Core type theory

Neil Tennant's core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the possibility of using it as a type theory, in the same kind of way intuitionistic logic is often used as a type theory. Our proof system is not Tennant's own, but it is very closely related. The difference matters for our purposes, and we discuss this. We then turn to the question of strong normalization, showing that although Tennant's proof system for core logic is not strongly normalizing, our modified system is.