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Abstract: In 1933 Gödel introduced a modal logic of provability (S4) and left open the problem of a formal provability semantics for this logic. We give a complete solution to this problem. We find a sound and complete axiom system for the logic (LP) with atomic propositions for explicit proofs "t is a proof of F ", and construct an exact realization of S4 in LP . In LP the reflection principle is valid, which circumvents some of the restrictions imposed on the provability operator by Gödel's second... (Update)
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BibTeX entry: (Update)
@misc{ artemov-logic,
author = "Sergei N. Artemov",
title = "Logic of Proofs: a Unified Semantics for Modality and lambda-Terms",
url = "citeseer.ist.psu.edu/artemov98logic.html" }
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15 Eine Interpretation des intuitionistischen Aussagenkalkuls (context) - Godel - 1933
14 Operational Modal Logic - Artemov - 1995
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7 Oxford Science Publications (context) - Chagrov, Zakharyaschev et al. - 1997
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6 Provability Logic with Operations on Proofs (context) - Sidon - 1997 ACM DBLP
5 Kolmogorov logic of problems and a provability interpretatio.. (context) - Artemov - 1990
5 Proof realizations of typed -calculi (context) - Artemov - 1997
4 Intuitionistic Logic (context) - Uspensky, Plisko - 1985
4 Intensional Mathematics and Constructive Mathematics (context) - Shapiro - 1985
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4 a modal lambda-calculus for S4 (context) - Pfenning, Wong - 1995
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2 Models for the Logic of Proofs (context) - Mkrtychev - 1997
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