Decidability of Pseudo-Transitive Modal Logics

We call a modal logic “pseudo-transitive” if it obeys the axiom A ⊃ A. The question whether the modal logic K extended with this axiom is decidable, is a known open problem. In this paper, I will present a cut-free deductive system which is sound and complete for that logic, and which is suitable for proof search. In fact, the system induces a terminating proof search procedure, which entails decidability of the logic. Independently from cut elimination, I will also give a semantic proof of the finite model property.