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The Monotone Lambek Calculus Is NP-Complete

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Categories and Types in Logic, Language, and Physics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8222))

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Abstract

We consider the Lambek calculus with the additional structural rule of monotonicity (weakening). We show that the derivability problem for this calculus is NP-complete (both for the full calculus and for the product-free fragment). The same holds for the variant that allows empty antecedents. To prove NP-hardness of the product-free fragment, we provide a mapping reduction from the classical satisfiability problem \( \textit{SAT} \). This reduction is similar to the one used by Yury Savateev in 2008 to prove NP-hardness (and hence NP-completeness) of the product-free Lambek calculus.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    Mati Pentus

Authors
  1. Mati Pentus
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Editors and Affiliations

  1. Department of Philosophy, Education and Quantitative Economics, Gabriele D’Annunzio University, Chieti-Pescara, Via dei Vestini 31, 60100, Chieti, Italy

    Claudia Casadio

  2. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Bob Coecke

  3. Utrecht Institute of Linguistics OTS, Utrecht University, Trans 10,, 3512 JK, Utrecht, The Netherlands

    Michael Moortgat

  4. Department of Mathematics, University of Ottawa, 585 King Edward, K1N 6N5, Ottawa, ON, Canada

    Philip Scott

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Pentus, M. (2014). The Monotone Lambek Calculus Is NP-Complete. In: Casadio, C., Coecke, B., Moortgat, M., Scott, P. (eds) Categories and Types in Logic, Language, and Physics. Lecture Notes in Computer Science, vol 8222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54789-8_20

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  • DOI: https://doi.org/10.1007/978-3-642-54789-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54788-1

  • Online ISBN: 978-3-642-54789-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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