Gentzen-style axiomatizations for some conservative extensions of basic propositional logic

We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of [1], in the sense that it has a kind of the subformula property and is a slight modification of [6]. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic. © 2001 Kluwer Academic Publishers.