Global and Iterated Contraction and Revision: An Exploration of Uniform and Semi-Uniform Approaches
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In order to clarify the problems of iterated (global) belief change it is useful to study simple cases, in particular consecutive contractions by sentences that are both logically and epistemically independent. Models in which the selection mechanism is kept constant are much more plausible in this case than what they are in general. One such model, namely uniform specified meet contraction, has the advantage of being closely connected with the AGM model. Its properties seem fairly adequate for the intended type of contraction. However, the revision operator based on it via the Levi identity collapses into an implausible operation that loses all old information when revising by new information. A weaker version, semi-uniform specified meet contraction, avoids the collapse but has the disadvantage of a remarkably weak logic. It is left as an open issue whether there is an intermediate class of contraction operators that yields a more satisfactory logic.
KeywordsIterated contraction Iterated revision Specified meet contraction Belief revision Global belief change Global operator
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- 6.Gärdenfors, P. (1988). Knowledge in flux. Modeling the dynamics of epistemic states. Cambridge: MIT Press.Google Scholar
- 11.Hansson, S. O. (1999). A textbook of belief dynamics. Theory change and database updating. Norwell: Kluwer.Google Scholar
- 15.Nayak, A., Goebel, R., Orgun, M., & Pham, T. (2006). Taking Levi identity seriously: A plea for iterated belief contraction. In Proceedings of the first international conference on knowledge science, engineering and management (KSEM’06), LNAI 4092 (pp. 305–317). Berlin: Springer.Google Scholar
- 16.Nayak, A. C., Goebel, R., & Orgun, M. A. (2007). Iterated belief contraction from first principles. In Proceedings of the twentieth international joint conference of artificial intelligence (IJCAI-07) (pp. 2568–2573).Google Scholar
- 17.Parikh, R. (1999). Beliefs, belief revision, and splitting languages. In J. Ginzburg, L. Moss, & M. de Rijke (Eds.), Logic, language and computation (pp. 266–278). Stanford: CSLI.Google Scholar
- 18.Peppas, P., Chopra, S., & Foo, N. (2004). Distance semantics for relevance-sensitive belief revision. In D. Dubois, C. Welty, & M.-A. Williams (Eds.), Principles of knowledge representation and reasoning: Proceedings of the ninth international conference (KR2004) (pp. 319–328). Menlo Park: AAAI Press.Google Scholar
- 19.Peppas, P., Fotinopoulos, A. M., & Seremetaki, S. (2008). Conflicts between relevance-sensitive and iterated belief revision. In Proceedings of ECAI 2008. Amsterdam: IOS Press.Google Scholar
- 20.Rott, H. (2001). Change, choice and inference: A study of belief revision and nonmonotonic reasoning. Oxford: Oxford University Press.Google Scholar