Abstract
We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. 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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Aghaei, M., Ardeshir, M. Gentzen-Style Axiomatizations for Some Conservative Extensions of Basic Propositional Logic. Studia Logica 68, 263–285 (2001). https://doi.org/10.1023/A:1012499207246
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DOI: https://doi.org/10.1023/A:1012499207246