Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-20T16:51:00.040Z Has data issue: false hasContentIssue false
  • English
  • Français

ARROW UPDATE LOGIC

Published online by Cambridge University Press:  13 October 2011

BARTELD KOOI  and
BRYAN RENNE
BARTELD KOOI*
Affiliation:
Faculty of Philosophy, University of Groningen
BRYAN RENNE*
Affiliation:
Faculty of Philosophy, University of Groningen
*
*FACULTY OF PHILOSOPHY, UNIVERSITY OF GRONINGEN, OUDE BOTERINGESTRAAT 52, 9712 GL GRONINGEN, THE NETHERLANDS. E-mail: b.p.Kooi@rug.nl
†FACULTY OF PHILOSOPHY, UNIVERSITY OF GRONINGEN, OUDE BOTERINGESTRAAT 52, 9712 GL GRONINGEN, THE NETHERLANDS. E-mail: bryan@renne.org
Get access Rights & Permissions [Opens in a new window]

Abstract

We present Arrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing “arrow updates” of Arrow Update Logic can be transformed into equivalent belief-changing “action models” from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logic’s perspective of eliminating access to epistemic possibilities, Arrow Update Logic is a valuable addition to the repertoire of logics of information change. In addition to proving basic results about Arrow Update Logic, we introduce a new notion of common knowledge that generalizes both ordinary common knowledge and the “relativized” common knowledge familiar from the Dynamic Epistemic Logic literature.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 4 , December 2011 , pp. 536 - 559
Copyright
Copyright © Association for Symbolic Logic 2011

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

Aucher, G., Balbiani, P., Fariñas del Cerro, L., & Herzig, A. (2009). Global and local graph modifiers. Electronic Notes in Theoretical Computer Science, 231, 293–307.CrossRefGoogle Scholar
Baltag, A., & Moss, L. S. (2004). Logics for epistemic programs. Synthese, 139(2), 165–224.CrossRefGoogle Scholar
Baltag, A., Moss, L. S., & 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 (TARK VII). Evanston, IL, pp. 43–56.Google Scholar
Baltag, A., Moss, L. S., & Solecki, S. (2005). Logics for epistemic actions: Completeness, decidability, expressivity. Manuscript.Google Scholar
Baltag, A., & Smets, S. (2007). A qualitative theory of dynamic interactive belief revision. In Bonanno, G., van der Hoek, W., and Wooldridge, M., editors. Selected Papers from LOFT’06, Texts in Logic and Games. Amsterdam: Amsterdam University Press.Google Scholar
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge University Press.CrossRefGoogle Scholar
Clark, M. (2007). Paradoxes from A to Z (second edition). London: Routledge.CrossRefGoogle Scholar
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about Knowledge. Cambridge: The MIT Press.Google Scholar
Gerbrandy, J. (1999). Bisimulations on planet Kripke. PhD Thesis, University of Amsterdam. ILLC Dissertation Series DS-1999-01.Google Scholar
Gerbrandy, J. (2007). The surprise examination in dynamic epistemic logic. Synthese, 155(1), 21–33.Google Scholar
Gerbrandy, J., & Groeneveld, W. (1997). Reasoning about information change. Journal of Logic, Language and Information, 6(2), 147–169.CrossRefGoogle Scholar
Kooi, B., & Renne, B. (2011). Generalized arrow update logic. In Apt, K. R., editor. Proceedings of the 13th Conference of Theoretical Aspects of Rationality and Knowledge (TARK XIII). Groningen, The Netherlands: ACM, pp. 205–211.CrossRefGoogle Scholar
Kooi, B., & van Benthem, J. (2004). Reduction axioms for epistemic actions. In Schmidt, R., Pratt-Hartmann, I., Reynolds, M., and Wansing, H., editors. AiML-2004: Advances in Modal Logic (Preliminary Proceedings). Manchester, UK, pp. 197–211.Google Scholar
Lutz, C. (2006). Complexity and succinctness of public announcement logic. In Proceedings of the 5th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS-06). Hakodate, Japan: Association for Computing Machinery (ACM), pp. 137–144.CrossRefGoogle Scholar
Plaza, J. (1989). Logics of public communications. In Emrich, M. L., Pfeifer, M. S., Hadzikadic, M., and Ras, Z. W., editors, Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems (ISMIS 1989): Poster Session Program. Charlotte, NC: Oak Ridge National Laboratory ORNL/DSRD-24, pp. 201–216.Google Scholar
Plaza, J. (2007). Logics of public communications. Synthese, 158(2), 165–179.CrossRefGoogle Scholar
Renardel de Lavalette, G. R. (2004). Changing modalities. Journal of Logic and Computation, 14(2), 215–249.CrossRefGoogle Scholar
Renne, B. (2008). Public and private communication are different: Results on relative expressivity. Synthese, 165(2), 225–245.CrossRefGoogle Scholar
Renne, B., Sack, J., & Yap, A. (2009). Dynamic epistemic temporal logic. In He, X., Horty, J., & Pacuit, E., editors. Logic, Rationality, and Interaction, Second International Workshop, LORI 2009, Chongqing, China, October 8–11, 2009, Proceedings, Volume 5834/2009 of Lecture Notes in Computer Science. Berlin/Heidelberg, Germany: Springer, pp. 263–277.Google Scholar
Renne, B., Sack, J., & Yap, A. (2010). Dynamic epistemic temporal logic. Extended Manuscript.Google Scholar
Steiner, D. (2006). A system for consistency preserving belief change. In Artemov, S., and Parikh, R., editors. Proceedings of the Workshop on Rationality and Knowledge, 18th European Summer School in Logic, Language, and Information (ESSLLI). Málaga, Spain, pp. 133–144.Google Scholar
van Benthem, J. (2004). Dynamic logic for belief revision. Journal of Applied Non-Classical Logics, 14(2), 129–155.Google Scholar
van Benthem, J. (2005). An essay on sabotage and obstruction. In Hutter, D., editor. Mechanizing Mathematical Reasoning, Essays in Honor of Jörg Siekmann on the Occasion of his 69th Birthday. Cambridge, Massachusetts: Springer. pp. 268–276.Google Scholar
van Benthem, J., van Eijck, J., & Kooi, B. (2006). Logics of communication and change. Information and Computation, 204(11), 1620–1662.CrossRefGoogle Scholar
van Ditmarsch, H. (2000). Knowledge games. PhD Thesis, University of Groningen. ILLC Dissertation Series DS-2000-06.Google Scholar
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic Epistemic Logic, Vol. 337 of Synthese Library. Dordrecht, The Netherlands: Springer.Google Scholar
van Ditmarsch, H., van Eijck, J., Sietsma, F., & Wang, Y. (2010). On the logic of lying. Manuscript.Google Scholar
van Eijck, J., Ruan, J., & Sadzik, T. (2008). Action emulation. Manuscript.Google Scholar