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Decidable and Undecidable Fragments of Halpern and Shoham’s Interval Temporal Logic: Towards a Complete Classification

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5330))

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Abstract

Interval temporal logics are based on temporal structures where time intervals, rather than time instants, are the primitive ontological entities. They employ modal operators corresponding to various relations between intervals, known as Allen’s relations. Technically, validity in interval temporal logics translates to dyadic second-order logic, thus explaining their complex computational behavior. The full modal logic of Allen’s relations, called HS, has been proved to be undecidable by Halpern and Shoham under very weak assumptions on the class of interval structures, and this result was discouraging attempts for practical applications and further research in the field. A renewed interest has been recently stimulated by the discovery of interesting decidable fragments of HS. This paper contributes to the characterization of the boundary between decidability and undecidability of HS fragments. It summarizes known positive and negative results, it describes the main techniques applied so far in both directions, and it establishes a number of new undecidability results for relatively small fragments of HS.

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Author information

Authors and Affiliations

  1. University of Verona, Verona, Italy

    Davide Bresolin

  2. University of Udine, Udine, Italy

    Dario Della Monica & Angelo Montanari

  3. University of Witwatersrand, Johannesburg, South Africa

    Valentin Goranko

  4. University of Murcia, Murcia, Spain

    Guido Sciavicco

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

Editors and Affiliations

  1. Carnegie Mellon University, Doha, Qatar

    Iliano Cervesato

  2. Technische Universität Darmstadt, Germany

    Helmut Veith

  3. University of Manchester, UK

    Andrei Voronkov

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Bresolin, D., Della Monica, D., Goranko, V., Montanari, A., Sciavicco, G. (2008). Decidable and Undecidable Fragments of Halpern and Shoham’s Interval Temporal Logic: Towards a Complete Classification. In: Cervesato, I., Veith, H., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2008. Lecture Notes in Computer Science(), vol 5330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89439-1_41

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  • DOI: https://doi.org/10.1007/978-3-540-89439-1_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89438-4

  • Online ISBN: 978-3-540-89439-1

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