Intuitionistic Control Logic

We introduce a propositional logic ICL, which adds to intuitionistic logic elements of classical reasoning without collapsing it into classical logic. This logic includes a new constant for false, which augments false in intuitionistic logic and in minimal logic. The new constant requires a simple-yet-significant modification of intuitionistic logic both semantically and proof-theoretically. We define a Kripke-style semantics as well as a topological space interpretation in which the new constant is given a precise denotation. We define a sequent calculus and prove cut-elimination. We then formulate a natural deduction proof system with a term calculus, one that gives a direct, computational interpretation of contraction. This calculus shows that ICL is fully capable of typing programming language control constructs such as call/cc while maintaining intuitionistic implication as a genuine connective.