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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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