Kripke semantics for the logic of problems and propositions

Abstract

In this paper we study the propositional fragment of the joint logic of problems and propositions introduced by Melikhov. We provide Kripke semantics for this logic and show that is complete with respect to those models and has the finite model property. We consider examples of the use of -models usage. In particular, we prove that is a conservative extension of the logic . We also show that the logic is complete with respect to Kripke frames with sets of audit worlds introduced by Artemov and Protopopescu (who called them audit set models). Bibliography: 31 titles.