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Logic Journal of IGPL Advance Access published online on September 3, 2009
Logic Journal of IGPL, doi:10.1093/jigpal/jzp047
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Logics of Kripke meta-models

Sergey Babenyshev

Department of Computing and Mathematics, Manchester Metropolitan University, John Dalton Building, Chester Street, Manchester M1 5GD, U.K.
E-mail: S.Babenyshev{at}mmu.ac.uk

Vladimir Rybakov

Department of Computing and Mathematics, Manchester Metropolitan University, John Dalton Building, Chester Street, Manchester M1 5GD, U.K.
E-mail: V.Rybakov{at}mmu.ac.uk


  Abstract

This paper introduces and studies a new type of logical construction, which allows to combine various non-classical propositional logics with the temporal or modal background. The possible candidates include (but are not restricted to) a number of epistemic, multi-agent, deontological and other well-studied logics. In this construction, that we call refinement, the Kripke structure of a chosen Kripke complete logic is imposed on clusters of the background transitive frame. Refinements fit in a wider framework of fibred logics, while having some unique features. First of all, when applied to classes of frames of Kripke complete logics, refinement preserves good meta-logical properties of constituent logics, in contrast with the well-known products of logics. Another advantage of refinements is that they allow for augmented languages of considerable expressive power, while preserving good meta-logical and semantical properties. In particular we show that refinement of logics preserves the effective finite model property and decidability for a wide class of constituent logics.

Key Words: fibred logics • multi-modal logics • decision algorithms • satisfiability • Kripke semantics

Received for publication 29 July 2009.
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