Filtrations and the Finite Frame Property in Boolean Semantics

Publisher Summary This chapter reviews that in modal logic, it is often interesting to know whether certain logic has the finite model property (FMP), because it, then, immediately follows that it is decidable, provided it is finitely axiomatizable. For a logic to have the FMP means to be characterized by a class of finite models or, equivalently, that each non-theorem is rejected by some finite model for the logic in question. The chapter also focuses on the finite frame property (FFP), which means that every non-theorem is rejected by some finite frame for the logic. It is trivial that the FFP entails the FMP. Although the fact that logic has the FFP is independent of which kind of frames are used, the techniques for proving this may differ in complexity. The chapter uses Boolean semantics to describe a comparatively simple filtration method.