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Gentzen Style Axiomatization for some Conservative Extensions of Basic Propositional Calculus, Studia Logica, 68(2), 263-285, July 2001

We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an improvement of [1], in the sense that it has a kind of the subformula property and is a slight modification of [7]. 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.

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