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    Horn fragments of the Halpern-Shoham Interval Temporal Logic

    Bresolin, D. and Kurucz, A. and Muñoz-Velasco, E. and Ryzhikov, V. and Sciavicco, G. and Zakharyaschev, Michael (2017) Horn fragments of the Halpern-Shoham Interval Temporal Logic. ACM Transactions on Computational Logic 18 (3), pp. 1-39. ISSN 1529-3785.

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    Abstract

    We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of Horn formulas with diamonds is undecidable for any type of linear orders and semantics. On the contrary, satisfiability of Horn formulas with boxes is tractable over both discrete and dense orders under the reflexive semantics and over dense orders under the irreflexive semantics but becomes undecidable over discrete orders under the irreflexive semantics. Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics.

    Metadata

    Item Type: Article
    Additional Information: © ACM, 2017. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published at the link above.
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Administrator
    Date Deposited: 07 Dec 2017 07:56
    Last Modified: 16 Jan 2018 16:33
    URI: http://eprints.bbk.ac.uk/id/eprint/20550

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