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.
Supported by the Swiss Nationalfonds (projects 21-27878.89 and 20-32705.91) during two stays at the University of Berne in January 1992 and January 1993.
Supported by the Union Bank of Switzerland (UBS/SBG) and by the Swiss Nationalfonds (projects 21-27878.89 and 20-32705.91).
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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. https://doi.org/10.1007/BFb0022556
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DOI: https://doi.org/10.1007/BFb0022556
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