Annals of Mathematics and Artificial Intelligence

, Volume 69, Issue 1, pp 73–101 | Cite as

Confluence operators and their relationships with revision, update and merging

Article

Abstract

In this paper we introduce confluence operators, that are inspired by the existing links between belief revision, update and merging operators. Roughly, update operators can be considered as pointwise revision, whereas revision operators can be considered as special case of merging operators. Confluence operators are to merging operators what update operators are to revision operators. Similarly, update operators can be considered as special case of confluence operators just as revision can be considered as special case of merging operators. Confluence operators gives all possible agreement situations from a set of belief bases.

Keywords

Belief dynamics Belief revision Update Merging Confluence 

Mathematics Subject Classifications (2010)

03B42 68T27 68T30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alchourrón, C., Makinson, D.: On the logic of theory change: Safe contraction. Stud. Log. 44, 405–422 (1985)CrossRefMATHGoogle Scholar
  2. 2.
    Alchourrón, C.E., Gärdenfors, P., Makinson D.: On the logic of theory change: Partial meet contraction and revision functions. J. Symb. Log. 50, 510–530 (1985)CrossRefMATHGoogle Scholar
  3. 3.
    Baral, C., Kraus, S., Minker, J.: Combining multiple knowledge bases. IEEE Trans. Knowl. Data Eng. 3(2), 208–220 (1991)CrossRefGoogle Scholar
  4. 4.
    Baral, C., Kraus, S., Minker, J., Subrahmanian, V.S.: Combining knowledge bases consisting of first-order theories. Comput. Intell. 8(1), 45–71 (1992)CrossRefGoogle Scholar
  5. 5.
    Benferhat, S., Lagrue, S., Papini, O.: Revision of partially ordered information: axiomatization, semantics and iteration. In: Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI’05), pp. 376–381 (2005)Google Scholar
  6. 6.
    Booth, R.: Social contraction and belief negotiation. In: Proceedings of the Eighth Conference on Principles of Knowledge Representation and Reasoning (KR’02), pp. 374–384 (2002)Google Scholar
  7. 7.
    Dalal, M.: Investigations into a theory of knowledge base revision: preliminary report. In: Proceedings of the American National Conference on Artificial Intelligence (AAAI’88), pp. 475–479 (1988)Google Scholar
  8. 8.
    Delgrande, J.P., Dubois, D., Lang, J.: Iterated revision as prioritized merging. In: Proceedings of the Tenth International Conference on Knowledge Representation and Reasoning (KR’06), pp. 210–220 (2006)Google Scholar
  9. 9.
    de Saint-Cyr, F.D., 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’02), pp. 497–508 (2002)Google Scholar
  10. 10.
    Gärdenfors, P.: Knowledge in Flux. MIT Press (1988)Google Scholar
  11. 11.
    Gärdenfors, P., Makinson, D.: Revisions of knowledge systems using epistemic entrenchment. In: Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, pp. 83–95 (1988)Google Scholar
  12. 12.
    Grove, A.: Two modellings for theory change. J. Philos. Logic 17, 157–170 (1988)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Hansson, S.O. (ed.): Theoria. Special Issue on Non-Prioritized Belief Revision, vol. 63, nos. 1–2. Wiley (1997)Google Scholar
  14. 14.
    Herzig, A., Rifi, O.: Update operations: a review. In: Proceedings of the Thirteenth European Conference on Artificial Intelligence (ECAI’98), pp. 13–17 (1998)Google Scholar
  15. 15.
    Herzig, A., Rifi, O.: Propositional belief base update and minimal change. Artif. Intell. 115(1), 107–138 (1999)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Katsuno, H., Mendelzon, A.O.: Propositional knowledge base revision and minimal change. Artif. Intell. 52, 263–294 (1991)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Katsuno, H., Mendelzon, A.O.: On the difference between updating a knowledge base and revising it. In: Gärdenfors, P. (ed.) Belief Revision. Cambridge University Press (1992)Google Scholar
  18. 18.
    Konieczny, S.: Belief base merging as a game. J. Appl. Non-Class. Log. 14(3), 275–294 (2004)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Konieczny, S., Lang, J., Marquis, P.: DA2 merging operators. Artif. Intell. 157(1–2), 49–79 (2004)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Konieczny, S., Pino Pérez, R.: Merging information under constraints: a logical framework. J. Log. Comput. 12(5), 773–808 (2002)CrossRefMATHGoogle Scholar
  21. 21.
    Konieczny, S., Pino Pérez, R.: Logic based merging. J. Philos. Logic 40(2), 239–270 (2011)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Konieczny, S., Pino Pérez, R.: Confluence operators. In: Proceedings of the Eleventh European Conference on Logics in Artificial Intelligence (JELIA’08), pp. 272–284 (2008)Google Scholar
  23. 23.
    Lang, J.: Belief update revisited. In: Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI’07), pp. 2517–2522 (2007)Google Scholar
  24. 24.
    Lehmann, D., Magidor, M., Schlechta, K.: Distance semantics for belief revision. J. Symb. Log. 66(1), 295–317 (2001)CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    Liberatore, P., Schaerf, M.: Arbitration (or how to merge knowledge bases). IEEE Trans. Knowl. Data Eng. 10(1), 76–90 (1998)CrossRefGoogle Scholar
  26. 26.
    Lin, J., Mendelzon, A.O.: Merging databases under constraints. Int. J. Cooperative Inf. Syst. 7(1), 55–76 (1998)CrossRefGoogle Scholar
  27. 27.
    Meyer, T., Foo, N., Zhang, D., Kwok, R.: Logical foundations of negotiation: Outcome, concession and adaptation. In: Proceedings of the American National Conference on Artificial Intelligence (AAAI’04), pp. 293–298 (2004)Google Scholar
  28. 28.
    Meyer, T., Foo, N., Zhang, D., Kwok, R.: Logical foundations of negotiation: Strategies and preferences. In: Proceedings of the Ninth Conference on Principles of Knowledge Representation and Reasoning (KR’04), pp. 311–318 (2004)Google Scholar
  29. 29.
    Revesz, P.Z.: On the semantics of arbitration. Int. J. Algebra Comput. 7(2), 133–160 (1997)CrossRefMathSciNetGoogle Scholar
  30. 30.
    Schlechta, K., Lehmann, D., Magidor, M.: Distance semantics for belief revision. In: Proceedings of: Theoretical Aspects of Rationality and Knowledge, Tark VI, pp. 137–145 (1996)Google Scholar
  31. 31.
    Tversky, A., Kahneman, D.: Extensional vs. intuitive reasoning: the conjunction fallacy in probability judgment. Psychol. Rev. 91(4), 293–315 (1983)CrossRefGoogle Scholar
  32. 32.
    Zhang, D., Foo, N., Meyer, T., Kwok, R.: Negotiation as mutual belief revision. In: Proceedings of the American National Conference on Artificial Intelligence (AAAI’04), pp. 317–322 (2004)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Centre de Recherche en Informatique de Lens (CRIL)LensFrance
  2. 2.Centro Interdisciplinario de Lógica y Álgebra (CILA), Departamento de Matemáticas, Facultad de CienciasUniversidad de Los AndesMéridaVenezuela

Personalised recommendations