Duality between Merging Operators and Social Contraction Operators

  • José Luis Chacón
  • Ramón Pino Pérez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7180)

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.

Keywords

Social Contraction Integrity Constraint Belief Base Strong Duality Contraction Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    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)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Alchourrón, C.E., Makinson, D.: The logic of theory change: Contraction functions and their associated revision functions. Theoria 48, 14–37 (1982)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Alchourrón, C.E., Makinson, D.: On the logic of theory change: Safe contraction. Studia Logica 44, 405–422 (1985)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Alchourrón, C.E., Makinson, D.: Maps between some different kinds of contraction function: the finite case. Studia Logica 45, 187–198 (1986)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Baral, C., Kraus, S., Minker, J.: Combining multiple knowledge bases. IEEE Transactions on Knowledge and Data Engineering 3(2), 208–220 (1991)CrossRefGoogle Scholar
  6. 6.
    Baral, C., Kraus, S., Minker, J., Subrahmanian, V.S.: Combining knowledge bases consisting of first-order theories. Computational Intelligence 8(1), 45–71 (1992)CrossRefGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    Booth, R.: Social contraction and belief negotiation. Information Fusion 7(1), 19–34 (2006)CrossRefGoogle Scholar
  9. 9.
    Booth, R., Meyer, T.: Equilibria in social belief removal. Synthese 177(supplement-1), 97–123 (2010)MATHCrossRefGoogle Scholar
  10. 10.
    Chacón, J.L., Pino Pérez, R.: Merging operators: Beyond the finite case. Information Fusion 7(1), 41–60 (2006)CrossRefGoogle Scholar
  11. 11.
    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)MATHCrossRefGoogle Scholar
  12. 12.
    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)Google Scholar
  13. 13.
    Gärdenfors, P.: Knowledge in flux. MIT Press (1988)Google Scholar
  14. 14.
    Gärdenfors, P. (ed.): Belief Revision. Cambridge University Press (1992)Google Scholar
  15. 15.
    Harper, W.L.: Rational conceptual change. In: PSA 1976 East Lansing, vol. 12, pp. 462–494. Philosophy of Science Association, Mich. (1977)Google Scholar
  16. 16.
    Herzig, A., Rifi, O.: Update operations: a review. In: Proceedings of the Thirteenth European Conference on Artificial Intelligence (ECAI 1998), pp. 13–17 (1998)Google Scholar
  17. 17.
    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)Google Scholar
  18. 18.
    Katsuno, H., Mendelzon, A.O.: Propositional knowledge base revision and minimal change. Artificial Intelligence 52, 263–294 (1991)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Konieczny, S., Lang, J., Marquis, P.: DA2 merging operators. Artificial Intelligence 157(1-2), 49–79 (2004)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Konieczny, S., Pino Pérez, R.: Merging information under constraints: a logical framework. Journal of Logic and Computation 12(5), 773–808 (2002)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Konieczny, S., Pino Pérez, R.: Logic based merging. Journal of Philosophical Logic 40, 239–270 (2011)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Levi, I.: Subjunctives, dispositions and chances. Synthese 34, 423–455 (1977)MATHCrossRefGoogle Scholar
  23. 23.
    Liberatore, P., Schaerf, M.: Arbitration (or how to merge knowledge bases). IEEE Transactions on Knowledge and Data Engineering 10(1), 76–90 (1998)CrossRefGoogle Scholar
  24. 24.
    Lin, J.: Integration of weighted knowledge bases. Artificial Intelligence 83(2), 363–378 (1996)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Lin, J., Mendelzon, A.O.: Merging databases under constraints. International Journal of Cooperative Information System 7(1), 55–76 (1998)CrossRefGoogle Scholar
  26. 26.
    Lin, J., Mendelzon, A.O.: Knowledge base merging by majority. In: Dynamic Worlds: From the Frame Problem to Knowledge Management. Kluwer (1999)Google Scholar
  27. 27.
    Lobo, J., Uzcátegui, C.: Abductive change operators. Fundamenta Informaticae 27(4), 385–411 (1996)MathSciNetMATHGoogle Scholar
  28. 28.
    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)Google Scholar
  29. 29.
    Revesz, P.Z.: On the semantics of arbitration. International Journal of Algebra and Computation 7(2), 133–160 (1997)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • José Luis Chacón
    • 1
  • Ramón Pino Pérez
    • 1
  1. 1.Departamento de Matemáticas Facultad de CienciasUniversidad de Los AndesMéridaVenezuela

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