Realizations and LP

Annals of Pure and Applied Logic 161 (3):368-387 (2009)
LP can be seen as a logic of knowledge with justifications. See [S. Artemov, The logic of justification, The Review of Symbolic Logic 1 477–513] for a recent comprehensive survey of justification logics generally. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If the machinery of justifications is to be applied to artificial intelligence, or better yet, to everyday reasoning, we will need to work with whatever justifications we may have at hand—one version may not be interchangeable with another, even though they realize the same S4 formula. In this paper we begin the process of providing tools for reasoning about justifications directly. The tools are somewhat complex, but in retrospect this should not be surprising. Among other things, we provide machinery for combining two realizations of the same formula, and for replacing subformulas by equivalent subformulas. The results are algorithmic in nature—semantics for LP plays no role. We apply our results to provide a new algorithmic proof of Artemov’s Realization Theorem itself. This paper is a much extended version of [M.C. Fitting, Realizations and LP, in: S. Artemov, A. Nerode , Logical Foundations of Computer Science—New York ’07, in: Lecture Notes in Computer Science, vol. 4514, Springer-Verlag, 2007, pp. 212–223]
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DOI 10.1016/j.apal.2009.07.010
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References found in this work BETA
Explicit Provability and Constructive Semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
The Logic of Justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
The Logic of Proofs, Semantically.Melvin Fitting - 2005 - Annals of Pure and Applied Logic 132 (1):1-25.
Realizations and LP.Melvin Fitting - 2009 - Annals of Pure and Applied Logic 161 (3):368-387.

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Citations of this work BETA
Realizations and LP.Melvin Fitting - 2009 - Annals of Pure and Applied Logic 161 (3):368-387.
Self-Referentiality of Brouwer–Heyting–Kolmogorov Semantics.Junhua Yu - 2014 - Annals of Pure and Applied Logic 165 (1):371-388.

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