Abstract
The problem of how to remove information from an agent's stock of beliefs is of paramount concern in the belief change literature. An inquiring agent may remove beliefs for a variety of reasons: a belief may be called into doubt or the agent may simply wish to entertain other possibilities. In the prominent AGM framework for belief change, upon which the work here is based, one of the three central operations, contraction, addresses this concern (the other two deal with the incorporation of new information). Makinson has generalised this work by introducing the notion of a withdrawal operation. Underlying the account proffered by AGM is the idea of rational belief change. A belief change operation should be guided by certain principles or integrity constraints in order to characterise change by a rational agent. One of the most noted principles within the context of AGM is the Principle of Informational Economy. However, adoption of this principle in its purest form has been rejected by AGM leading to a more relaxed interpretation. In this paper, we argue that this weakening of the Principle of Informational Economy suggests that it is only one of a number of principles which should be taken into account. Furthermore, this weakening points toward a Principle of Indifference. This motivates the introduction of a belief removal operation that we call severe withdrawal. We provide rationality postulates for severe withdrawal and explore its relationship with AGM contraction. Moreover, we furnish possible worlds and epistemic entrenchment semantics for severe withdrawals.
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REFERENCES
Alchourrón, C. E., Gärdenfors, P. and Makinson, D.: On the logic of theory change: Partial meet contraction and revision functions, J. Symbolic Logic 50 (1985), 510–530.
Alchourrón, C. E. and Makinson, D.: The logic of theory change: Contraction functions and their associated revision functions, Theoria 48 (1982), 14–37.
Bell, J. L. and Slomson, A. B.: Models and Ultraproducts, North-Holland, 1969.
Cantwell, J.: Some logics of iterated belief change, Studia Logica (to appear).
Cohn, P. M.: Universal Algebra, Harper & Row, 1965.
Fermé, E. and Rodriguez, R. O.: Semi-contraction: Axioms and construction, Unpublished manuscript, Universidád de Buenos Aires, 1997.
Fermé, E. and Rodriguez, R. O.: A brief note about Rott contraction, J. of the IGPL (to appear).
Fuhrmann, A. and Hansson, S. O.: A survey of multiple contractions, J. Logic, Language and Inform. 3(1) (1994), 39–76.
Gärdenfors, P.: Knowledge in Flux: Modeling the Dynamics of Epistemic States, Bradford Books, MIT Press, Cambridge, MA, 1988.
Gärdenfors, P. and Makinson, D.: Revisions of knowledge systems using epistemic entrenchment, in Proceedings of the Second Conference on Theoretical Aspect of Reasoning About Knowledge, 1998, pp. 83–96.
Gärdenfors, P. and Makinson, D.: Nonmonotonic inference based on expectations, Artif. Intell. 65 (1994), 197–245.
Gärdenfors, P. and Rott, H.: Belief revision, in D. M. Gabbay, C. J. Hogger, and J. A. Robinson (eds), Handbook of Logic in Artificial Intelligence and Logic Programming - Volume IV: Epistemic and Temporal Reasoning, Oxford University Press, 1995, pp. 35–132.
Grove, A.: Two modellings for theory change, J. Philos. Logic 17 (1988), 157–170.
Hansson, S. O.: Belief contraction without recovery, Studia Logica 50 (1991), 251–260.
Hansson, S. O.: A Textbook of Belief Dynamics: Theory Change and Database Updating, Book draft, February 1996. To be published by Kluwer Academic Publishers.
Hansson, S. O. and Olsson, E.: Levi contractions and AGM contractions: A comparison, Notre Dame J. Formal Logic 36(1) (1995), 103–119.
Harman, G. H.: Change in View: Principles of Reasoning, MIT Press, 1986.
Kaluzhny, Y. and Lehmann, D.: Deductive nonmonotonic inference operations: Antitonic representations, J. Logic Comput. 5(1) (1995), 111–122.
Levi, I.: The Fixation of Belief and its Undoing: Changing Beliefs Through Enquiry, Cambridge University Press, 1991.
Levi, I.: For the Sake of the Argument: Ramsey Test Conditionals, Inductive Inference, and Nonmonotonic Reasoning, Cambridge University Press, 1996.
Levi, I.: Contraction and information value, Unpublished manuscript (sixth version), Columbia University, February 1998.
Lewis, D.: Counterfactuals, Basil Blackwell, Oxford, 1986.
Lindström, S. and Rabinowicz, W.: Epistemic entrenchment with incomparabilities and relational belief revision, in A. Fuhrmann and M. Morreau (eds), The Logic of Theory Change, LNAI 465, Springer-Verlag, Berlin, 1991, pp. 93–126.
Makinson, D.: On the status of the postulate of recovery in the logic of theory change, J. Philos. Logic 16 (1987), 383–394.
Makinson, D.: General patterns in nonmonotonic reasoning, in D. M. Gabbay, C. J. Hogger, and J. A. Robinson (eds), Handbook of Logic in Artificial Intelligence and Logic Programming - Volume III: Nonmonotonic Reasoning and Uncertain Reasoning, Oxford University Press, 1994, pp. 35–110.
Makinson, D.: On the force of some apparent counterexamples to recovery, in E. G. Valdés, W. Krawietz, G. H. von Wright and R. Zimmerling (eds), Festschrift for Carlos E. Alchourrón and Eugenio Bulygin, Duncker and Humblot, Berlin, 1997, pp. 475–481.
Meyer, T. A., Labuschagne, W. A. and Heidema, J.: A semantic weakening of the recovery postulate for theory contraction, Research Report 258/98(4), Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, March 1998.
Pagnucco, M.: The Role of Abductive Reasoning Within the Process of Belief Revision, PhD Thesis, Department of Computer Science, University of Sydney, February 1996.
Priest, G., Surendonk, T. J. and Tanaka, K.: An error in Grove's proof, Technical Report TR-ARP-07-96, Automated Reasoning Project, Australian National University, 1996.
Rott, H.: Two methods of constructing contractions and revisions of knowledge systems, J. Philos. Logic 20 (1991), 149–173.
Rott, H.: Preferential belief change using generalized epistemic entrenchment, J. Logic, Language and Inform. 1(1) (1992), 45–78.
Rott, H.: Making Up One's Mind: Foundations, Coherence, Nonmonotonicity, Habilitationsschrift, Philosophische Fakultät, Universität Konstanz, October 1996. To be published under the title Change, Choice and Inference by Oxford University Press.
Williams, M.-A.: On the logic of theory base change, in C. MacNish, D. Pearce, and L. M. Pereira (eds), Logics in Artificial Intelligence, Lecture Notes in Artificial Intelligence 838, Springer-Verlag, 1994, pp. 86–105.
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Rott, H., Pagnucco, M. Severe Withdrawal (and Recovery). Journal of Philosophical Logic 28, 501–547 (1999). https://doi.org/10.1023/A:1004344003217
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DOI: https://doi.org/10.1023/A:1004344003217