Abstract
LP can be seen as a logic of knowledge with justifications. Artemov’s Realization Theorem says justifications can be extracted from validities in the Hintikka-style logic of knowledge S4, where they are not explicitly present. We provide tools for reasoning about justifications directly. 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.
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References
Artemov, S.: Explicit provability and constructive semantics. The Bulletin for Symbolic Logic 7(1), 1–36 (2001)
Gödel, K.: Eine Interpretation des intuitionistischen Aussagenkalküls. Ergebnisse eines mathematischen Kolloquiums 4, 39–40 (1933), English translation in: Feferman, S., Kleene, J.D., Moore, S.C., Solovay, G.H., van Heijenoort, R.M.J. (eds.): Kurt Gödel Collected Works, vol. 1. Oxford University Press, New York (1986)
Fitting, M.C.: The logic of proofs, semantically. Annals of Pure and Applied Logic 132, 1–25 (2005)
Kuznets, R.: On self-referentiality in modal logic. The Bulletin of Symbolic Logic 12(3), 510 (2006)
Fitting, M.C.: A replacement theorem for LP. Technical report, CUNY Ph.D. Program in Computer Science (2006), http://www.cs.gc.cuny.edu/tr/
Rubtsova, N.: Evidence reconstruction of epistemic modal logic S5. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 313–321. Springer, Heidelberg (2006)
Feferman, S., Kleene, J.D., Moore, S.C., Solovay, G.H., van Heijenoort, R.M.J. (eds.): Kurt Gödel Collected Works, vol. 1. Oxford University Press, New York (1986)
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Fitting, M. (2007). Realizations and LP . In: Artemov, S.N., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2007. Lecture Notes in Computer Science, vol 4514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72734-7_15
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DOI: https://doi.org/10.1007/978-3-540-72734-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72732-3
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