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  1. Arnon Avron (1984). On Modal Systems Having Arithmetical Interpretations. Journal of Symbolic Logic 49 (3):935-942.
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  2. George Boolos (1993). The Logic of Provability. 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 (CUP, 1979). Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self referential' (...)
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  3. George Boolos (1980). On Systems of Modal Logic with Provability Interpretations. Theoria 46 (1):7-18.
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  4. George Boolos (1980). Provability, Truth, and Modal Logic. Journal of Philosophical Logic 9 (1):1 - 7.
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  5. Samuel R. Buss (1990). The Modal Logic of Pure Provability. Notre Dame Journal of Formal Logic 31 (2):225-231.
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  6. Paul Égré (2005). The Knower Paradox in the Light of Provability Interpretations of Modal Logic. 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. Konstantin N. Ignatiev (1993). On Strong Provability Predicates and the Associated Modal Logics. 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. Storrs McCall (1999). Can a Turing Machine Know That the Godel Sentence is True? Journal of Philosophy 96 (10):525-32.