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 $R^{\ast }={\cup }_{i\le m}{R}^i$ for some $m\ge 0$, where $R^{\ast }$ is the transitive reflexive closure of $R$. By the height of $(W,R)$ we mean the height of the preorder $(W,R^{\ast })$. Special partitionings (filtrations) are described for pretransitive frames of finite height, which implies finite model property and decidability of logics of these frames.

In Russian. 35 pages