Control effects as a modality

Abstract

Abstract We combine ideas from types for continuations, effect systems and monads in a very simple setting by defining a version of classical propositional logic in which double-negation elimination is combined with a modality. The modality corresponds to control effects, and it includes a form of effect masking. Erasing the modality from formulas gives classical logic. On the other hand, the logic is conservative over intuitionistic logic.