Hypersequent calculi for some intermediate logics with bounded Kripke models (Q2720315)

In this paper cut-free hypersequent calculi are provided for three families of intermediate propositional logics; those characterized by the classes of posets of width at most \(k\), of cardinality at most \(k\), and of linear orders of at most \(k\) elements, respectively, among which the logics of the third family are also known as finite-valued Gödel logics. The logics of each family are formulated in the hypersequent system of intuitionistic logic by adjoining a structural rule which is given with respect to the family in a uniform schema reflecting the structural characteristic of the semantical framework.