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
Ardeshir, M., Aspects of Basic Logic, PhD thesis, Marquette University, Wisconsin, U.S.A., 1995.
Ardeshir, M., and W. Ruitenburg, 'Basic propositional caculus I', Mathematical Logic Quarterly 44 (1998), 317-343.
Ardeshir, M., and W. Ruitenburg, 'Basic propositional calculus II. Interpolation', Arch. Math. Logic 40 (2001), 349-364.
Ruitenburg, W., 'Constuctive logic and the paradoxes', Modern Logic 1 (1990), 271-301.
Ruitenburg, W., 'Basic predicate calculus', Notre Dame Journal of Formal Logic 39 (1998), 18-46.
Sasaki, K., 'A Gentzen-style axiomatization of Visser's propositional logic', Nanzan Management Review 12 (1998), 343-451.
Suzuki, Y., F. Wolter and M. Zakharechiaev, 'Speaking about transitive frames in propositional languages', Journal of Logic, Language and Information 7 (1998), 317-339.
Troelstra, A.S., and H. Schwichtenburg, Basic Proof Theory, Cambridge Univ. Press, 1996.
Visser, A., 'A propositional logic with explicit fixed points', Studia Logica 40 (1981), 155-175.
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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