A General Family of Preferential Belief Removal Operators

  • Richard Booth
  • Thomas Meyer
  • Chattrakul Sombattheera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5834)


Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in [5]. However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of [5] to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases.


Belief Revision Belief Change Nonmonotonic Reasoning Strict Partial Order Removal Function 
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  1. 1.
    Alchourrón, C., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50(2), 510–530 (1985)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Benferhat, S., Lagrue, S., Papini, O.: Revision of partially ordered information: Axiomatization, semantics and iteration. In: Pack Kaelbling, L., Saffiotti, A. (eds.) IJCAI, pp. 376–381. Professional Book Center (2005)Google Scholar
  3. 3.
    Bochman, A.: A Logical Theory of Nonmonotonic Inference and Belief Change. Springer, Heidelberg (2001)CrossRefMATHGoogle Scholar
  4. 4.
    Booth, R., Chopra, S., Ghose, A., Meyer, T.: Belief liberation (and retraction). Studia Logica 79(1), 47–72 (2005)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Booth, R., Chopra, S., Meyer, T., Ghose, A.: A unifying semantics for belief change. In: Proceedings of ECAI 2004, pp. 793–797 (2004)Google Scholar
  6. 6.
    Booth, R., Meyer, T.: Equilibria in social belief removal. In: KR, pp. 145–155 (2008)Google Scholar
  7. 7.
    Cantwell, J.: Relevant contraction. In: Proceedings of the Dutch-German Workshop on Non-Monotonic Reasoning, DGNMR 1999 (1999)Google Scholar
  8. 8.
    Cantwell, J.: Eligible contraction. Studia Logica 73, 167–182 (2003)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Arló Costa, H.: Rationality and value: The epistemological role of indeterminate and agent-dependent values. Philosophical Studies 128(1), 7–48 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hansson, S.O.: Belief contraction without recovery. Studia Logica 50(2), 251–260 (1991)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Hansson, S.O.: Changes on disjunctively closed bases. Journal of Logic, Language and Information 2, 255–284 (1993)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Katsuno, H., Mendelzon, A.O.: Propositional knowledge base revision and minimal change. Artif. Intell. 52(3), 263–294 (1992)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 167–207 (1991)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Levi, I.: The Fixation of Belief and Its Undoing. Cambridge University Press, Cambridge (1991)CrossRefGoogle Scholar
  15. 15.
    Maynard-Zhang, P., Lehmann, D.: Representing and aggregating conflicting beliefs. Journal of Artificial Intelligence Research 19, 155–203 (2003)MathSciNetMATHGoogle Scholar
  16. 16.
    Meyer, T., Heidema, J., Labuschagne, W., Leenen, L.: Systematic withdrawal. Journal of Philosophical Logic 31(5), 415–443 (2002)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Rott, H.: Preferential belief change using generalized epistemic entrenchment. Journal of Logic, Language and Information 1, 45–78 (1992)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Rott, H.: Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning. Oxford University Press, Oxford (2001)MATHGoogle Scholar
  19. 19.
    Rott, H., Pagnucco, M.: Severe withdrawal (and recovery). Journal of Philosophical Logic 28, 501–547 (1999)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Shoham, Y.: A semantical approach to nonmonotic logics. In: LICS, pp. 275–279 (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Richard Booth
    • 1
  • Thomas Meyer
    • 2
  • Chattrakul Sombattheera
    • 1
  1. 1.Faculty of InformaticsMahasarakham UniversityMahasarakhamThailand
  2. 2.Meraka Institute, CSIR and School of Computer ScienceUniversity of Kwazulu-NatalSouth Africa

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