Wijesekera-style constructive modal logics

Abstract

We define a family of propositional constructive modal logics corresponding each to a different classical modal system. The logics are defined in the style of Wijesekera's constructive modal logic, and are both proof-theoretically and semantically motivated. On the one hand, they correspond to the single-succedent restriction of standard sequent calculi for classical modal logics. On the other hand, they are obtained by incorporating the hereditariness of intuitionistic Kripke models into the classical satisfaction clauses for modal formulas. We show that, for the considered classical logics, the proof-theoretical and the semantical approach return the same constructive systems.