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Undecidability of the Lambek Calculus with Subexponential and Bracket Modalities

P. 326–340.
Kanovich M., Scedrov A., Kuznetsov S.

The Lambek calculus is a well-known logical formalism for modelling natural language syntax. The original calculus covered a substantial number of intricate natural language phenomena, but only those restricted to the context-free setting. In order to address more subtle linguistic issues, the Lambek calculus has been extended in various ways. In particular, Morrill and Valentín (2015) introduce an extension with so-called exponential and bracket modalities. Their extension is based on a non-standard contraction rule for the exponential that interacts with the bracket structure in an intricate way. The standard contraction rule is not admissible in this calculus. In this paper we prove undecidability of the derivability problem in their calculus. We also investigate restricted decidable fragments considered by Morrill and Valentín and we show that these fragments belong to the NP class.

Language: English
DOI
Text on another site
Keywords: Lambek calculus
Publication based on the results of:
Explanation-oriented Methods of  Data Analysis for Semantically Rich Data and Their Applications (2017)

In book

21st International Symposium, Fundamentals of Computation Theory 2017, FCT 2017
Springer, 2017.
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