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

Aghaei, M ; Sharif University of Technology | 2001

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  1. Type of Document: Article
  2. DOI: 10.1023/A:1012499207246
  3. Publisher: Springer Netherlands , 2001
  4. Abstract:
  5. We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of [1], in the sense that it has a kind of the subformula property and is a slight modification of [6]. 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. © 2001 Kluwer Academic Publishers
  6. Keywords:
  7. Basic logic ; Cut-elimination ; Interpolation ; Sequent calculus
  8. Source: Studia Logica ; Volume 68, Issue 2 , 2001 , Pages 263-285 ; 00393215 (ISSN)
  9. URL: https://link.springer.com/article/10.1023/A:1012499207246