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International Workshop on Computer Science Logic

CSL 1992: Computer Science Logic pp 14–28Cite as

The basic logic of proofs

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Part of the book series: Lecture Notes in Computer Science ((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.

Supported by the Swiss Nationalfonds (project 21-27878.89) during a stay at the University of Berne in January 1992.

Financed by the Union Bank of Switzerland (UBS/SBG) and by the Swiss Nationalfonds (projects 21-27878.89 and 20-32705.91).

The authors wish to thank the anonymous referee for his valuable suggestions.

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References

  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.

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  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.

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  3. G. Boolos, The unprovability of consistency: an essay in modal logic. Cambridge: Cambridge University Press, 1979.

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  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.

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  5. R. M. Solovay, “Provability interpretations of modal logic,” Israel Journal of Mathematics, vol. 25, pp. 287–304, 1976.

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Author information

Authors and Affiliations

  1. Steklov Mathematical Institute, Vavilov str. 42, 117966, Moscow, Russia

    Sergei Artëmov

  2. University of Berne, IAM, Länggassstr. 51, CH-3012, Berne

    Tyko Straßen

Authors
  1. Sergei Artëmov
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  2. Tyko Straßen
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Editor information

E. Börger G. Jäger H. Kleine Büning S. Martini M. M. Richter

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© 1993 Springer-Verlag Berlin Heidelberg

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Artëmov, S., Straßen, T. (1993). The basic logic of proofs. In: Börger, E., Jäger, G., Kleine Büning, H., Martini, S., Richter, M.M. (eds) Computer Science Logic. CSL 1992. Lecture Notes in Computer Science, vol 702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56992-8_3

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  • DOI: https://doi.org/10.1007/3-540-56992-8_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56992-3

  • Online ISBN: 978-3-540-47890-4

  • eBook Packages: Springer Book Archive

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