Deduction Systems for Multimodal Logics with Operations on Modalities

Abstract

This article is a brief, user friendly discourse on extensions of multi- modal logics with operations on modalities. Such logics are considered from a general point of view with the emphasis on the theory of deduc- tion systems. The first part of the article concentrates on developing general tools that lead to partial completeness results for logics where the algebra of modalities is effectively axiomatizable. The second part is devoted to the completeness issue of multimodal logic with union and intersection of modalities. A natural, straightforward axiomatization and a proof of completeness are given.