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Abstract: In 1933 Godel introduced a modal logic of provability (S4) and left open the problem of a formal provability semantics for this logic. Since then numerous attempts have been made to give an adequate provability semantics to Godel's provability logic with only partial success. In this paper we give the complete solution to this problem in the Logic of Proofs (LP). LP implements Godel's suggestion (1938) of replacing formulas "F is provable" by the propositions for explicit proofs "t is a proof... (Update)
Context of citations to this paper: More
...Benthem 1977 on intrinsic versus translationist views of temporal logic. For a contemporary example, in the logic of proofs of Artemov 1998, the box modality [ is not a universal quantifier (over all accessible worlds) but an existential one (running over available...
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BibTeX entry: (Update)
S. Artemov, 1998, "Explicit Modal Logic', in Proceedings AiML-II, Philosophical Institute, Uppsala, 22 -- 31. http://citeseer.ist.psu.edu/artemov98explicit.html More
@inproceedings{ artemov98explicit,
author = "S. Artemov",
title = "Explicit Modal Logic",
booktitle = "Workshop Proceedings \emph{Advances in Modal Logic}",
volume = "2",
address = "Uppsala",
pages = "22 -- 31",
year = "1998",
url = "citeseer.ist.psu.edu/artemov98explicit.html",
url = "http://www.cs.cornell.edu/Info/People/artemov/publ.html" }
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6 Some Remarks on the Notion of Proof (context) - Myhill - 1960
6 Finite problems (context) - Medvedev - 1962
6 New Foundations for Lewis's modal systems (context) - Lemmon - 1957
5 Kolmogorov logic of problems and a provability interpretatio.. (context) - Artemov - 1990
5 Proof realizations of typed -calculi (context) - Artemov - 1997
4 The logic of provability (context) - Kuznetsov, Yu - 1976
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4 Arithmetical necessity, provability and intuitionistic logic (context) - Goldblatt - 1978
4 Intensional Set Theory (context) - Myhill - 1985
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