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Abstract: We introduce a propositional modal logic PP of "pure" provability in arbitrary theories (propositional or first-order) where the # operator means "provable in all extensions". This modal logic has been considered in another guise by Kripke. An axiomatization and a decision procedure are given and the ## subtheory is characterized. (Update)
Context of citations to this paper: More
.... [27] 28] Kripke [18] Montague [26] Mints [25] Kuznetsov Muravitskii [19] Goldblatt [14] Boolos [7] 8] Shapiro [30] 31] Buss [9], Artemov [1] and many others. However, the problem of a formal provability semantics for S4 has remained open. A principal difficulty...
.... [39] 40] Kripke [26] Montague [38] Mints [35] Kuznetsov Muravitskii [28] Goldblatt [19] Boolos [9] 10] Shapiro [43] 44] Buss [12], Artemov [1] and many others. However, the problem of a formal provability semantics for S4 has remained open. A principal difficulty...
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6: New Foundations for Lewis's modal systems (context) - Lemmon - 1957
6: The unprovability of consistency: an essay in modal logic (context) - Boolos - 1979
6: North-Holland (context) - Takeuti - 1987
BibTeX entry: (Update)
S. Buss, "The Modal Logic of Pure Provability", Notre Dame Journal of Formal Logic, v. 31, No. 2, 1990 http://citeseer.ist.psu.edu/buss90modal.html More
@article{ buss90modal,
author = "Samuel R. Buss",
title = "The Modal Logic of Pure Provability",
journal = "Notre Dame Journal of Formal Logic",
volume = "31",
number = "2",
pages = "225-231",
year = "1990",
url = "citeseer.ist.psu.edu/buss90modal.html" }
Citations (may not include all citations):102 Semantical considerations on modal logic (context) - Kripke - 1963
62 Nonmonotonic logic II: Nonmonotonic modal theories (context) - McDermott - 1982 DBLP
30 Provability interpretations of modal logic (context) - Solovay - 1976
11 Non-monotonic logic (context) - McDermott, Doyle - 1980
6 provability and intuitionistic logic (context) - Goldblatt - 1978
2 On systems of modal logic with provability interpretations (context) - Boolos - 1980
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