Intuitionistic Hybrid Logic

Abstract

In this chapter we introduce intuitionistic hybrid logic and its proof-theory. Intuitionistic hybrid logic is hybrid modal logic over an intuitionistic logic basis instead of a classical logical basis. The chapter is structured as follows. In the first section of the chapter we introduce intuitionistic hybrid logic (this is taken from Brauner and de Paiva (2006)). In the second section we introduce a natural deduction system for intuitionistic hybrid logic (taken from Brauner and de Paiva (2006)) and in the third and fourth sections we introduce axiom systems for intuitionistic and paraconsistent hybrid logic (taken from Brauner and de Paiva (2006)). In the last section we discuss certain other work, namely a Curry-Howard interpretation of intuitionistic hybrid logic.