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arXiv:2011.02205 [math.LO]AbstractReferencesReviewsResources

Completeness of logics with the transitive closure modality and related logics

Stanislav Kikot, Ilya Shapirovsky, Evgeny Zolin

Published 2020-11-04Version 1

We give a sufficient condition for Kripke completeness of modal logics enriched with the transitive closure modality. More precisely, we show that if a logic admits what we call definable filtration (ADF), then such an expansion of the logic is complete; in addition, has the finite model property, and again ADF. This argument can be iterated, and as an application we obtain the finite model property for PDL-like expansions of logics that ADF.

Journal: Proceedings of Advances in Modal Logic 2020
Categories: math.LO
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