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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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