Abstract
Most work on iterated belief change has focused on iterated belief revision, namely how to compute (K \(^{\rm *}_{x}\))\(^{\rm *}_{y}\). Historically however, belief revision can be defined in terms of belief expansion and belief contraction, where expansion and contraction are viewed as primary operators. Accordingly, our attention to iterated belief change should be focused on constructions like (K \(^{\rm +}_{x}\))\(^{\rm +}_{y}\), (K \(^{\rm --}_{x}\))\(^{\rm +}_{y}\), (K \(^{\rm +}_{x}\))\(^{\rm --}_{y}\) and (K \(^{\rm --}_{x}\))\(^{\rm --}_{y}\). The first two of these are relatively straightforward, but the last two are more problematic. Here we consider these latter, and formulate iterated belief change by employing the Levi identity and the Harper Identity as the guiding principles.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change. Journal of Symbolic Logic 50, 510–530 (1985)
Benferhat, S., Konieczny, S., Papini, O., Pino Pèrez, R.: Iterated Revision by epistemic states: axioms, semantics and syntax. In: Horn, W. (ed.) Proceedings of ECAI 2000: 14th European Conference on Artificial Intelligence, pp. 13–17. IOS Press, Amsterdam (2000)
Bochman, A.: Contraction of epistemic states: A general theory. In: Williams, M.-A., Rott, H. (eds.) Frontiers in Belief Revision, pp. 195–220. Kluwer Academic Publishers, Dordrecht (2001)
Booth, R., Chopra, S., Ghose, A., Meyer, T.: A unifying semantics for belief change. In: Lopez De Mantaras, R., Saitta, L. (eds.) Proceedings of ECAI 2004: Sixteenth European Conference on Artificial Intelligence, pp. 793–797. IOS Press, Amsterdam (2004)
Boutilier, C.: Iterated revision and Minimal Revision of Conditional Beliefs. Journal of Philosophical Logic 25, 262–304 (1996)
Darwiche, A., Pearl, J.: On the Logic of Iterated Belief Revision. Artifical Intelligence 89, 1–29 (1997)
Gärdenfors, P.: Knowledge in Flux: Modeling the Dynamics of Epistemic States. MIT Press, Cambridge Massachusetts (1988)
Grove, A.: Two modellings for theory change. Journal of Philosophical Logic 17, 157–170 (1988)
Nayak, A.C.: Iterated Belief Change Based on Epistemic Entrenchment. Erkenntnis 41, 353–390 (1994)
Nayak, A.C., Pagnucco, M., Peppas, P.: Dynamic belief revision operators. Artifical Intelligence, 193–228 (2003)
Rott, H.: Change, Choice and Inference: A study of belief revision and nonmonotonic reasoning. Oxford Science Publications, Clarendon Press (2001)
Rott, H.: Adjusting Priorities: Simple Representations for 27 Iterated Theory Change Operators (manuscrript) (October 2004)
Williams, M.-A.: Transmutations of Knowledge Systems. In: Doyle, J., Sandewall, E. (eds.) Proceedings of the Fourth International Conference on Principles of Knowledge Representation and Reasoning, pp. 619–629 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nayak, A., Goebel, R., Orgun, M., Pham, T. (2006). Taking Levi Identity Seriously: A Plea for Iterated Belief Contraction. In: Lang, J., Lin, F., Wang, J. (eds) Knowledge Science, Engineering and Management. KSEM 2006. Lecture Notes in Computer Science(), vol 4092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11811220_26
Download citation
DOI: https://doi.org/10.1007/11811220_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37033-8
Online ISBN: 978-3-540-37035-2
eBook Packages: Computer ScienceComputer Science (R0)