Quasi-characteristic inference rules for modal logics

Abstract

The aim of this paper is to develop techniques characterizing quasi-characteristic inference rules for modal logics. We describe a necessary and sufficient condition for a quasi-characteristic rule to be valid on an algebra and obtain basic properties concerning derivability of quasi-characteristic rules. Using this approach we characterize all structurally complete logics with the finite model property. The main results of this paper characterize admissible quasi-characteristic inference rules for modal logics S4 and K4. We also show that the set of all quasi-characteristic inference rules admissible in the logic S4 have a finite basis consisting of three special rules which are precisely described.