Global and Iterated Contraction and Revision: An Exploration of Uniform and Semi-Uniform Approaches Authors
First Online: 11 June 2011 Received: 07 November 2009 Accepted: 06 March 2011 DOI:
Cite this article as: Hansson, S.O. J Philos Logic (2012) 41: 143. doi:10.1007/s10992-011-9205-3 Abstract
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.
Keywords Iterated contraction Iterated revision Specified meet contraction Belief revision Global belief change Global operator References
Alchourrón, C. E., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions.
Journal of Symbolic Logic, 50
Alchourrón, C. E., & Makinson, D. (1981). Hierarchies of regulation and their logic. In R. Hilpinen (Ed.),
New studies in deontic logic
(pp. 125–148). Dordrecht: Reidel.
Alchourrón, C. E., & Makinson, D. (1982). On the logic of theory change: Contraction functions and their associated revision functions.
Chopra, S., Ghose, A., Meyer, T., & Wong, K. S. (2008). Iterated belief change and the recovery axiom.
Journal of Philosophical Logic, 37
Darwiche, A., & Pearl, J. (1997). On the logic of iterated belief revision.
Artificial Intelligence, 89
Gärdenfors, P. (1988).
Knowledge in flux. Modeling the dynamics of epistemic states. Cambridge: MIT Press.
Hansson, S. O. (1992). In defense of base contraction.
Hansson, S. O. (1993). Theory contraction and base contraction unified.
Journal of Symbolic Logic, 58
Hansson, S. O. (1993). Reversing the Levi identity.
Journal of Philosophical Logic, 22
Hansson, S. O. (1994). Kernel contraction.
Journal of Symbolic Logic, 59
Hansson, S. O. (1999).
A textbook of belief dynamics. Theory change and database updating. Norwell: Kluwer.
Hansson, S. O. (2007). Contraction based on sentential selection.
Journal of Logic and Computation, 17
Hansson, S. O. (2008). Specified meet contraction.
Hild, M., & Spohn, W. (2008). The measurement of ranks and the laws of iterated contraction.
Artificial Intelligence, 172
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.
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).
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.
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.
Peppas, P., Fotinopoulos, A. M., & Seremetaki, S. (2008). Conflicts between relevance-sensitive and iterated belief revision. In
Proceedings of ECAI 2008. Amsterdam: IOS Press.
Rott, H. (2001).
Change, choice and inference: A study of belief revision and nonmonotonic reasoning. Oxford: Oxford University Press.
Tamminga, A. (2004). Expansion and contraction of finite states.
Studia Logica, 76
CrossRef Copyright information
© Springer Science+Business Media B.V. 2011