Logics with the universal modality and admissible consecutions

Abstract

In this paper1 we study admissible consecutions (inference rules) in multi-modal logics with the universal modality. We consider extensions of multi-modal logic S4n augmented with the universal modality. Admissible consecutions form the largest class of rules, under which a logic (as a set of theorems) is closed. We propose an approach based on the context effective finite model property. Theorem 7, the main result of the paper, gives sufficient conditions for decidability of admissible...