Hypersequent Calculi for some Intermediate Logics with Bounded Kripke Models

In this paper we define cut-free hypersequent calculi for some intermediate logics semantically characterized by bounded Kripke models. In particular we consider the logics characterized by Kripke models of bounded width Bwk, by Kripke models of bounded cardinality Bck and by linearly ordered Kripke models of bounded cardinality Gk. The latter family of logics coincides with finite-valued Gödel logics. Our calculi turn out to be very simple and natural. Indeed, for each family of logics (respectively, Bwk, Bck and Gk), they are defined by adding just one structural rule to a common system, namely the hypersequent calculus for Intuitionistic Logic. This structural rule reflects in a natural way the characteristic semantical features of the corresponding logic.