The Logic of the Gödel Proof Predicate

TitleThe Logic of the Gödel Proof Predicate
Publication TypeConference Paper
Year of Publication1993
AuthorsArtemov, S, Strassen, T
EditorGottlob, G, Leitsch, A, Mundici, D
Conference NameComputational Logic and Proof Theory, Third Kurt Gödel Colloquium, KGC'93, Brno, Czech Republic, August 24–27, 1993, Proceedings
AbstractWe 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. Decidabillty 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.