Public Announcement Logic in Geometric Frameworks

• Autorzy: Başkent C.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce public announcement logic in different geometric frameworks. First, we consider topological models, and then extend our discussion to a more expressive model, namely, subset space models. Furthermore, we prove the completeness of public announcement logic in those frameworks. After that, we apply our results to different issues: announcement stabilization, backward induction and persistence.

Słowa kluczowe

EN

Public Announcement Logic; Topological Semantics; Subset Space Logic; Backward Induction

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 118, nr 3
• Strony: 207--223
• Opis fizyczny: Bibliogr. 39 poz., rys.

Twórcy

autor

Başkent C.

• Department of Computer Science, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, NY 10016, USA,,

Bibliografia

• [1] Aiello, M., van Benthem, J., Bezhanishvili, G.: Reasoning About Space: the Modal Way, Journal of Logic and Computation, 13(6), December 2003, 889-920.
• [2] Artemov, S.: Intelligent Players, Technical report, Department of Computer Science, The Graduate Center, The City University of New York, 2009.
• [3] Artemov, S.: Rational Decisions in Non-probablistic Setting, Technical Report TR-2009012, Department of Computer Science, The Graduate Center, The City University of New York, 2009.
• [4] Aumann, R. J.: Agreeing to Disagree, The Annals of Statistics, 4(6), November 1976, 1236-9.
• [5] Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., de Lima, T: 'Knowable' as 'known after an announcement', Review of Symbolic Logic, 1(3), 2008, 305-334.
• [6] Baltag, A., Moss, L. S.: Logics for Epistemic Programs, Synthese, 139(2), March 2004, 165-224.
• [7] Barwise, J.: Three Views of Common Knowledge, Proceedings of the 2nd conference on Theoretical aspects of reasoning about knowledge (M. K. Publishers, Ed.), 1988.
• [8] Başkent, C: Topics in Subset Space Logic, Master Thesis, Institute for Logic, Language and Computation, Universiteit van Amsterdam, July 2007.
• [9] Başkent, C: Completeness of Public Announcement Logic in Topological Spaces, Bulletin of Symbolic Logic, 17(1), 2011, 142.
• [10] Başkent, C: Geometric Public Announcement Logics, Proceedings of the 24th Florida Artificial Intelligence Research Society Conference (R. C. Murray, P. M. McCarthy, Eds.), FLAIRS-24, AAAI Press, 2011.
• [11] Baskent, C: Paraconsistency and Topological Semantics, http://arxiv.org/abs/! 107.4939, 2011.
• [12] van Benthem, J.: "One is a Lonely Number": Logic and Communication, Logic Colloquium '02 (Z. Chatzidakis, P. Koepke, W. Pohlers, Eds.), 27, Association for Symbolic Logic, 2006.
• [13] van Benthem, J.: Rational Dynamics and Epistemic Logic in Games, International Game Theory Review, 9(1), 2007, 13-45.
• [14] van Benthem, J., Bezhanishvili, G.: Modal Logics of Space, in: Handbook of Spatial Logics (M. Aiello, I. E. Pratt-Hartman, J. van Benthem, Eds.), Springer, 2007.
• [15] van Benthem, J., Bezhanishvili, G., Cate, B. t., Sarenac, D.: Modal Logics for Product Topologies, Studia Logica, 84(3), 2006, 375-99.
• [16| van Benthem, J., van Eijck, J., Kooi, B.: Logics of Communication and Change, Technical report, Institute for Logic, Language and Computation, 2005.
• [17] van Benthem, J., Gheerbrant, A.: Game Solution, Epistemic Dynamics and Fixed-Point Logics, Fundamenta Infomaticae, 100(1-4), 2010, 19-41.
• [18] van Benthem, J., Sarenac, D.: The Geometry of Knowledge, Aspects of Universal Logic, 11, 2004.
• [19] Bezhanishvili, G., Esakia, L., Gabelaia, D.: Some Results on Modal Axiomatization and Definability for Topological Spaces, Studia Logica, 81(3), December 2005, 325-55.
• [20] Bezhanishvili, G., Gehrke, M.: Completeness of S4 with respect to the Real Line: Revisited, Annals of Pure and Applied Logic, 131(??), ?? 2005, 287-301.
• [21] Cate, B. t., Gabelaia, D., Sustretov, D.: Modal Languages for Topology: Expressivity and Definability, Annals of Pure and Applied Logic, 159(1-2), May 2009, 146-170.
• [22] van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic, Springer, 2007.
• [23] Fagin, R., Halpern, J. Y., Moses, Y., Vardi, M. Y: Reasoning About Knowledge, MIT Press, 1995.
• [24] Gabbay, D. M., Kurucz, A., Wolter, F., Zakharyaschev, M.: Many Dimensional Modal Logics: Theory and Applications, vol. 145 of Studies in Logic and the Foundations of Mathematics, Elsevier, 2003.
• [25] Gerbrandy, J.: Bisimulations on Planet Kripke, Ph.D. Thesis, Institute of Logic, Language and Computation; Universiteit van Amsterdam, 1999.
• [26] Goldblatt, R.: Mathematical Modal Logic: A View of Its Evolution, in: Handbook of History of Logic (D. M. Gabbay, J. Woods, Eds.), vol. 6, Elsevier, 2006.
• [27] Halpern, J. Y: Substantive Rationality and Backward Induction, Games and Economic Behavior, 37(2), November 2001, 425-435.
• [28] Kooi, B.: Expressivity and Completeness for Public Update Logics via Reduction Axioms, Journal of Applied Non-Classical Logics, 17(2), 2007, 231-253.
• [29] McKinsey, J. C. C, Tarski, A.: The Algebra of Topology, The Annals of Mathematics, 45(1), January 1944, 141-191.
• [30] McKinsey, J. C. C, Tarski, A.: On Closed Elements in Closure Algebras, The Annals of Mathematics, 47( 1), January 1946, 122-162.C. Backent /Public Announcement Logic in Geometric Frameworks
• [31] Mortensen, C: Topological Seperation Principles and Logical Theories, Synthese, 125(1-2), January 2000, 169-178.
• [32] Moss, L. S., Parikh, R.: Topological Reasoning and the Logic of Knowledge, Proceedings of TARK IV (Y. Moses, Ed.), 1992.
• [33] Parikh, R.: Finite and Infinite Dialogues, Proceedings of a Workshop on Logic from Computer Science (Y. Moschovakis, Ed.), Springer, 1991.
• [34] Parikh, R., Moss, L. S., Steinsvold, C: Topology and Epistemic Logic, in: Handbook of Spatial Logics (M. Aiello, I. E. Pratt-Hartman, J. van Benthem, Eds.), Springer, 2007.
• [35] Plaza, J. A.: Logic of Public Communication, 4th International Symposium on Methodologies for Intelligent Systems (M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, Z. W. Ras, Eds.), 1989.
• [36] Schwalbe, U., Walker, P.: Zermelo and the Early History of Game Theory, Games and Economic Behavior, 34(1), January 2001, 123-137.
• [37] Stalnaker, R.: On the Evaluation of Solution Concepts, Theory and Decision, 37(1), July 1994,49-73.
• [38] Stalnaker, R.: Knowledge, Belief and Counterfactual Reasoning in Games, Economics and Philosophy, 12(2), 1996, 133-163.
• [391 Stalnaker, R.: Belief Revision in Games: Forward and Backward Induction, Mathematical Social Sciences, 36(1), 1998,31-56.