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  1. The logic of justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
    We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...)
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  • Logic of proofs.Sergei Artëmov - 1994 - Annals of Pure and Applied Logic 67 (1-3):29-59.
    In this paper individual proofs are integrated into provability logic. Systems of axioms for a logic with operators “A is provable” and “p is a proof of A” are introduced, provided with Kripke semantics and decision procedure. Completeness theorems with respect to the arithmetical interpretation are proved.
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  • Explicit provability and constructive semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
    In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...)
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  • Justification logic, inference tracking, and data privacy.Thomas Studer - 2011 - Logic and Logical Philosophy 20 (4):297-306.
    Internalization is a key property of justification logics. It states that justification logics internalize their own notion of proof which is essential for the proof of the realization theorem. The aim of this note is to show how to make use of internalization to track where an agent’s knowledge comes from and how to apply this to the problem of data privacy.
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  • Derivability in certain subsystems of the Logic of Proofs is-complete.Robert Milnikel - 2007 - Annals of Pure and Applied Logic 145 (3):223-239.
    The Logic of Proofs realizes the modalities from traditional modal logics with proof polynomials, so an expression □F becomes t:F where t is a proof polynomial representing a proof of or evidence for F. The pioneering work on explicating the modal logic is due to S. Artemov and was extended to several subsystems by V. Brezhnev. In 2000, R. Kuznets presented a algorithm for deducibility in these logics; in the present paper we will show that the deducibility problem is -complete. (...)
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  • Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
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  • The logic of proofs, semantically.Melvin Fitting - 2005 - Annals of Pure and Applied Logic 132 (1):1-25.
    A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventional approach, via soundness and completeness results.
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