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Traditionally, Epistemic Logic represents epistemic scenarios using a single model. This, however, covers only complete descriptions that specify truth values of all assertions. Indeed, many -- and perhaps most -- epistemic descriptions are not complete. Syntactic Epistemic Logic, SEL, suggests viewing an epistemic situation as a set of syntactic conditions rather than as a model. This allows us to naturally capture incomplete descriptions; we discuss a case study in which our proposal is successful. In Epistemic Game Theory, this closes the conceptual and technical gap, identified by R. Aumann, between the syntactic character of game-descriptions and semantic representations of games.
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Tom
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49--62
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Bibliogr. 19 poz., rys.
Twórcy
Bibliografia
- [1] Arieli I, Aumann R. The logic of backward induction. doi:10.2139/ssrn.2133302, 2012.
- [2] Artemov S. On Definitive Solutions of Strategic Games. Alexandru Baltag and Sonja Smets, eds. Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic 5:487-507, Springer, 2014. doi: 10.1007/978-3-319-06025-5 17.
- [3] Artemov S. Syntactic Epistemic Logic. Book of Abstracts. 15th Congress of Logic, Methodology and Philosophy of Science, University of Helsinki, 2015, 109-110.
- [4] Artemov S. Hyperderivations. The Hausdorff Trimester Program: Types, Sets and Constructions, Hausdorff Center for Mathematics, Bonn, 2018. https://www.youtube.com/watch?v=kytYAi6Ln7U&t=1276s
- [5] Artemov S, Nogina E. On completeness of epistemic theories. The Bulletin of Symbolic Logic, 24(2):232, 2018. https://doi.org/10.1017/bsl.2018.13.
- [6] Aumann R. Agreeing to disagree. The Annals of Statistics, 4(6):12361239, 1976. https://doi.org/10.1214/aos/1176343654.
- [7] Aumann R. Backward induction and common knowledge of rationality. Games and Economic Behavior, 8(1):6-19, 1995. https://doi.org/10.1016/S0899-8256(05)80015-6.
- [8] Aumann R. Interactive epistemology I: Knowledge. International Journal of Game Theory, 28:263-300, 1999. https://doi.org/10.1007/s001820050111
- [9] Aumann R. Epistemic Logic: 5 Questions, 2010. Vincent F. Hendricks and Olivier Roy, eds. Automatic Press/VIP, pp. 21-33. ISBN 8792130240, 9788792130242
- [10] Blackburn P, de Rijke M, Venema Y. Modal Logic. Cambridge Tracts in Theoretical Computer Science, 53, 2001.
- [11] Blackburn P, van Benthem J. Modal logic: A semantic perspective. Handbook of Modal Logic. pp.1-84. Studies in Logic and Practical Reasoning 3, Elsevier, 2007. https://doi.org/10.1016/S1570-2464(07)80004-8
- [12] Brandenburger A. The Language of Game Theory: Putting Epistemics Into the Mathematics of Games. World Scientific Publishing Company, 2014. ISSN 2251-2071.
- [13] Chagrov A, Zakharyaschev M. Modal Logic. Oxford Logic Guides 35, 1997. ISBN-13: 978-0198537793; ISBN-10: 0198537794.
- [14] Fagin R, Halpern J, Moses Y, Vardi M. Reasoning About Knowledge. MIT Press, 1995. ISBN-13: 978-0262562003; ISBN-10: 9780262562003.
- [15] Fitting M. Modal proof theory. Handbook of Modal Logic. pp.85-138. Studies in Logic and Practical Reasoning 3, Elsevier, 2007. https://doi.org/10.1016/S1570-2464(07)80005-X
- [16] Meyer JJC, van der Hoek W. Epistemic Logic for AI and Computer Science. Cambridge Tracts in Theoretical Computer Science 41, 1995.
- [17] Osborne M, Rubinstein A. A Course in Game Theory. MIT Press, 1994.
- [18] Pauly M, van der Hoek W. Modal logic for games and information. Handbook of Modal Logic. pp.1077-1148. Studies in Logic and Practical Reasoning 3, Elsevier, 2007. https://doi.org/10.1016/S1570-2464(07)80023-1
- [19] Van Benthem J. Logic in Games. MIT Press, 2014.
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Bibliografia
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