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    Decidable and undecidable fragments of first-order branching temporal logics

    Hodkinson, I.M. and Wolter, F. and Zakharyaschev, Michael (2002) Decidable and undecidable fragments of first-order branching temporal logics. In: UNSPECIFIED (ed.) LICS 2002: 17th IEEE Symposium on Logic in Computer Science. IEEE Computer Society, pp. 393-402. ISBN 9780769514839.

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    Abstract

    In this paper we analyze the decision problem for fragments of first-order extensions of branching time temporal logics such as computational tree logics CTL and CTL* or Prior's Ockhamist logic of historical necessity. On the one hand, we show that the one-variable fragments of logics like first-order CTL*-such as the product of propositional CTL* with simple propositional modal logic S5, or even the one-variable bundled first-order temporal logic with sole temporal operator 'some time in the future'-are undecidable. On the other hand, it is proved that by restricting applications of first-order quantifiers to state (i.e., path-independent) formulas, and applications of temporal operators and path quantifiers to formulas with at most one free variable, we can obtain decidable fragments. The positive decidability results can serve as a unifying framework for devising expressive and effective time-dependent knowledge representation formalisms, e.g., temporal description or spatio-temporal logics.

    Metadata

    Item Type: Book Section
    School: School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Sarah Hall
    Date Deposited: 08 Nov 2021 14:04
    Last Modified: 08 Nov 2021 14:08
    URI: https://eprints.bbk.ac.uk/id/eprint/46626

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