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    On dynamic topological and metric logics

    Konev, B. and Kontchakov, Roman and Wolter, F. and Zakharyaschev, M. (2006) On dynamic topological and metric logics. Studia Logica 84 (1), pp. 129-160. ISSN 0039-3215.

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    Abstract

    We investigate computational properties of propositional logics for dynamical systems. First, we consider logics for dynamic topological systems (W.f), fi, where W is a topological space and f a homeomorphism on W. The logics come with ‘modal’ operators interpreted by the topological closure and interior, and temporal operators interpreted along the orbits {w, f(w), f2 (w), ˙˙˙} of points w ε W. We show that for various classes of topological spaces the resulting logics are not recursively enumerable (and so not recursively axiomatisable). This gives a ‘negative’ solution to a conjecture of Kremer and Mints. Second, we consider logics for dynamical systems (W, f), where W is a metric space and f and isometric function. The operators for topological interior/closure are replaced by distance operators of the form ‘everywhere/somewhere in the ball of radius a, ‘for a ε Q +. In contrast to the topological case, the resulting logic turns out to be decidable, but not in time bounded by any elementary function.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Sarah Hall
    Date Deposited: 11 May 2021 14:48
    Last Modified: 11 May 2021 14:48
    URI: https://eprints.bbk.ac.uk/id/eprint/44223

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