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Revision over Partial Pre-orders: A Postulational Study

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7520)

Abstract

Belief revision is the process that incorporates, in a consistent way, a new piece of information, called input, into a belief base. When both belief bases and inputs are propositional formulas, a set of natural and rational properties, known as AGM postulates, have been proposed to define genuine revision operations. This paper addresses the following important issue : How to revise a partially pre-ordered information (representing initial beliefs) with a new partially pre-ordered information (representing inputs) while preserving AGM postulates? We first provide a particular representation of partial pre-orders (called units) using the concept of closed sets of units. Then we restate AGM postulates in this framework by defining counterparts of the notions of logical entailment and logical consistency. In the second part of the paper, we provide some examples of revision operations that respect our set of postulates. We also prove that our revision methods extend well-known lexicographic revision and natural revision for both cases where the input is either a single propositional formula or a total pre-order.

Keywords

  • Epistemic State
  • Belief Revision
  • Belief Base
  • Belief Change
  • Propositional Formula

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. Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet functions for contraction and revision. Symb. Log. 50, 510–530 (1985)

    MATH  CrossRef  Google Scholar 

  2. Benferhat, S., Dubois, D., Prade, H.: Representing default rules in possibilistic logic. In: Procs. of KR, pp. 673–684 (1992)

    Google Scholar 

  3. Benferhat, S., Konieczny, S., Papini, O., Pérez, R.P.: Iterated revision by epistemic states: Axioms, semantics and syntax. In: Proc. of ECAI 2000, pp. 13–17 (2000)

    Google Scholar 

  4. Benferhat, S., Lagrue, S., Papini, O.: Revision of partially ordered information: Axiomatization, semantics and iteration. In: IJCAI 2005, pp. 376–381 (2005)

    Google Scholar 

  5. Bochman, A.: A logical theory of nonmonotonic inference and belief change. Springer (2001)

    Google Scholar 

  6. Boutilier, C.: Revision sequences and nested conditionals. In: Procs. of IJCAI, pp. 519–525. Morgan Kaufmann Publishers Inc., San Francisco (1993)

    Google Scholar 

  7. Chan, H., Darwiche, A.: On the revision of probabilistic beliefs using uncertain evidence. Artif. Intell. 163(1), 67–90 (2005)

    MathSciNet  MATH  CrossRef  Google Scholar 

  8. Darwiche, A., Pearl, J.: On the logic of iterated belief revision. Artificial Intelligence 89, 1–29 (1997)

    MathSciNet  MATH  CrossRef  Google Scholar 

  9. Dubois, D., Moral, S., Prade, H.: Belief change rules in ordinal and numerical uncertainty theories. Handbook of Defeasible Reasoning and Uncertainty Management Systems 3, 311–392 (1998)

    MathSciNet  Google Scholar 

  10. Fermé, E., Hansson, S.O. (eds.): Journal of Philosophical Logic. Special Issue on 25 Years of AGM Theory, vol. 40(2). Springer, Netherlands (2011)

    Google Scholar 

  11. Hunter, A., Konieczny, S.: Shapley inconsistency values. In: Proc. of KR 2006, pp. 249–259 (2006)

    Google Scholar 

  12. Jeffrey, R.: The logic of decision, 2nd edn. Chicago University Press (1983)

    Google Scholar 

  13. Jin, Y., Thielscher, M.: Iterated belief revision, revised. Artificial Intelligence 171, 1–18 (2007)

    MathSciNet  MATH  CrossRef  Google Scholar 

  14. Katsuno, H., Mendelzon, A.O.: Propositional knowledge base revision and minimal change. Artificial Intelligence 52, 263–294 (1991)

    MathSciNet  MATH  CrossRef  Google Scholar 

  15. Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001)

    MATH  CrossRef  Google Scholar 

  16. Kern-Isberner, G.: Handling conditionals adequately in uncertain reasoning and belief revision. Journal of Applied Non-Classical Logics 12(2), 215–237 (2002)

    MathSciNet  MATH  CrossRef  Google Scholar 

  17. Kern-Isberner, G., Krümpelmann, P.: A constructive approach to independent and evidence retaining belief revision by general information sets. In: Procs. of IJCAI, pp. 937–942 (2011)

    Google Scholar 

  18. Konieczny, S., Pérez, R.P.: Improvement operators. In: Procs. of KR, pp. 177–187 (2008)

    Google Scholar 

  19. Kourousias, G., Makinson, D.: Parallel interpolation, splitting, and relevance in belief change. J. Symb. Log. 72(3), 994–1002 (2007)

    MathSciNet  MATH  CrossRef  Google Scholar 

  20. Lang, J., van der Torre, L.: From belief change to preference change. In: Procs. of ECAI, pp. 351–355 (2008)

    Google Scholar 

  21. Ma, J., Benferhat, S., Liu, W.: Revising partial pre-orders with partial pre-orders: A unit-based revision framework. In: (Short paper) Procs. of KR (2012)

    Google Scholar 

  22. Ma, J., Liu, W.: A general model for epistemic state revision using plausibility measures. In: Procs. of ECAI, pp. 356–360 (2008)

    Google Scholar 

  23. Ma, J., Liu, W.: Modeling belief change on epistemic states. In: Proc. of 22th Flairs, pp. 553–558. AAAI Press (2009)

    Google Scholar 

  24. Ma, J., Liu, W.: A framework for managing uncertain inputs: An axiomization of rewarding. Inter. Journ. of Approx. Reasoning 52(7), 917–934 (2011)

    MathSciNet  MATH  CrossRef  Google Scholar 

  25. Ma, J., Liu, W., Benferhat, S.: A belief revision framework for revising epistemic states with partial epistemic states. In: Procs. of AAAI 2010, pp. 333–338 (2010)

    Google Scholar 

  26. Ma, J., Liu, W., Dubois, D., Prade, H.: Revision rules in the theory of evidence. In: Procs. of ICTAI, pp. 295–302 (2010)

    Google Scholar 

  27. Ma, J., Liu, W., Dubois, D., Prade, H.: Bridging jeffrey’s rule, agm revision and dempster conditioning in the theory of evidence. International Journal on Artificial Intelligence Tools 20(4), 691–720 (2011)

    CrossRef  Google Scholar 

  28. Ma, J., Liu, W., Hunter, A.: Modeling and reasoning with qualitative comparative clinical knowledge. International Journal of Intelligent Systems 26(1), 25–46 (2011)

    MATH  CrossRef  Google Scholar 

  29. Nayak, A.C.: Iterated belief change based on epistemic entrenchment. Erkenntnis 41, 353–390 (1994)

    MathSciNet  CrossRef  Google Scholar 

  30. Nayak, A.C., Pagnucco, M., Peppas, P.: Dynamic belief revision operators. Artificial Intelligence 146, 193–228 (2003)

    MathSciNet  MATH  CrossRef  Google Scholar 

  31. Spohn, W.: Ordinal conditional functions: A dynamic theory of epistemic states. Causation in Decision, Belief Change, and Statistics 2, 105–134 (1988)

    CrossRef  Google Scholar 

  32. Tamargo, L.H., Falappa, M.A., García, A.J., Simari, G.R.: A Change Model for Credibility Partial Order. In: Benferhat, S., Grant, J. (eds.) SUM 2011. LNCS, vol. 6929, pp. 317–330. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  33. Williams, M.A.: Transmutations of knowledge systems. In: Proc. of KR 1994, pp. 619–629 (1994)

    Google Scholar 

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Ma, J., Benferhat, S., Liu, W. (2012). Revision over Partial Pre-orders: A Postulational Study. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds) Scalable Uncertainty Management. SUM 2012. Lecture Notes in Computer Science(), vol 7520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33362-0_17

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  • DOI: https://doi.org/10.1007/978-3-642-33362-0_17

  • Publisher Name: Springer, Berlin, Heidelberg

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