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  1. On Modal Systems Having Arithmetical Interpretations.Arnon Avron - 1984 - Journal of Symbolic Logic 49 (3):935-942.
  2. On Systems of Modal Logic with Provability Interpretations.George Boolos - 1980 - Theoria 46 (1):7-18.
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  3. Provability, Truth, and Modal Logic.George Boolos - 1980 - Journal of Philosophical Logic 9 (1):1 - 7.
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  4. The Logic of Provability.George S. Boolos - 1993 - Cambridge University Press.
    This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency. Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does (...)
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  5. The Modal Logic of Pure Provability.Samuel R. Buss - 1990 - Notre Dame Journal of Formal Logic 31 (2):225-231.
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  6. The Knower Paradox in the Light of Provability Interpretations of Modal Logic.Paul Égré - 2005 - Journal of Logic, Language and Information 14 (1):13-48.
    This paper propounds a systematic examination of the link between the Knower Paradox and provability interpretations of modal logic. The aim of the paper is threefold: to give a streamlined presentation of the Knower Paradox and related results; to clarify the notion of a syntactical treatment of modalities; finally, to discuss the kind of solution that modal provability logic provides to the Paradox. I discuss the respective strength of different versions of the Knower Paradox, both in the framework of first-order (...)
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  7. On Strong Provability Predicates and the Associated Modal Logics.Konstantin N. Ignatiev - 1993 - Journal of Symbolic Logic 58 (1):249-290.
    PA is Peano Arithmetic. Pr(x) is the usual Σ1-formula representing provability in PA. A strong provability predicate is a formula which has the same properties as Pr(·) but is not Σ1. An example: Q is ω-provable if PA + ¬ Q is ω-inconsistent (Boolos [4]). In [5] Dzhaparidze introduced a joint provability logic for iterated ω-provability and obtained its arithmetical completeness. In this paper we prove some further modal properties of Dzhaparidze's logic, e.g., the fixed point property and the Craig (...)
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  8. Can a Turing Machine Know That the Gödel Sentence is True?Storrs McCall - 1999 - Journal of Philosophy 96 (10):525 - 532.
  9. Johdatus modaalilogiikkaan.Veikko Rantala & Ari Virtanen - 2004 - Gaudeamus.
    The book studies philosophical and mathematical-logical problems of modal notions. Its starting points are possible worlds semantics and Kripke models, and it also concentrates on proof-theoretic methods.
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