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Parallel belief revision: revising by sets of formulas. (English) Zbl 1243.03018
Summary: The area of belief revision studies how a rational agent may incorporate new information about a domain into its belief corpus. An agent is characterised by a belief state \(K\), and receives a new item of information \(\alpha \) which is to be included among its set of beliefs. Revision then is a function from a belief state and a formula to a new belief state.
We propose here a more general framework for belief revision, in which revision is a function from a belief state and a finite set of formulas to a new belief state. In particular, we distinguish revision by the set \(\{\alpha ,\beta \}\) from the set \(\{\alpha \land \beta \}\). This seemingly innocuous change has significant ramifications with respect to iterated belief revision. A problem in approaches to iterated belief revision is that, after first revising by a formula and then by a formula that is inconsistent with the first formula, all information in the original formula is lost.
This problem is avoided here in that, in revising by a set of formulas \(S\), the resulting belief state contains not just the information that members of \(S\) are believed to be true, but also the counterfactual supposition that if some members of \(S\) were later believed to be false, then the remaining members would nonetheless still be believed to be true. Thus if some members of \(S\) were in fact later believed to be false, then the other elements of \(S\) would still be believed to be true. Hence, we provide a more nuanced approach to belief revision. The general approach, which we call parallel belief revision, is independent of extant approaches to iterated revision. We present first a basic approach to parallel belief revision. Following this we combine the basic approach with an approach due to Jin and Thielscher for iterated revision. Postulates and semantic conditions characterising these approaches are given, and representation results provided. We conclude with a discussion of the possible ramifications of this approach in belief revision in general.

MSC:
03B42 Logics of knowledge and belief (including belief change)
68T27 Logic in artificial intelligence
68T30 Knowledge representation
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[1] Alchourrón, C.E.; Gärdenfors, P.; Makinson, D., On the logic of theory change: partial meet functions for contraction and revision, Journal of symbolic logic, 50, 2, 510-530, (1985) · Zbl 0578.03011
[2] S. Benferhat, D. Dubois, H. Prade, Representing default rules in possibilistic logic, in: Proceedings of the Third International Conference on the Principles of Knowledge Representation and Reasoning, Cambridge, MA, October 1992, pp. 673-684.
[3] Benferhat, S.; Kaci, S.; Le Berre, D.; Williams, M.-A., Weakening conflicting information for iterated revision and knowledge integration, Artificial intelligence, 153, 339-371, (2004) · Zbl 1085.68156
[4] S. Benferhat, C. Cayrol, D. Dubois, J. Lang, H. Prade, Inconsistency management and prioritized syntax-based entailment, in: Proceedings of the International Joint Conference on Artificial Intelligence, Chambéry, France, 1993, pp. 640-645.
[5] Booth, R.; Meyer, T.A., Admissible and restrained revision, Journal of artificial intelligence research, 26, 127-151, (2006) · Zbl 1182.68284
[6] C. Boutilier, Revision sequences and nested conditionals, in: Proceedings of the International Joint Conference on Artificial Intelligence, 1993, pp. 519-531.
[7] Boutilier, C., Conditional logics of normality: A modal approach, Artificial intelligence, 68, 1, 87-154, (1994) · Zbl 0811.68114
[8] Boutilier, C., Unifying default reasoning and belief revision in a modal framework, Artificial intelligence, 68, 1, 33-85, (1994) · Zbl 0811.68113
[9] Darwiche, A.; Pearl, J., On the logic of iterated belief revision, Artificial intelligence, 89, 1-29, (1997) · Zbl 1018.03012
[10] J. Delgrande, Y. Jin, Parallel belief revision, in: Proceedings of the AAAI National Conference on Artificial Intelligence, 2008, pp. 317-322.
[11] Delgrande, J.; Schaub, T., A consistency-based approach for belief change, Artificial intelligence, 151, 1-2, 1-41, (2003) · Zbl 1082.68818
[12] Delgrande, J.; Wassermann, R., Horn clause contraction functions: belief set and belief base approaches, (), 143-152
[13] Falappa, M.A.; Kern-Isberner, G.; Simari, G.R., Explanations, belief revision and defeasible reasoning, Artificial intelligence, 141, 1-2, 1-28, (2002) · Zbl 1043.68095
[14] Fermé, E.L.; Saez, K.; Sanz, P., Multiple kernel contraction, Studia logica, 73, 2, 183-195, (2003) · Zbl 1018.03013
[15] Fuhrmann, A.; Hansson, S.O., A survey of multiple contractions, Journal of logic, language, and information, 3, 39-76, (1994)
[16] Gärdenfors, P., Knowledge in flux: modelling the dynamics of epistemic states, (1988), MIT Press Cambridge, MA · Zbl 1229.03008
[17] Geffner, H.; Pearl, J., Conditional entailment: bridging two approaches to default reasoning, Artificial intelligence, 53, 2-3, 209-244, (1992) · Zbl 1193.68235
[18] M. Goldszmidt, P. Morris, J. Pearl, A maximum entropy approach to nonmonotonic reasoning, in: Proceedings of the AAAI National Conference on Artificial Intelligence, Boston, MA, 1990.
[19] Grove, A., Two modellings for theory change, Journal of philosophical logic, 17, 157-170, (1988) · Zbl 0639.03025
[20] Hansson, S.O., A textbook of belief dynamics, Applied logic series, (1999), Kluwer Academic Publishers
[21] Jin, Y.; Thielscher, M., Iterated belief revision, revised, Artificial intelligence, 171, 1, 1-18, (2007) · Zbl 1168.03318
[22] Katsuno, H.; Mendelzon, A.O., Propositional knowledge base revision and minimal change, Artificial intelligence, 52, 3, 263-294, (1991) · Zbl 0792.68182
[23] Konieczny, S.; Pino Pérez, R., A framework for iterated revision, Journal of applied non-classical logics, 10, 3-4, 339-367, (2000) · Zbl 1033.03506
[24] S. Konieczny, J. Lang, P. Marquis, Reasoning under inconsistency: The forgotten connective, in: Proceedings of the International Joint Conference on Artificial Intelligence, Edinburgh, 2005, pp. 484-489.
[25] Kraus, S.; Lehmann, D.; Magidor, M., Nonmonotonic reasoning, preferential models and cumulative logics, Artificial intelligence, 44, 1-2, 167-207, (1990) · Zbl 0782.03012
[26] P. Lamarre, S4 as the conditional logic of nonmonotonicity, in: Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning, Cambridge, MA, April 1991, pp. 357-367. · Zbl 0765.03013
[27] Lehmann, D., Another perspective on default reasoning, Annals of mathematics and artificial intelligence, 15, 1, 61-82, (1995) · Zbl 0857.68096
[28] Lehmann, D., Belief revision, revised, (), 1534-1540
[29] Lehmann, D.; Magidor, M., What does a conditional knowledge base entail?, Artificial intelligence, 55, 1, 1-60, (1992) · Zbl 0762.68057
[30] Meyer, T., Basic infobase change, Studia logica, 67, 2, 215-242, (2001) · Zbl 0995.03012
[31] Nayak, A.C., Iterated belief change based on epistemic entrenchment, Erkenntnis, 41, 353-390, (1994)
[32] Nayak, A.C.; Pagnucco, M.; Peppas, P., Dynamic belief revision operators, Artificial intelligence, 146, 2, 193-228, (2003) · Zbl 1082.03503
[33] Pearl, J., System Z: A natural ordering of defaults with tractable applications to nonmonotonic reasoning, (), 121-135
[34] Peppas, P., The limit assumption and multiple revision, Journal of logic and computation, 14, 3, 355-371, (2004) · Zbl 1060.03035
[35] Peppas, P., Belief revision, (), 317-359
[36] Rott, H., Change, choice and inference - A study of belief revision and nonmonotonic reasoning, (2001), Clarendon Press Oxford · Zbl 1018.03004
[37] Spohn, W., Ordinal conditional functions: A dynamic theory of epistemic states, (), 105-134
[38] Spohn, W., A reason for explanation: explanations provide stable reasons, (), 165-196
[39] M.-A. Williams, Transmutations of knowledge systems, in: J. Doyle, P. Torasso, E. Sandewall (Eds.), Proceedings of the Fourth International Conference on the Principles of Knowledge Representation and Reasoning, Bonn, Germany, May 1994, pp. 619-629.
[40] Zhang, D., Properties of iterated multiple belief revision, (), 314-325 · Zbl 1122.03305
[41] Zhang, D.; Foo, N., Infinitary belief revision, Journal of philosophical logic, 30, 6, 525-570, (2001) · Zbl 0992.03024
[42] Zhang, D.; Chen, S.; Zhu, W.; Chen, Z., Representation theorems for multiple belief changes, (), 89-94
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