Intuitionistic counterparts of finitely-valued logics

Abstract

We investigate the relation between Kripke's model structures for intuitionistic logic and the simple syntactical restriction that turns the classical sequent calculus into an intuitionistic one. For this purpose we generalize ordinary Kripke structures to ones based on arbitrary finite sets of truth values and show that imposing a proper syntactical restriction on many-placed sequents leads to calculi that are correct and cut-free complete for the new logics.