On partitioning Kripke frames of finite height

Abstract: The paper proves finite model property and decidability for a family of modal logics. A binary relation $R$ is called pretransitive, if $R^{*=\cup_{i\leq} m} R<sup>i$ for some $m\geq 0$, where $R<sup>*$ is the transitive reflexive closure of $R$. By the height of $(W,R)$ we mean the height of the preorder $(W,R<sup>*)$. Special partitionings (filtrations) are described for pretransitive frames of finite height, which implies finite model property and decidability of logics of these frames.