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Belief contraction as nonmonotonic inference

Published online by Cambridge University Press:  12 March 2014

Alexander Bochman
Alexander Bochman*
Affiliation:
Computer Science Department, Technological Academic Institute Holon, 52 Golomb St., Pob 305 Holon 58102, Israel, E-mail: [email protected]
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Abstract

A notion of an epistemic state is introduced as a generalization of common representations suggested for belief change. Based on it, a new kind of nonmonotonic inference relation corresponding to belief contractions is defined. A number of representation results is established that cover both traditional AGM contractions and contractions that do not satisfy recovery.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 605 - 626
Copyright
Copyright © Association for Symbolic Logic 2000

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References

REFERENCES

[1]Alchourrón, C., Gärdenfors, P., and Makinson, D., On the logic of theory change: Partial meet contraction and revision functions, this Journal, vol. 50 (1985), pp. 510–530.Google Scholar
[2]Bochman, A., A foundational theory of belief and belief change, Artificial Intelligence, vol. 108 (1999), pp. 309–352.CrossRefGoogle Scholar
[3]Freund, M., Injective models and disjunctive relations, Journal of Logic and Computation, vol. 3 (1992), pp. 231–247.CrossRefGoogle Scholar
[4]Fuhrmann, A., Theory contraction through base contraction, Journal of Philosophical Logic, vol. 20 (1991), pp. 175–203.CrossRefGoogle Scholar
[5]Fuhrmann, A. and Hansson, S. O., A survey of multiple contractions, Journal of Logic, Language and Information, vol. 3 (1994), pp. 39–76.CrossRefGoogle Scholar
[6]Gärdenfors, P., Knowledge in Flux: Modeling the Dynamics of Epistemic States, Bradford Books, MIT Press, 1988.Google Scholar
[7]Gärdenfors, P., The dynamics of belief systems: Foundations vs. coherence theories, Revue Internationale de Philosophic vol. 44 (1990), pp. 24–46.Google Scholar
[8]Gärdenfors, P. and Makinson, D., Nonmonotonic inference based on expectations, Artificial Intelligence, vol. 65 (1994), pp. 197–245.CrossRefGoogle Scholar
[9]Hansson, S. O., Theory contraction and base contraction unified, this Journal, vol. 58 (1993), pp. 602–625.Google Scholar
[10]Hansson, S. O. and Olsson, E. J., Levi contractions and AGM contractions: a comparison, Notre Dame Journal of Formal Logic, vol. 36 (1995), pp. 103–119.CrossRefGoogle Scholar
[11]Kraus, S., Lehmann, D., and Magidor, M., Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, vol. 44 (1990), pp. 167–207.CrossRefGoogle Scholar
[12]Lehmann, D. and Magidor, M., What does a conditional knowledge base entail?, Artificial Intelligence, vol. 55 (1992), pp. 1–60.CrossRefGoogle Scholar
[13]Levi, I., The Fixation of Belief and Its Undoing, Cambridge University Press, 1991.CrossRefGoogle Scholar
[14]Makinson, D., General theory of cumulative inference, Nonmonotonic reasoning (Reinfrank, M., editor), Springer, 1989, Lecture Notes in AI, 346, pp. 1–18.Google Scholar
[15]Makinson, D. and Gärdenfors, P., Relations between the logic of theory change and nonmonotonic logic, The Logic of Theory Change (Fuhrmann, A. and Morreau, M., editors), Lecture Notes in AI, 465, Springer Verlag, 1991, pp. 185–205.Google Scholar
[16]Nayak, A. C., Foundational belief change, Journal of Philosophical Logic, vol. 23 (1994), pp. 495–533.CrossRefGoogle Scholar
[17]Nebel, B., A knowledge level analysis of belief revision, Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning (Brachman, R. J.et al., editors), Morgan Kauffman, 1989, pp. 301–311.Google Scholar
[18]Nebel, B., Syntax-based approaches to belief revision, Belief revision (Gärdenfors, P., editor), Cambridge University Press, 1992, pp. 52–88.CrossRefGoogle Scholar
[19]Rott, H., Preferential belief change using generalized epistemic entrenchment, Journal of Logic, Language and Information, vol. 1 (1992), pp. 45–78.CrossRefGoogle Scholar
[20]Rott, H., Belief contraction in the context of the general theory of rational choice, this Journal, vol. 58 (1993), pp. 1426–1450.Google Scholar