Geodesic
Partitioning Kripke frames of finite height
Izvestiya. Mathematics , Tome 81 (2017) no. 3, pp. 592-617

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In this paper we prove the finite model property and decidability of a family of modal logics. A binary relation $R$ is said to be pretransitive if $R^*=\bigcup_{i\leqslant m} R^i$ for some $m\geqslant 0$, where $R^*$ is the transitive reflexive closure of $R$. By the height of a frame $(W,R)$ we mean the height of the preorder $(W,R^*)$. We construct special partitions (filtrations) of pretransitive frames of finite height, which implies the finite model property and decidability of their modal logics.
Keywords: modal logic, finite model property, decidability, finite height.
Mots-clés : pretransitive relation 
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     author = {A. V. Kudinov and I. B. Shapirovsky},
     title = {Partitioning {Kripke} frames of finite height},
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A. V. Kudinov; I. B. Shapirovsky. Partitioning Kripke frames of finite height. Izvestiya. Mathematics , Tome 81 (2017) no. 3, pp. 592-617. http://geodesic.mathdoc.fr/item/IM2_2017_81_3_a5/