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

Studia Logica 68 (2):263-285 (2001)
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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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References found in this work

Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
Basic Predicate Calculus.Wim Ruitenburg - 1998 - Notre Dame Journal of Formal Logic 39 (1):18-46.
Basic Propositional Calculus I.Mohamed Ardeshir & Wim Ruitenberg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.

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