# The logic of the Gödel proof predicate

Contributed Papers

- First Online:

DOI: 10.1007/BFb0022556

- 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