Terminating Sequent Calculi for Two Intuitionistic Modal Logics

This paper presents sequent calculi in which proof search is terminating for two intuitionistic modal logics, the intuitionistic versions of the classical modal logics K and KD without a diamond operator. The calculi are extensions of the terminating sequent calculus G4ip for intuitionistic propositional logic that was discovered independently by Dyckhoff and Hudelmaier around 1990. It is shown by proof–theoretic means that these terminating calculi are equivalent to the cutfree extensions of G3ip that form some of the standard calculi for intuitionistic modal logics