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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Official URL: https://doi.org/10.1007/s11225-006-9005-x

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:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	11 May 2021 14:48
Last Modified:	09 Aug 2023 12:50
URI:	https://eprints.bbk.ac.uk/id/eprint/44223

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