The logic of the Gödel proof predicate

  • Sergei Artëmov
  • Tyko Straßen
Contributed Papers

DOI: 10.1007/BFb0022556

Volume 713 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Artëmov S., Straßen T. (1993) The logic of the Gödel proof predicate. In: Gottlob G., Leitsch A., Mundici D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg

Abstract

We discuss the logics of the operators “p is a proof of A” and “p is a proof containing A” for the standard Gödel proof predicate in Peano Arithmetic. Decidability and arithmetical completeness of these logics are proved. We use the same semantics as for the Provability Logic where the operator “A is provable” is studied.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

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