Abstract
Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in [5]. However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of [5] to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alchourrón, C., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50(2), 510–530 (1985)
Benferhat, S., Lagrue, S., Papini, O.: Revision of partially ordered information: Axiomatization, semantics and iteration. In: Pack Kaelbling, L., Saffiotti, A. (eds.) IJCAI, pp. 376–381. Professional Book Center (2005)
Bochman, A.: A Logical Theory of Nonmonotonic Inference and Belief Change. Springer, Heidelberg (2001)
Booth, R., Chopra, S., Ghose, A., Meyer, T.: Belief liberation (and retraction). Studia Logica 79(1), 47–72 (2005)
Booth, R., Chopra, S., Meyer, T., Ghose, A.: A unifying semantics for belief change. In: Proceedings of ECAI 2004, pp. 793–797 (2004)
Booth, R., Meyer, T.: Equilibria in social belief removal. In: KR, pp. 145–155 (2008)
Cantwell, J.: Relevant contraction. In: Proceedings of the Dutch-German Workshop on Non-Monotonic Reasoning, DGNMR 1999 (1999)
Cantwell, J.: Eligible contraction. Studia Logica 73, 167–182 (2003)
Arló Costa, H.: Rationality and value: The epistemological role of indeterminate and agent-dependent values. Philosophical Studies 128(1), 7–48 (2006)
Hansson, S.O.: Belief contraction without recovery. Studia Logica 50(2), 251–260 (1991)
Hansson, S.O.: Changes on disjunctively closed bases. Journal of Logic, Language and Information 2, 255–284 (1993)
Katsuno, H., Mendelzon, A.O.: Propositional knowledge base revision and minimal change. Artif. Intell. 52(3), 263–294 (1992)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 167–207 (1991)
Levi, I.: The Fixation of Belief and Its Undoing. Cambridge University Press, Cambridge (1991)
Maynard-Zhang, P., Lehmann, D.: Representing and aggregating conflicting beliefs. Journal of Artificial Intelligence Research 19, 155–203 (2003)
Meyer, T., Heidema, J., Labuschagne, W., Leenen, L.: Systematic withdrawal. Journal of Philosophical Logic 31(5), 415–443 (2002)
Rott, H.: Preferential belief change using generalized epistemic entrenchment. Journal of Logic, Language and Information 1, 45–78 (1992)
Rott, H.: Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning. Oxford University Press, Oxford (2001)
Rott, H., Pagnucco, M.: Severe withdrawal (and recovery). Journal of Philosophical Logic 28, 501–547 (1999)
Shoham, Y.: A semantical approach to nonmonotic logics. In: LICS, pp. 275–279 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Booth, R., Meyer, T., Sombattheera, C. (2009). A General Family of Preferential Belief Removal Operators. In: He, X., Horty, J., Pacuit, E. (eds) Logic, Rationality, and Interaction. LORI 2009. Lecture Notes in Computer Science(), vol 5834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04893-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-04893-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04892-0
Online ISBN: 978-3-642-04893-7
eBook Packages: Computer ScienceComputer Science (R0)