Some Modal Calculi Based On IC

Publisher Summary This chapter discusses some modal calculi based on IC. It reviews those modal logics that are acceptable to intuitionists. Of the two approaches described in the chapter, the first accepts this thesis, and the second avoids it. The first system formalizes the position that, while contingent propositions obey intuitionist logic, necessary propositions obey classical logic. The first system is suggested by the Wajsberg completeness proof of S5 with respect to the Henle model. It can be shown that the axiom system has a characteristic normal model, using the equivalence classes of words. The chapter shows that the axiom system has the finite model property, and is therefore decidable.