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On Decidability and Expressiveness of Propositional Interval Neighborhood Logics

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Logical Foundations of Computer Science (LFCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4514))

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Abstract

Interval-based temporal logics are an important research area in computer science and artificial intelligence. In this paper we investigate decidability and expressiveness issues for Propositional Neighborhood Logics (PNLs). We begin by comparing the expressiveness of the different PNLs. Then, we focus on the most expressive one, namely, PNLπ + , and we show that it is decidable over various classes of linear orders by reducing its satisfiability problem to that of the two-variable fragment of first-order logic with binary relations over linearly ordered domains, due to Otto. Next, we prove that PNLπ +  is expressively complete with respect to such a fragment. We conclude the paper by comparing PNLπ +  expressiveness with that of other interval-based temporal logics.

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Authors and Affiliations

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

    Davide Bresolin & Angelo Montanari

  2. School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa

    Valentin Goranko

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

    Guido Sciavicco

Authors
  1. Davide Bresolin
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  2. Valentin Goranko
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  3. Angelo Montanari
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  4. Guido Sciavicco
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Editor information

Sergei N. Artemov Anil Nerode

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Bresolin, D., Goranko, V., Montanari, A., Sciavicco, G. (2007). On Decidability and Expressiveness of Propositional Interval Neighborhood Logics. In: Artemov, S.N., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2007. Lecture Notes in Computer Science, vol 4514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72734-7_7

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  • DOI: https://doi.org/10.1007/978-3-540-72734-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72732-3

  • Online ISBN: 978-3-540-72734-7

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