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Studia Logica

, Volume 50, Issue 2, pp 241–250 | Cite as

A note on the interpretability logic of finitely axiomatized theories

  • Maarten de Rijke
Article

Abstract

In [6] Albert Visser shows that ILP completely axiomatizes all schemata about provability and relative interpretability that are provable in finitely axiomatized theories. In this paper we introduce a system called ILPω that completely axiomatizes the arithmetically valid principles of provability in and interpretability over such theories. To prove the arithmetical completeness of ILPω we use a suitable kind of tail models; as a byproduct we obtain a somewhat modified proof of Visser's completeness result.

Keywords

Mathematical Logic Computational Linguistic Completeness Result Valid Principle Tail Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Dick de Jongh and Frank Veltman. Provability Logics for Relative Interpretability. In: P.P. Petkov (ed.) Mathematical Logic, Proceedings of the 1988 Heyting Conference, Plenum Press, New York, 1990, 31–42.Google Scholar
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    Craig Smoryński. Self-Reference and Modal Logic. Springer Verlag, New York, 1985.Google Scholar
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    Albert Visser. The Provability Logics of Recursively Enumerable Theories Extending Peano Arithmetic at Arbitrary Theories Extending Peano Arithmetic. Journal of Philosophical Logic 13 (1984), 97–113.Google Scholar
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    Albert Visser. Preliminary Notes on Interpretability Logic. Logic Group Preprint Series No. 14, Department of Philosophy, University of Utrecht, 1988.Google Scholar
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    Albert Visser. Interpretability Logic. In: P.P. Petkov (ed.) Mathematical Logic, Proceedings of the 1988 Heyting Conference, Plenum Press, New York, 1990, 175–210.Google Scholar
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    A.J. Wilkie and J.B. Paris. On the Scheme of Induction for Bounded Arithmetic Formulas. Annals of Pure and Applied Logic 35 (1987), 261–302.Google Scholar

Copyright information

© Polish Academy of Sciences 1991

Authors and Affiliations

  • Maarten de Rijke
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of AmsterdamTV AmsterdamThe Netherlands

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