Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-18T06:15:42.735Z Has data issue: false hasContentIssue false
  • English
  • Français

THE EXPRESSIVITY OF FACTUAL CHANGE IN DYNAMIC EPISTEMIC LOGIC

Published online by Cambridge University Press:  28 November 2013

LOUWE B. KUIJER
LOUWE B. KUIJER*
Affiliation:
University of Groningen
*
*FACULTY OF PHILOSOPHY, UNIVERSITY OF GRONINGEN OUDE BOTERINGESTRAAT 52 9712 GL GRONINGEN THE NETHERLANDS E-mail: l.b.kruijer@rug.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

A commonly used dynamic epistemic logic is one obtained by adding commonknowledge and public announcements to a basic epistemic logic. It is known from Kooi (2007) that adding public substitutions to such a logic adds expressivity over the class K of models. Here I show that substitutions also add expressivity over the classes KD45, S4 and S5 of models. Since the combination of common knowledge, public announcements and substitutions, was shown in Kooi (2007) to be equally expressive to relativized common knowledge these results also show that relativized common knowledge is more expressive than common knowledge and public announcements over KD45, S4 and S5. These results therefore extend the result from van Benthem et al. (2006) that shows that relativized common knowledge is more expressive than common knowledge and public announcements over K.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 7 , Issue 2 , June 2014 , pp. 208 - 221
Copyright
Copyright © Association for Symbolic Logic 2013 

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

Baltag, A., Moss, L., & Solecki, S. (1998). The logic of public announcements, common knowledge, and private suspicions. In Gilboa, I., editor. Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge, Evanston, IL, July 22–24, 1998. Burlington, MA: Morgan Kaufmann Publishers Inc., pp. 43–56.Google Scholar
van Benthem, J. (2007). Dynamic logic for belief revision. Journal of AppliedNon-Classical Logics, 17, 129–155.CrossRefGoogle Scholar
van Benthem, J., van Eijck, J., & Kooi, B. (2006) Logics of communication and change. Information and Computation, 204, 1620–1662.CrossRefGoogle Scholar
van Ditmarsch et al., 25–29 2005van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2005). Dynamic epistemic logic with assignment. Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multiagent Systems, Utrecht, The Netherlands, July 25–29 2005. New York, NY: ACM, pp. 141–148.Google Scholar
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic Epistemic Logic. Dordrecht, The Netherlands: Springer.Google Scholar
van Eijck, J. (2004). Guarded Actions. CWI Technical Report SEN-E 0425, Amsterdam, The Netherlands: CWI.Google Scholar
Gerbrandy, J. (1999). Bisimulations on planet kripke. PhD Thesis, University of Amsterdam.Google Scholar
Kooi, B. (2007). Expressivity and completeness for public update logics via reduction axioms. Journal of Applied Non-Classical Logics, 17, 231–253.CrossRefGoogle Scholar
Lutz, C. (2006). Complexity and succinctness of public announcement logic. In Stone, P., and Weiss, G., editors. Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems, Hakodate, Japan, May 08–12, 2006. New York, NY: ACM, pp. 137–143.Google Scholar
Plaza, J. (1989). Logics of public communication. In Emrich, M.L., Phifer, M.S., Hadzikadic, M., and Ras, Z.W., editors. Proceedings of the Fourth International Symposium on Methodologies for Intelligent Systems, Poster Session Program. Oak Ridge National Laboratory, ORNL/DSRD-24. Reprinted as Plaza (2007), pp. 201–216.Google Scholar
Plaza, J. (2007). Logics of public communication. Synthese, 158, 165–179.Google Scholar