Advertisement

A General Framework for Revising Belief Bases Using Qualitative Jeffrey’s Rule

  • Salem Benferhat
  • Didier Dubois
  • Henri Prade
  • Mary-Anne Williams
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5722)

Abstract

Intelligent agents require methods to revise their epistemic state as they acquire new information. Jeffrey’s rule, which extends conditioning to uncertain inputs, is currently used for revising probabilistic epistemic states when new information is uncertain. This paper analyses the expressive power of two possibilistic counterparts of Jeffrey’s rule for modeling belief revision in intelligent agents. We show that this rule can be used to recover most of the existing approaches proposed in knowledge base revision, such as adjustment, natural belief revision, drastic belief revision, revision of an epistemic by another epistemic state. In addition, we also show that that some recent forms of revision, namely improvement operators, can also be recovered in our framework.

Keywords

Intelligent Agent Epistemic State Belief Revision Belief Change Possibility Distribution 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ben Amor, N., Benferhat, S., Dubois, D., Geffner, H., Prade, H.: Independence in qualitative uncertainty frameworks. In: Seventh International Conference on Principles of Knowledge Representation and Reasoning KR2000, Breckenridge, Colorado, pp. 235–246. Morgan Kaufmann, San Francisco (2000)Google Scholar
  2. 2.
    Benferhat, S., Dubois, D., Prade, H., Williams, M.-A.: A practical approach to revising prioritized knowledge bases. Studia Logica Journal 70, 105–130 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Benferhat, S., Konieczny, S., Papini, O., Pino Pérez, R.: Iterated revision by epistemic states: axioms, semantics and syntax. In: Proc. of the 14th European Conf. on Artificial Intelligence (ECAI 2000), Berlin, Allemagne, August 2000, pp. 13–17. IOS Press, Amsterdam (2000)Google Scholar
  4. 4.
    Boutilier, C.: Revision Sequences and Nested Conditionals. In: Proc. of the 13th Inter. Joint Conf. on Artificial Intelligence (IJCAI 1993), pp. 519–531 (1993)Google Scholar
  5. 5.
    Chan, H., Darwiche, A.: On the revision of probabilistic beliefs using uncertain evidence. Artificial Intelligence 163, 67–90 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Darwiche, A., Pearl, J.: On the logic of iterated revision. Artificial Intelligence 89, 1–29 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Dubois, D., Prade, H.: Updating with belief functions, ordinal conditional functions and possibility measures. In: Bonissone, P.P., Henrion, M., Kanal, L.N., Lemmer, J.F. (eds.) Uncertainty in Artificial Intelligence 6, pp. 311–329. Elsevier Science Publ. B.V., Amsterdam (1991)Google Scholar
  8. 8.
    Dubois, D., Prade, H.: A synthetic view of belief revision with uncertain inputs in the framework of possibility theory. Int. J. Approx. Reasoning 17, 295–324 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dubois, D., Prade, H.: Possibility theory: qualitative and quantitative aspects. In: Gabbay, D., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems. Quantified Representation of Uncertainty and Imprecision, vol. 1, pp. 169–226 (1998)Google Scholar
  10. 10.
    Dubois, D.: Three scenarios for the revision of epistemic states. J. Log. Comput. 18(5), 721–738 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Dubois, D., Fargier, H., Prade, H.: Ordinal and probabilistic representations of acceptance. J. Artif. Intell. Res. (JAIR) 22, 23–56 (2004)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Gärdenfors, P.: Knowledge in Flux: Modeling the Dynamics of Epistemic States. Bradford Books, MIT Press, Cambridge (1988)zbMATHGoogle Scholar
  13. 13.
    Jeffrey, R.C.: The logic of decision. Mc. Graw Hill, New York (1965)Google Scholar
  14. 14.
    Konieczny, S., Pino Pérez, R.: A framework for iterated revision. Journ. of Applied Non-Classical Logics 10(3-4) (2000)Google Scholar
  15. 15.
    Konieczny, S., Pino Perez, R.: Improvement operators. In: 11th International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), pp. 177–186 (2008)Google Scholar
  16. 16.
    Makinson, D.: General patterns in nonmonotonic inference. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A., Nute, D. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 35–110. Oxford University Press, Oxford (1994)Google Scholar
  17. 17.
    Nayak, A.: Iterated belief change based on epistemic entrenchment. Erkenntnis 41, 353–390 (1994)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Nebel, B.: Base revision operations and schemes: semantics, representation, and complexity. In: Proceedings of the Eleventh European Conference on Artificial Intelligence (ECAI 1994), pp. 341–345 (1994)Google Scholar
  19. 19.
    Papini, O.: Iterated revision operations stemming from the history of an agent’s observations. Frontiers of Belief Revision (to appear, 2000)Google Scholar
  20. 20.
    Spohn, W.: Ordinal conditiona functions: a dynamic theory of epistemic states. Causation in Decision, Belief Change, and Statistics 2, 105–134 (1988)CrossRefGoogle Scholar
  21. 21.
    Thielscher, M.: Handling implicational and universal quantification constraints in flux. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 667–681. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  22. 22.
    Williams, M.A.: Transmutations of Knowledge Systems. In: Doyle, J., et al. (eds.) Inter. Conf. on principles of Knowledge Representation and reasoning (KR 1994), pp. 619–629. Morgan Kaufmann, San Francisco (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Salem Benferhat
    • 1
  • Didier Dubois
    • 2
  • Henri Prade
    • 2
  • Mary-Anne Williams
    • 3
  1. 1.CRIL-CNRS, UMR 8188, Faculté Jean PerrinUniversité d’ArtoisLensFrance
  2. 2.IRITUniversité Paul SabatierToulouse cedex 09France
  3. 3.Innovation and Enterprise Research LaboratoryUniversity of TechnologySydneyAustralia

Personalised recommendations