Logics of Kripke meta-models

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 t...

• Type: Journal
• Year: 2010
• Where: IGPL
• Authors: Sergey Babenyshev, Vladimir V. Rybakov
• Keywords: Constituent Logics, Formal Methods, IGPL 2010, Kripke Complete Logics, Logics