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European Conference on Logics in Artificial Intelligence

JELIA 2019: Logics in Artificial Intelligence pp 744–759Cite as

Computational Complexity of Core Fragments of Modal Logics T, K4, and S4

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11468))

Abstract

We show that the satisfiability problem in core fragments of modal logics T, K4, and S4 in whose languages diamond modal operators are disallowed is NL-complete. Moreover, we provide deterministic procedures for satisfiability checking. We show that the above fragments correspond to certain core fragments of linear temporal logic, hence our results imply NL-completeness of the latter.

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Acknowledgments

This work is supported by the National Science Centre in Poland (NCN) grant 2016/23/N/HS1/02168 and by the Foundation for Polish Science (FNP).

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Authors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, UK

    Przemysław Andrzej Wałęga

  2. Institute of Philosophy, University of Warsaw, Warsaw, Poland

    Przemysław Andrzej Wałęga

Authors
  1. Przemysław Andrzej Wałęga
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Correspondence to Przemysław Andrzej Wałęga .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Francesco Calimeri

  2. University of Calabria, Rende, Italy

    Nicola Leone

  3. Mathematics and Computer Science, University of Calabria, Rende, Italy

    Marco Manna

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Wałęga, P.A. (2019). Computational Complexity of Core Fragments of Modal Logics T, K4, and S4. In: Calimeri, F., Leone, N., Manna, M. (eds) Logics in Artificial Intelligence. JELIA 2019. Lecture Notes in Computer Science(), vol 11468. Springer, Cham. https://doi.org/10.1007/978-3-030-19570-0_48

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  • DOI: https://doi.org/10.1007/978-3-030-19570-0_48

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19569-4

  • Online ISBN: 978-3-030-19570-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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