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Optimal Tableau Systems for Propositional Neighborhood Logic over All, Dense, and Discrete Linear Orders

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6793))

Abstract

In this paper, we focus our attention on tableau systems for the propositional interval logic of temporal neighborhood (Propositional Neighborhood Logic, PNL for short). PNL is the proper subset of Halpern and Shoham’s modal logic of intervals whose modalities correspond to Allen’s relations meets and met by. We first prove by a model-theoretic argument that the satisfiability problem for PNL over the class of all (resp., dense, discrete) linear orders is decidable (and NEXPTIME-complete). Then, we develop sound and complete tableau-based decision procedures for all the considered classes of orders, and we prove their optimality. (As a matter of fact, decidability with respect to the class of all linear orders had been already proved via a reduction to the decidable satisfiability problem for the two-variable fragment of first-order logic of binary relational structures over ordered domains).

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Davide Bresolin & Pietro Sala

  2. Department of Mathematics and Computer Science, University of Udine, Udine, Italy

    Angelo Montanari

  3. Department of Information, Engineering and Communications, University of Murcia, Murcia, Spain

    Guido Sciavicco

  4. University of Information Science and Technology, Ohrid, Macedonia

    Guido Sciavicco

Authors
  1. Davide Bresolin
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  2. Angelo Montanari
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  3. Pietro Sala
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  4. Guido Sciavicco
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Editor information

Editors and Affiliations

  1. Institut für Informatik und Angewandte Mathematik, Universität Bern, Neubrückstr. 10, 3012, Bern, Switzerland

    Kai Brünnler

  2. Mathematisches Institut, Universität Bern, Sidlerstr. 5, 3012, Bern, Switzerland

    George Metcalfe

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Bresolin, D., Montanari, A., Sala, P., Sciavicco, G. (2011). Optimal Tableau Systems for Propositional Neighborhood Logic over All, Dense, and Discrete Linear Orders. In: Brünnler, K., Metcalfe, G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2011. Lecture Notes in Computer Science(), vol 6793. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22119-4_8

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  • DOI: https://doi.org/10.1007/978-3-642-22119-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22118-7

  • Online ISBN: 978-3-642-22119-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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