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    Horn fragments of the Halpern-Shoham Interval Temporal Logic

    Bresolin, D. and Kurucz, A. and Muñoz-Velasco, E. and Ryzhikov, Vladislav 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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    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.


    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 Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Administrator
    Date Deposited: 07 Dec 2017 07:56
    Last Modified: 09 Aug 2023 12:42


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