Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T19:34:55.299Z Has data issue: false hasContentIssue false
  • English
  • Français

SOME COMPLETENESS THEOREMS IN THE DYNAMIC DOXASTIC LOGIC OF ITERATED BELIEF REVISION

Published online by Cambridge University Press:  19 March 2010

KRISTER SEGERBERG
KRISTER SEGERBERG*
Affiliation:
Philosophy Department, Uppsala University
*
†PHILOSOPHY DEPARTMENT, BOX 627, S-751 26 UPPSALA, SWEDEN E-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The success of the AGM paradigm—the theory of belief change initiated by Alchourrón, Gärdenfors, and Makinson—is remarkable, as even a quick look at the literature it has generated will testify. But it is also remarkable, at least in hindsight, how limited was the original effort. For example, the theory concerns the beliefs of just one agent; all incoming information is accepted; belief change is uniquely determined by the new information; there is no provision for nested beliefs. And perhaps most surprising: there is no analysis of iterated change.

In this paper it is that last restriction that is at issue. Our medium of study is dynamic doxastic logic (DDL). The success of the AGM paradigm The particular contribution of the paper is detailed completeness proofs for three dynamic doxastic logics of iterated belief revision.

The problem of extending the AGM paradigm to include iterated change has been discussed for years, but systematic discussions have appeared only recently (see Segerberg, 2007 and forthcoming, but also van Benthem, 2007; Rott, 2006; Zvesper, 2007).

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 2 , June 2010 , pp. 228 - 246
Copyright
Copyright © Association for Symbolic Logic 2010

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

Alchourrón, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change. The Journal of Symbolic Logic, 50, 510–530.CrossRefGoogle Scholar
van Benthem, J. (2007). Dynamic logic of belief revision. Journal of Applied Non-Classical Logics, 17, 129–155.CrossRefGoogle Scholar
Lewis, D. K. (1973). Counterfactuals. Cambridge, MA: Harvard University Press.Google Scholar
Rott, H. (2006). Shifting priorities: Simple representation for twenty-seven iterated theory change operators. In Lagerlund, H., Lindström, S., and Sliwinski, R., editors. Modality Matters, Vol. 53. Uppsala, Sweden: Uppsala Philosophical Studies, pp. 359–383.Google Scholar
Segerberg, K. (2001). The basic dynamic doxastic logic of AGM. In Williams, M.-A., and Rott, H., editors. Frontiers in Belief Revision, Vol. 22. Applied Logic Series, Dordrecht, The Netherlands: Kluwer, pp. 57–84.CrossRefGoogle Scholar
Segerberg, K. (2007). Iterated belief revision in dynamic doxastic logic. In Gupta, A., Parikh, R., and van Benthem, J., editors. Logic at the Crossroads: An Interdisciplinary View. New Delhi, India: Allied Publishers Pvt. Ltd, pp. 331–343.Google Scholar
Segerberg, K. (Forthcoming). Strategies for belief revision. In van Eijck, J., and Verbrugge, R., editors.Google Scholar
Zvesper, J. (2007). Belief revision and epistemic acts. MSc Thesis, I.L.L.C., University of Amsterdam.Google Scholar