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International Conference on Computational Intelligence

Fuzzy Days 2001: Computational Intelligence. Theory and Applications pp 194–217Cite as

Representing and Learning Conditional Information in Possibility Theory

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2206))

Abstract

Conditionals (if-then-rules, default rules) are most important objects in knowledge representation and commonsense reasoning. Due to their non-classical nature, however, they are not easily dealt with. In this paper, we present a new approach to represent conditionals inductively in a possibilistic framework. The algebraic theory which underlies this approach proves to guarantee a most appropriate handling of conditional information. Moreover, this novel conditional theory is a very fundamental one, in that it can also be applied to guide possibilistic belief revision and gives rise to a new methodology to learn rules from data.

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References

  1. S. Benferhat, D. Dubois, and H. Prade. Nonmonotonic reasoning, conditional objects and possibility theory. Artificial Intelligence, 92:259–276, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Benferhat, D. Dubois, and H. Prade. Possibilistic and standard probabilistic semantics of conditional knowledge bases. Journal of Logic and Computation, 9(6):873–895, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. Boutilier and M. Goldszmidt. Revision by conditional beliefs. In Proceedings 11th National Conference on Artificial Intelligence (AAAI’93), pages 649–654, Washington, DC., 1993.

    Google Scholar 

  4. S. Benferhat, A. Saffiotti, and P. Smets. Belief functions and default reasoning. Artificial Intelligence, 122:1–69, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  5. P.G. Calabrese. Deduction and inference using conditional logic and probability. In I.R. Goodman, M.M. Gupta, H.T. Nguyen, and G.S. Rogers, editors, Conditional Logic in Expert Systems, pages 71–100. Elsevier, North Holland, 1991.

    Google Scholar 

  6. B. DeFinetti. Theory of Probability, volume 1,2. John Wiley and Sons, New York, 1974.

    Google Scholar 

  7. D. Dubois, I.R. Goodman, and P.G. Calabrese. Special issue on the conditional event algebra. IEEE Transactions on Systems, Man, and Cybernetics, 24(12), 1994.

    Google Scholar 

  8. D. Dubois, J. Lang, and H. Prade. Possibilistic logic. In D.M. Gabbay, C.H. Hogger, and J.A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, volume 3, pages 439–513. Oxford University Press, 1994.

    Google Scholar 

  9. D. Dubois and H. Prade. Conditional objects and non-monotonic reasoning. In Proceedings 2nd Int. Conference on Principles of Knowledge Representation and Reasoning (KR’91), pages 175–185. Morgan Kaufmann, 1991.

    Google Scholar 

  10. D. Dubois and H. Prade. Conditioning, non-monotonic logic and nonstandard uncertainty models. In I.R. Goodman, M.M. Gupta, H.T. Nguyen, and G.S. Rogers, editors, Conditional Logic in Expert Systems, pages 115–158. Elsevier, North Holland, 1991.

    Google Scholar 

  11. D. Dubois and H. Prade. Epistemic entrenchment and possibilistic logic. Artificial Intelligence, 50:223–239, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Dubois and H. Prade. A survey of belief revision and updating rules in various uncertainty models. Intern. Journal of Intelligent Systems, 9:61–100, 1994.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  14. N. Friedman and J.Y. Halpern. Conditional logics of belief change. In Proceedings 12th National Conference on Artificial Intelligence, AAAI-94, 1994.

    Google Scholar 

  15. J. Gebhardt and R. Kruse. Background and perspectives of possibilistic graphical models. In Proceedings First International Joint Conference on Qualitative and Quantitative Practical Reasoning, ECSQARU-FAPR’97,, pages 108–121. Springer, 1997.

    Google Scholar 

  16. M. Goldszmidt, P. Morris, and J. Pearl. A maximum entropy approach to nonmonotonic reasoning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(3):220–232, 1993.

    Article  Google Scholar 

  17. I.R. Goodman and H.T. Nguyen. Conditional objects and the modeling of uncertainties. In M.M. Gupta and T. Yamakawa, editors, Fuzzy Computing — Theory, Hardware and Applications, pages 119–138. North-Holland, 1988.

    Google Scholar 

  18. G. Kern-Isberner. Characterizing the principle of minimum cross-entropy within a conditional-logical framework. Artificial Intelligence, 98:169–208, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  19. G. Kern-Isberner. A unifying framework for symbolic and numerical approaches to nonmonotonic reasoning and belief revision. Department of Computer Science, FernUniversität Hagen, 1999. Habilitation thesis.

    Google Scholar 

  20. G. Kern-Isberner. Conditional preservation and conditional indifference (preliminary version). In Proceedings 8th International Workshop on Nonmonotonic Reasoning (NMR’2000), Breckenridge, Colorado, 2000.

    Google Scholar 

  21. G. Kern-Isberner. Solving the inverse representation problem. In Proceedings 14th European Conference on Artificial Intelligence, ECAI’2000, pages 581–585, Berlin, 2000. IOS Press.

    Google Scholar 

  22. G. Kern-Isberner. Conditionals in nonmonotonic reasoning and belief revision. Springer, Lecture Notes in Artificial Intelligence, 2001. (to appear).

    Google Scholar 

  23. G. Kern-Isberner. Handling conditionals adequately in uncertain reasoning. In Proceedings ECSQARU’01, 2001. (to appear).

    Google Scholar 

  24. H. Katsuno and K. Satoh. A unified view of consequence relation, belief revision and conditional logic. In Proceedings Twelfth International Joint Conference on Artificial Intelligence, IJCAI-91, pages 406–412, 1991.

    Google Scholar 

  25. D. Lewis. Probabilities of conditionals and conditional probabilities. The Philosophical Review, 85:297–315, 1976.

    Article  Google Scholar 

  26. D. Lehmann and M. Magidor. What does a conditional knowledge base entail? Artificial Intelligence, 55:1–60, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  27. R.C. Lyndon and P.E. Schupp. Combinatorial group theory. Springer, Berlin Heidelberg New York, 1977.

    MATH  Google Scholar 

  28. D. Nute. Topics in Conditional Logic. D. Reidel Publishing Company, Dordrecht, Holland, 1980.

    MATH  Google Scholar 

  29. H.T. Nguyen and E.A. Walker. A history and introduction to the algebra of conditional events and probability logic. IEEE Transactions on Systems, Man, and Cybernetics, 24(12):1671–1675, 1994.

    Article  MathSciNet  Google Scholar 

  30. J.B. Paris. The uncertain reasoner’s companion — A mathematical perspective. Cambridge University Press, 1994.

    Google Scholar 

  31. H. Rott. A nonmonotonic conditional logic for belief revision, part I: Semantics and logic of simple conditionals. In A. Fuhrmann and M. Morreau, editors, The logic of theory change, pages 135–181. Springer, Berlin, Heidelberg, New York, 1991.

    Chapter  Google Scholar 

  32. W. Spohn. Ordinal conditional functions: a dynamic theory of epistemic states. In W.L. Harper and B. Skyrms, editors, Causation in Decision, Belief Change, and Statistics, II, pages 105–134. Kluwer Academic Publishers, 1988.

    Google Scholar 

  33. E.A. Walker. Stone algebras, conditional events, and three valued logic. IEEE Transactions on Systems, Man, and Cybernetics (Special Issue on The Conditional Event Algebra), 24(12):1699–1707, 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, FernUniversität Hagen, P.O. Box 940, D-58084, Hagen, Germany

    Gabriele Kern-Isberner

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  1. Gabriele Kern-Isberner
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Editor information

Editors and Affiliations

  1. Computer Science I, University of Dortmund, 44221, Dortmund, Germany

    Bernd Reusch

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© 2001 Springer-Verlag Berlin Heidelberg

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Kern-Isberner, G. (2001). Representing and Learning Conditional Information in Possibility Theory. In: Reusch, B. (eds) Computational Intelligence. Theory and Applications. Fuzzy Days 2001. Lecture Notes in Computer Science, vol 2206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45493-4_24

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  • DOI: https://doi.org/10.1007/3-540-45493-4_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42732-2

  • Online ISBN: 978-3-540-45493-9

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