An Intuitionistic Logic for Sequential Control

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. We define Kripke models for ICL and show how they translate to several other forms of semantics. We define a sequent calculus and prove cut-elimination. We then formulate a natural deduction proof system with a term calculus that gives a direct, computational interpretation of contraction. This calculus shows that ICL is fully capable of typing programming language control operators such as call/cc while maintaining intuitionistic implication as a genuine connective.