Tree-sequent methods for subintuitionistic predicate logics

Abstract

Subintuitionistic logics are a class of logics defined by using Kripke models with more general conditions than those for intuitionistic logic. In this paper we study predicate logics of this kind by the method of tree-sequent calculus (a special form of Labelled Deductive System). After proving the completeness with respect to some classes of Kripke models, we introduce Hilbert-style axiom systems and prove their completeness through a translation from the tree-sequent calculi. This gives a solution to the problem posed by Restall. © Springer-Verlag Berlin Heidelberg 2007.