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On the Complexity of Two-Agent Justification Logic

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Computational Logic in Multi-Agent Systems (CLIMA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8624))

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Abstract

Justification Logic provides a refined version of epistemic modal logic in which the proofs/justifications are taken into account. As a practical tool, Justification Logic has the ability to model argumentation and track evidence in the full logic context, to measure the complexity of the arguments, to keep the logical omniscience at bay, etc. The complexity of single-agent justification logics has been well-studied and shown to be generally lower than the complexity of their modal counterparts. In this paper we investigate the complexity of two-agent Justification Logic. We show that for most cases the upper complexity bounds established for the single-agent cases are maintained: these logics’ derivability problem is in the second step of the polynomial hierarchy. For certain logics, though, we discover a complexity jump to PSPACE-completeness, which is a new phenomenon for Justification Logic.

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Author information

Authors and Affiliations

  1. The Graduate Center of CUNY, New York, USA

    Antonis Achilleos

Authors
  1. Antonis Achilleos
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Editor information

Editors and Affiliations

  1. Clausthal University of Technology, Adolph-Römer-Strasse 2A, 38678, Clausthal-Zellerfeld, Germany

    Nils Bulling

  2. University of Luxembourg, Campus Kirchberg, 6, rue Richard Doudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Leendert van der Torre

  3. Inria Sophia Antipolis-Méditerranée, 2004, route des Lucioles - BP 93, 06902, Sophia Antipolis, France

    Serena Villata

  4. University of Luxembourg, Computer Science and Communication Research Unit, Interdisciplinary Centre of Security, Reliability and Trust, Campus Kirchberg, 6, rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Wojtek Jamroga

  5. Department of Computing Science, University of Aberdeen, Meston Building, Room 232, Old Aberdeen, AB24 3UE, Aberdeen, UK

    Wamberto Vasconcelos

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Achilleos, A. (2014). On the Complexity of Two-Agent Justification Logic. In: Bulling, N., van der Torre, L., Villata, S., Jamroga, W., Vasconcelos, W. (eds) Computational Logic in Multi-Agent Systems. CLIMA 2014. Lecture Notes in Computer Science(), vol 8624. Springer, Cham. https://doi.org/10.1007/978-3-319-09764-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-09764-0_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09763-3

  • Online ISBN: 978-3-319-09764-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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