Abstract
Although AGM theory contraction (Alchourrón et al., 1985; Alchourrón and Makinson, 1985) occupies a central position in the literature on belief change, there is one aspect about it that has created a fair amount of controversy. It involves the inclusion of the postulate known as Recovery. As a result, a number of alternatives to AGM theory contraction have been proposed that do not always satisfy the Recovery postulate (Levi, 1991, 1998; Hansson and Olsson, 1995; Fermé, 1998; Fermé and Rodriguez, 1998; Rott and Pagnucco, 1999). In this paper we present a new addition, systematic withdrawal, to the family of withdrawal operations, as they have become known. We define systematic withdrawal semantically, in terms of a set of preorders, and show that it can be characterised by a set of postulates. In a comparison of withdrawal operations we show that AGM contraction, systematic withdrawal and the severe withdrawal of Rott and Pagnucco (1999) are intimately connected by virtue of their definition in terms of sets of preorders. In a future paper it will be shown that this connection can be extended to include the epistemic entrenchment orderings of Gärdenfors (1988) and Gärdenfors and Makinson (1988) and the refined entrenchment orderings of Meyer et al. (2000).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Alchourrón, C. E. and Makinson, D.: 1982, On the logic of theory change: Contraction functions and their associated revision functions, Theoria 48, 14-37. bl
Alchourrón, C. E. and Makinson, D.: 1985, On the logic of theory change: Safe contraction, Studia Logica 44, 405-422.
Alchourrón, C. E., Gärdenfors, P. and Makinson, D.: 1985, On the logic of theory change: Partial meet functions for contraction and revision, J. Symbolic Logic 50, 510-530.
Boutilier, C.: 1994, Unifying default reasoning and belief revision in a modal framework, Artificial Intelligence 68, 33-85.
Cantwell, J.: 1999, Some logics of iterated belief change, Studia Logica 63(1), 49-84.
Fermé, E.: 1998, On the logic of theory change: Contraction without recovery, J. Logic, Language and Inform. 7(2), 122-137.
Fermé, E. and Rodriguez, R.: 1998, Semi-contraction: Axioms and construction, Unpublished manuscript, Universidad de Buenos Aires.
Fuhrmann, A.: 1991, Theory contraction through base contraction, J. Philos. Logic 20, 175-203.
Gärdenfors, P.: 1988, Knowledge in Flux: Modeling the Dynamics of Epistemic States, The MIT Press, Cambridge, MA.
Gärdenfors, P. and Makinson, D.: 1988, Revisions of knowledge systems using epistemic entrenchment, in M. Vardi (ed.), Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge, Morgan Kaufmann, Los Altos, California, pp. 83-95.
Ginsberg, M. L.: 1986, Counterfactuals, Artificial Intelligence 30, 35-79.
Grove, A.: 1988, Two modellings for theory change, J. Philos. Logic 17, 157-170.
Hansson, S. O.: 1991, Belief contraction without recovery, Studia Logica 50, 251-260.
Hansson, S. O.: 1992, A dyadic representation of belief, in P. Gärdenfors (ed.), Belief Revision, Cambridge University Press, Cambridge, pp. 89-121.
Hansson, S. O.: 1993, Theory contraction and base contraction unified, J. Symbolic Logic 58(2), 602-625.
Hansson, S. O.: 1996, Knowledge-level analysis of belief base operations, Artificial Intelligence 82, 215-235.
Hansson, S. O.: 1999, A Textbook of Belief Dynamics, Theory Change and Database Updating, Kluwer Academic Publishers, Dordrecht.
Hansson, S. O. and Olsson, E. J.: 1995, Levi contractions and AGM contractions: A comparison, Notre Dame J. Formal Logic 36(1), 103-119.
Katsuno, H. and Mendelzon, A.: 1991, Propositional knowledge base revision and minimal change, Artificial Intelligence 52, 263-294.
Lehmann, D. and Magidor, M.: 1992, What does a conditional knowledge base entail?, Artificial Intelligence 55, 1-60.
Levi, I.: 1991, The Fixation of Belief and Its Undoing, Cambridge University Press, Cambridge.
Levi, I.: 1998, Contraction and informational value, Unpublished manuscript, Columbia University.
Lindström, S. and Rabinowicz, W.: 1991, Epistemic entrenchment with incomparabilities and relational belief revision, in A. Fuhrmann and M. Morreau (eds.), The Logic of Theory Change: Workshop, Konstanz, FRG, October 1989, Proceedings, Lecture Notes in Artificial Intelligence 465, Springer-Verlag, Berlin, pp. 93-126.
Makinson, D.: 1987, On the status of the postulate of Recovery in the logic of theory change, J. Philos. Logic 16, 383-394.
Makinson, D.: 1997, On the force of some apparent counterexamples to Recovery, in E. G. Valdés, W. Krawietz, G. H. von Wright, and R. Zimmerling (eds.), Normative Systems in Legal and Moral Theory, Dunker and Humboldt, Berlin.
Meyer, T. A.: 1999, Semantic belief change, Ph.D. Thesis, Department of Computer Science and Information Systems, University of South Africa, Pretoria, South Africa.
Meyer, T. A., Labuschagne, W. A. and Heidema, J.: 2000, Refined epistemic entrenchment, J. Logic, Language and Inform. 9(2), 237-259.
Nayak, A. C.: 1994, Foundational belief change, J. Philos. Logic 23, 495-533.
Niederee, R.: 1991, Multiple contraction. A further case against Gärdenfors's principle of recovery, in A. Fuhrmann and M. Morreau (eds.), The Logic of Theory Change: Workshop, Konstanz, FRG, October 1989, Proceedings, Lecture Notes in Artificial Intelligence 465, Springer-Verlag, Berlin, pp. 322-334.
Pagnucco, M.: 1996, The role of abductive reasoning within the process of belief revision, Ph.D. Thesis, Basser Department of Computer Science, University of Sydney, Australia.
Rott, H.: 1992, Modellings for belief change: Prioritization and entrenchment, Theoria 58(1), 21-57.
Rott, H.: 1995, Just because. Taking belief bases very seriously, in S. O. Hansson and W. Rabinowicz (eds.), Logic for a Change, Vol. 9, Uppsala Prints and Preprints in Philosophy, pp. 106-124.
Rott, H. and Pagnucco, M.: 1999, Severe withdrawal (and Recovery), J. Philos. Logic 25(5), 501-547.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Meyer, T., Heidema, J., Labuschagne, W. et al. Systematic Withdrawal. Journal of Philosophical Logic 31, 415–443 (2002). https://doi.org/10.1023/A:1020199115746
Issue Date:
DOI: https://doi.org/10.1023/A:1020199115746