Explicit Proofs in Formal Provability Logic

Authors:
Evan Goris
Affiliations:
The Graduate Center of the City University of New York, 365 Fifth Avenue, 10016 New York, NY, U.S.A.
Venue:
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Year:
2007

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Abstract

In this paper we answer the question what implicit proof assertions in the provability logic GLcan be realized by explicit proof terms. In particular we show that the fragment of GLwhich can be realized by generalized proof terms of GLAis exactly S4驴 GLand equals the fragment that can be realized by proof-terms of LP. In the final sections of this paper we establish the disjunction property for GLAand give an axiomatization for GL驴 S4.