Modal Renderings of Intuitionistic Propositional Logic

Abstract

The two systems of non-standard propositional logic that have been most extensively studied to date are C. I. Lewis’ systems of ‘strict implication’ and the intuitionistic propositional logic as systematized by A. Heyting. The relationship between these systems, which has now been explored for over a generation, is of substantial interest. The aim of the present chapter is both to summarize and to extend what is known about this relationship. Its linkages with the established systems of modal logic represent one of the most significant bridges between modern intuitionistic logic and other branches of the subject whose historical rootings go far deeper.¹