Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T23:23:15.602Z Has data issue: false hasContentIssue false
  • English
  • Français

DYNAMIC GRADED EPISTEMIC LOGIC

Published online by Cambridge University Press:  12 July 2019

MINGHUI MA  and
HANS VAN DITMARSCH
MINGHUI MA*
Affiliation:
Institute of Logic and Cognition, Department of Philosophy, Sun Yat-Sen University
HANS VAN DITMARSCH*
Affiliation:
LORIA, CNRS, University of Lorraine
*
*INSTITUTE OF LOGIC AND COGNITION DEPARTMENT OF PHILOSOPHY, SUN YAT-SEN UNIVERSITY XINGANGXI ROAD 135, GUANGZHOU 510275, P. R. CHINA E-mail: mamh6@mail.sysu.edu.cn
†LORIA – CNRS/UNIVERSITY OF LORRAINE BP 239, 54506 VANDOEUVRE LES NANCY, FRANCE E-mail: hans.van-ditmarsch@loria.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Graded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics.

Keywords

03B4203B45graded epistemic logicgraded modelsdynamics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 4 , December 2019 , pp. 663 - 684
Copyright
Copyright © Association for Symbolic Logic 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Aceto, L., Ingólfsdóttir, A., & Sack, J. (2010). Resource bisimilarity and graded bisimilarity coincide. Information Processing Letters, 111(2), 68–76.CrossRefGoogle Scholar
Andersen, M., Bolander, T., van Ditmarsch, H., & Jensen, M. (2017). Bisimulation and expressivity for conditional belief, degrees of belief, and safe belief. Synthese, 194(7), 2447–2487.CrossRefGoogle Scholar
Aucher, G. (2003). A Combined System for Update Logic and Belief Revision. Master’s Thesis, ILLC, Amsterdam, the Netherlands: University of Amsterdam. ILLC report MoL-2003-03.Google Scholar
Balbiani, P., van Ditmarsch, H., Herzig, A., & de Lima, T. (2012). Some truths are best left unsaid. In Bolander, T., Braüner, T., Ghilardi, S., and Moss, L. S., editors. Proceedings of 9th Advances in Modal Logic. London: College Publications, pp. 36–54.Google Scholar
Baltag, A., Moss, L., & Solecki, S. (1998). The logic of public announcements, common knowledge, and private suspicions. In Gilboa, I., editor. Proceedings of 7th TARK. Burlington, MA: Morgan Kaufmann, pp. 43–56.Google Scholar
Corradini, F., De Nicola, R., & Labella, A. (1999). Graded modalities and resource bisimulation. In Pandu Rangan, C., Raman, V., and Ramanujam, R., editors. Proceedings of 19th FSTTCS. Lecture Notes in Computer Science, Vol. 1738. Berlin: Springer, pp. 381–393.Google Scholar
de Caro, F. (1988). Graded modalities II (canonical models). Studia Logica, 47, 1–10.CrossRefGoogle Scholar
de Rijke, M. (2000). A note on graded modal logic. Studia Logica, 64, 271–283.CrossRefGoogle Scholar
Fattorosi-Barnaba, M. & de Caro, F. (1985). Graded modalities I. Studia Logica, 44, 197–221.CrossRefGoogle Scholar
Fine, K. (1972). In so many possible worlds. Notre Dame Journal of Formal Logic, 13(4), 516–520.CrossRefGoogle Scholar
Ghosh, S. & de Jongh, D. (2013). Comparing strengths of beliefs explicitly. Logic Journal of the IGPL, 21(3), 288–514.CrossRefGoogle Scholar
Goble, L. (1970). Grades of modality. Logique et Analyse, 13(51), 323–334.Google Scholar
Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17, 157–170.CrossRefGoogle Scholar
Laverny, N. (2006). Révision, mises à jour et planification en logique doxastique graduelle. Ph.D. Thesis, Toulouse, France: Institut de Recherche en Informatique de Toulouse (IRIT).Google Scholar
Lenzen, W. (1978). Recent work in epistemic logic. Acta Philosophica Fennica, 30, 1–219.Google Scholar
Lenzen, W. (2003). Knowledge, belief, and subjective probability: Outlines of a unified system of epistemic/doxastic logic. In Hendricks, V., Jorgensen, K., and Pedersen, S., editors. Knowledge Contributors. Synthese Library, Vol. 322. Dordrecht: Kluwer Academic Publishers, pp. 17–31.CrossRefGoogle Scholar
Pacuit, E. & Salame, S. (2004). Majority logic. In Dubois, D., Welty, C. A., and Williams, M.-A., editors. Proceedings of 9th KR. Menlo Park, CA: AAAI Press, pp. 598–605.Google Scholar
Plaza, J. (1989). Logics of public communications. Proceedings of the 4th ISMIS. Oak Ridge National Laboratory, pp. 201–216.Google Scholar
Segerberg, K. (1971). Qualitative probability in a modal setting. In Fenstad, J., editor. Proceedings of the Second Scandinavian Logic Symposium. Studies in Logic and the Foundations of Mathematics, Vol. 63. Amsterdam: Elsevier, pp. 341–352.CrossRefGoogle Scholar
Segerberg, K. (1998). Irrevocable belief revision in dynamic doxastic logic. Notre Dame Journal of Formal Logic, 39(3), 287–306.CrossRefGoogle Scholar
Spohn, W. (1988). Ordinal conditional functions: A dynamic theory of epistemic states. In Harper, W. and Skyrms, B., editors. Causation in Decision, Belief Change, and Statistics, Vol. II. Dordrecht: Springer, pp. 105–134.CrossRefGoogle Scholar
van Benthem, J. (2011). Logical Dynamics of Information and Interaction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
van der Hoek, W. (1992). Modalities for Reasoning about Knowledge and Quantities. Ph.D. Thesis, Free University of Amsterdam.Google Scholar
van der Hoek, W. (1993). Systems for knowledge and beliefs. Journal of Logic and Computation, 3(2), 173–195.CrossRefGoogle Scholar
van der Hoek, W. & de Rijke, M. (1995). Counting objects. Journal of Logic and Computation, 5(3), 325–345.CrossRefGoogle Scholar
van der Hoek, W. & Meyer, J.-J. (1992). Graded modalities in epistemic logic. In Nerode, A. and Taitslin, M., editors. Logical Foundations of Computer Science—Tver’92. Lecture Notes in Computer Science, Vol. 620. Berlin: Springer, pp. 503–514.CrossRefGoogle Scholar
van Ditmarsch, H. (2005). Prolegomena to dynamic logic for belief revision. Synthese, 147, 229–275.CrossRefGoogle Scholar
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic Epistemic Logic. Synthese Library, Vol. 337. Berlin: Springer.Google Scholar
van Ditmarsch, H., Halpern, J., van der Hoek, W., & Kooi, B. (editors) (2015). Handbook of Epistemic Logic. London: College Publications.Google Scholar
van Eijck, J., Ruan, J., & Sadzik, T. (2012). Action emulation. Synthese, 185(1), 131–151.CrossRefGoogle Scholar
Wang, Y. & Cao, Q. (2013). On axiomatizations of public announcement logic. Synthese, 190(Supp. 1), 103–134.CrossRefGoogle Scholar