Abstract
This paper extends the AGM theory of belief revision to accommodate infinitary belief change. We generalize both axiomatization and modeling of the AGM theory. We show that most properties of the AGM belief change operations are preserved by the generalized operations whereas the infinitary belief change operations have their special properties. We prove that the extended axiomatic system for the generalized belief change operators with a Limit Postulate properly specifies infinite belief change. This framework provides a basis for first-order belief revision and the theory of revising a belief state by a belief state.
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REFERENCES
Alchourrón, E., Gärdenfors, P. and Makinson, D.: On the logic of theory change: partial meet contraction and revision functions, J. Symbolic Logic 50(2) (1985), 510–530.
Foo, N. and Zhang, D.: Convergency of iterated belief changes, in M. Thielscher (ed.), The 3rd Workshop on Nonmonotonic Reasoning, Action, and Change, 1999, pp. 73–77.
Freund, M. and Lehmann, D.: Nonmonotonic reasoning: from finitary relations to infinitary inference operations, Studia Logica 2(53) (1994), 161–201.
Fuhrmann, A.: Relevant Logics, Modal Logics and Theory Change, Doctoral Dissertation, Department of Philosophy and Automated Reasoning Project, Australian National University, 1988.
Fuhrmann, A.: An Essay on Contraction, Cambridge University Press, 1997.
Fuhrmann, A. and Hansson, S. O.: A survey of multiple contractions, J. Logic, Language, and Information 3 (1994), 39–76.
Gärdenfors, P.: Knowledge in Flux: Modeling the Dynamics of Epistemic States, The MIT Press, 1988.
Gärdenfors, P. and Makinson, D.: 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 Publ., Los Altos, CA, 1988, pp. 83–95.
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, Clarendon Press, Oxford, 1995, pp. 35–132.
Grove, A.: Two modelings for theory change, J. Philos. Logic 17 (1988), 157–170.
Hansson, S. O.: A dyadic representation of belief, in P. Gärdenfors (ed.), Belief Revision, Cambridge University Press, 1992, pp. 89–121.
Herre, H.: Compactness properties of nonmonotonic inference operations, in C. MacNish, D. Pearce and L. M. Pereira (eds.), Logics in Artificial Intelligence, LNAI 838, Springer-Verlag, 1994, pp. 19–33.
Konieczny, S. and Pino-Pérez, R.: On the logic of merging, in Principles of Knowledge Representation and Reasoning: Proceedings of the 6th International Conference (KR'98), Morgan Kaufmann, 1998, 488–498.
Lindström, S.: A semantic approach to nonmonotonic reasoning: inference operations and choice, Uppsala Prints and Preprints in Philosophy, No. 10, 1994.
Makinson, D.: General patterns in nonmonotonic reasoning, in D. Gabbay (ed.), Handbook of Logic in Artificial Intelligence and Logic Programming, Oxford University Press, 1993, pp. 35–110.
Makinson, D. and Gärdenfors, P.: Relations between the logic of theory change and nonmonotonic logic, in A. Fuhrmann and M. Morreau (eds.), The Logic of Theory Change, LNCS 465, Springer-Verlag, 1991, pp. 185–205.
Nayak, A.: Iterated belief change based on epistemic entrenchment, Erkenntnis 41 (1994), 353–390.
Niederèe, R.: Multiple contraction: a further case against Gärdenfors’ principle of recovery, in A. Fuhrmann and M. Morreau (eds.), The Logic of Theory Change, LNCS 465, Springer-Verlag, 1991, pp. 322–334.
Peppas, P.: Well behaved and multiple belief revision, in W. Wahlster (ed.), Proceedings of the 12th European Conference on Artificial Intelligence (ECAI-96), pp. 90–94.
Revesz, P. Z.: On the semantics of arbitration, Internat. J. Algebra Comput. 7(2) (1997), 133–160.
Rott, H.: Modelings for belief change: base contractions, multiple contractions, and epistemic entrenchment, in Logic in AI, LNAI 633, Springer-Verlag 1992, pp. 139–153.
Williams, M.: Transmutations of knowledge systems, in J. Doyle, E. Sandewall and P. Torasso (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR'94), Morgan Kaufman, 1994, pp. 619–629.
Zhang, D.: Belief revision by sets of sentences, J. Comput. Sci. Technol. 11(2) (1996), 108–125.
Zhang, D., Chen, S., Zhu, W. and Chen, Z.: Representation theorems for multiple belief changes, in M. Pollack (ed.), Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI-97), Morgan Kaufman, pp. 89–94.
Zhang, D., Chen, S., Zhu,W. and Li, H.: Nonmonotonic reasoning and multiple belief revision, in M. Pollack (ed.), Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI-97), Morgan Kaufman, pp. 95–100.
Zhang, D.: What could a natural deductive system for nonmonotonic reasoning look like? in M. Williams (ed.), The Third Australian Commonsense Reasoning Workshop, 1999, pp. 160–173.
Zhang, D., Zhu, Z. and Chen, S.: Default reasoning and belief revision, The 7th International Workshop on Nonmonotonic Reasoning, 1998.
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Zhang, D., Foo, N. Infinitary Belief Revision. Journal of Philosophical Logic 30, 525–570 (2001). https://doi.org/10.1023/A:1013356315540
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DOI: https://doi.org/10.1023/A:1013356315540