Completeness of logics with the transitive closure modality and related logics
Logic
2020-11-05 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2011.02205,
title = {Completeness of logics with the transitive closure modality and related logics},
author = {Stanislav Kikot and Ilya Shapirovsky and Evgeny Zolin},
journal= {arXiv preprint arXiv:2011.02205},
year = {2020}
}