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Revision over Partial Pre-orders: A Postulational Study

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Scalable Uncertainty Management (SUM 2012)

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

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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.

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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)

    Article  MATH  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)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  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)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  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)

    Article  MathSciNet  MATH  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)

    Article  MathSciNet  MATH  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)

    Article  MathSciNet  MATH  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)

    Article  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)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  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)

    Article  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)

    Chapter  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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Author information

Authors and Affiliations

  1. School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Belfast, BT7 1NN, UK

    Jianbing Ma & Weiru Liu

  2. CRIL-CNRS, UMR 8188, Faculté Jean Perrin, Université d’Artois, rue Jean Souvraz, 62307, Lens, France

    Salem Benferhat

Authors
  1. Jianbing Ma
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  2. Salem Benferhat
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  3. Weiru Liu
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Editors and Affiliations

  1. Department of Mathematics and Computer Science, Marburg University, Hans-Meerwein-Strasse 6, 35032, Marburg, Germany

    Eyke Hüllermeier , Thomas Fober  & Bernhard Seeger ,  & 

  2. Department of Computer Science, Auckland University, 38 Princes St., 1010, Auckland, New Zealand

    Sebastian Link

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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

  • Print ISBN: 978-3-642-33361-3

  • Online ISBN: 978-3-642-33362-0

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