## “School of Mathematics”

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Paper   IPM / M / 472
School of Mathematics
Title:   Gentzen-style axiomatizations for some conservative extensions of basic propositional logic
Author(s):
 1 M. Aghaei 2 M. Ardeshir
Status:   Published
Journal: Studia Logica
Vol.:  68
Year:  2001
Pages:   263-285
Supported by:  IPM
Abstract:
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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