Publishing Switzerland 2016. The Lambek calculus can be considered as a version of noncommutative 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.
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