Abstract
In the AGM (Alchourrón-Gärdenfors-Makinson) framework there exists a duality between revision operators and contraction operators. This duality is given by the Levi identity and the Harper identity. The former allows to define a revision operator starting from a contraction operator. The latter allows to define a contraction operator starting from a revision operator. In this work we show that this duality can be extended to a duality between merging operators and social contraction operators through some identities in the style of the Levi and Harper identities.
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References
Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50, 510–530 (1985)
Alchourrón, C.E., Makinson, D.: The logic of theory change: Contraction functions and their associated revision functions. Theoria 48, 14–37 (1982)
Alchourrón, C.E., Makinson, D.: On the logic of theory change: Safe contraction. Studia Logica 44, 405–422 (1985)
Alchourrón, C.E., Makinson, D.: Maps between some different kinds of contraction function: the finite case. Studia Logica 45, 187–198 (1986)
Baral, C., Kraus, S., Minker, J.: Combining multiple knowledge bases. IEEE Transactions on Knowledge and Data Engineering 3(2), 208–220 (1991)
Baral, C., Kraus, S., Minker, J., Subrahmanian, V.S.: Combining knowledge bases consisting of first-order theories. Computational Intelligence 8(1), 45–71 (1992)
Booth, R.: Social contraction and belief negotiation. In: Proceedings of the Eighth Conference on Principles of Knowledge Representation and Reasoning (KR 2002), pp. 374–384 (2002)
Booth, R.: Social contraction and belief negotiation. Information Fusion 7(1), 19–34 (2006)
Booth, R., Meyer, T.: Equilibria in social belief removal. Synthese 177(supplement-1), 97–123 (2010)
Chacón, J.L., Pino Pérez, R.: Merging operators: Beyond the finite case. Information Fusion 7(1), 41–60 (2006)
Dupin de Saint-Cyr, F., Lang, J.: Belief extrapolation (or how to reason about observations and unpredicted change). Artif. Intell. 175(2), 760–790 (2011)
Dupin de Saint-Cyr, F., Lang, J.: Belief extrapolation (or how to reason about observations and unpredicted change). In: Proceedings of the Eighth Conference on Principles of Knowledge Representation and Reasoning (KR 2002), pp. 497–508 (2002)
Gärdenfors, P.: Knowledge in flux. MIT Press (1988)
Gärdenfors, P. (ed.): Belief Revision. Cambridge University Press (1992)
Harper, W.L.: Rational conceptual change. In: PSA 1976 East Lansing, vol. 12, pp. 462–494. Philosophy of Science Association, Mich. (1977)
Herzig, A., Rifi, O.: Update operations: a review. In: Proceedings of the Thirteenth European Conference on Artificial Intelligence (ECAI 1998), pp. 13–17 (1998)
Katsuno, H., Mendelzon, A.O.: On the difference between updating a knowledge base and revising it. In: Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning (KR 1991), pp. 387–394 (1991)
Katsuno, H., Mendelzon, A.O.: Propositional knowledge base revision and minimal change. Artificial Intelligence 52, 263–294 (1991)
Konieczny, S., Lang, J., Marquis, P.: DA2 merging operators. Artificial Intelligence 157(1-2), 49–79 (2004)
Konieczny, S., Pino Pérez, R.: Merging information under constraints: a logical framework. Journal of Logic and Computation 12(5), 773–808 (2002)
Konieczny, S., Pino Pérez, R.: Logic based merging. Journal of Philosophical Logic 40, 239–270 (2011)
Levi, I.: Subjunctives, dispositions and chances. Synthese 34, 423–455 (1977)
Liberatore, P., Schaerf, M.: Arbitration (or how to merge knowledge bases). IEEE Transactions on Knowledge and Data Engineering 10(1), 76–90 (1998)
Lin, J.: Integration of weighted knowledge bases. Artificial Intelligence 83(2), 363–378 (1996)
Lin, J., Mendelzon, A.O.: Merging databases under constraints. International Journal of Cooperative Information System 7(1), 55–76 (1998)
Lin, J., Mendelzon, A.O.: Knowledge base merging by majority. In: Dynamic Worlds: From the Frame Problem to Knowledge Management. Kluwer (1999)
Lobo, J., Uzcátegui, C.: Abductive change operators. Fundamenta Informaticae 27(4), 385–411 (1996)
Revesz, P.Z.: On the semantics of theory change: arbitration between old and new information. In: Proceedings of the 12th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases, pp. 71–92 (1993)
Revesz, P.Z.: On the semantics of arbitration. International Journal of Algebra and Computation 7(2), 133–160 (1997)
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Chacón, J.L., Pino Pérez, R. (2012). Duality between Merging Operators and Social Contraction Operators. In: Bjørner, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2012. Lecture Notes in Computer Science, vol 7180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28717-6_16
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DOI: https://doi.org/10.1007/978-3-642-28717-6_16
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