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The basic logic of proofs

  • Sergei Artëmov
  • Tyko Straßen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 702)

Abstract

Propositional Provability Logic was axiomatized in [5]. This logic describes the behaviour of the arithmetical operator “y is provable”. The aim of the current paper is to provide propositional axiomatizations of the predicate “x is a proof of y”by means of modal logic, with the intention of meeting some of the needs of computer science.

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References

  1. [1]
    S. Artëmov and T. Straßen, “The Basic Logic of Proofs,” Tech. Rep. IAM 92-018, Department for computer science, University of Berne, Switzerland, September 1992.Google Scholar
  2. [2]
    S. Artëmov and T. Straßen, “Functionality in the Basic Logic of Proofs,” Tech. Rep. IAM 93-004, Department for computer science, University of Berne, Switzerland, January 1993.Google Scholar
  3. [3]
    G. Boolos, The unprovability of consistency: an essay in modal logic. Cambridge: Cambridge University Press, 1979.Google Scholar
  4. [4]
    C. Smoryński, “The incompleteness theorems,” in Handbook of Mathematical Logic (J. Barwise, ed.), ch. D.1, S3, pp. 821–865, North-Holland, Amsterdam, 1977.Google Scholar
  5. [5]
    R. M. Solovay, “Provability interpretations of modal logic,” Israel Journal of Mathematics, vol. 25, pp. 287–304, 1976.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Sergei Artëmov
    • 1
  • Tyko Straßen
    • 2
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.University of Berne, IAMBerne

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