Applied Intelligence

, Volume 13, Issue 3, pp 265–283 | Cite as

A Symbolic Approach To Uncertainty Management

  • Mohamed Chachoua
  • Daniel Pacholczyk
Article

Abstract

In this paper, we present a new symbolic approach to deal with the uncertainty encountered in common-sense reasoning. This approach enables us to represent the uncertainty by using linguistic expressions of the interval [Certain, Totally uncertain]. The original uncertainty scale that we use here, presents some advantages over other scales in the representation and in the management of the uncertainty. The axioms of our theory are inspired by Shannon's entropy theory and built on the substrate of a symbolic many-valued logic. So, the uncertainty management in the symbolic logic framework leads to new generalizations of classical inference rules.

artificial intelligence uncertainty representation qualitative reasoning uncertainty management ignorance belief entropy many-valued logic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Hern´andez, Qualitative Representation of Spatial Knowledge, Springer Verlag: Berlin, 1994.Google Scholar
  2. 2.
    M. Chachoua and D. Pacholczyk, “Symbolic processing of the uncertainty of common-sense reasoning,” in International Conference on Knowledge Based Computer Systems KBCS'96, Juhu, December 1996, pp. 217–228.Google Scholar
  3. 3.
    M. Chachoua, “Une th´eorie d'entropie symbolique pour l'exploitation des informations incertaines,” in Actes des Rencontres des Jeunes Chercheurs en Intelligence Artificielle (RJCIA'98), Toulouse, September, 1998, pp. 65–74.Google Scholar
  4. 4.
    M. Chachoua, “Une Th´eorie Symbolique de l'Entropie pour le raitement des Informations Incertaines,” Ph.D Thesis, Universit´e d'Angers, 1998.Google Scholar
  5. 5.
    A. Kaufmann, Les logiques humaines et artificielles, Editions Herm`es, 1988.Google Scholar
  6. 6.
    D. Dubois, “Belif structure, possibility theory, decomposable confidence measures on finite sets,” Computer and Artificial Intelligence, vol. 5, no. 5, pp. 403–417, 1986.Google Scholar
  7. 7.
    S.D. Parsons, “Some elements of the theory of qualitative possibilistic networks,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 2, pp. 42–51, 1994.Google Scholar
  8. 8.
    D. Dubois, J. Lang, and H. Prade, “Possibilistic logic,” in Handbook of Logic in Artificial Intelligence and Logic Programming,edited by C.J. Hogger, D.M. Gabbay, and J.A. Robinson, Vol. 3, Clarendon Press: Oxford, UK, pp. 439–513, 1994.Google Scholar
  9. 9.
    S.D. Parsons and E.H. Mamdani, “Qualitative Dempster-Shafer theory,” in Proceedings of the IMACS III, International Workshop on Qualitative Reasoning and Decision Technologies,1993, pp. 471–480.Google Scholar
  10. 10.
    L.J. Savage, The Foundations of Statistics, Wiley: New York, 1954.Google Scholar
  11. 11.
    P. G¨ardenfors, “Qualitative probability as an intensional logic,” Philosophical Logic, vol. 4, pp. 177–185, 1975.Google Scholar
  12. 12.
    M.P.Wellman, “Qualitative probabilistic networks for planning under uncertainty,” in Uncertainty in Artificial Intelligence 2, edited by J.F. Lemmer and L.N. Kanal, Elsevier Science: New York, pp. 197–217, 1988.Google Scholar
  13. 13.
    R. Aleliunas, “A new normative theory of probabilistic logic,” in Proceedings of CSCSI'88, 1988, pp. 67–74.Google Scholar
  14. 14.
    R. Aleliunas, “A Summary of a new normative theory of probabilistic logic,” in Uncertainty in Artificial Intelligence 4, edited by L.N. Kanal, R.D. Shachter, TS. Levtt, and J.F. Lemmer,Vol. 9, Elsevier Science Publishers: Amsterdam, pp. 199–206, 1990.Google Scholar
  15. 15.
    F. Bacchus, “A logic for statistical information,” in Uncertainty in Artificial Intelligence, edited by M. Henrion, R.D. Shachter, L.N. Kanal, and J.F. Lemmer, pp. 3–14, 1990.Google Scholar
  16. 16.
    F. Bacchus, Representing and Reasoning with Probabilistic Knowledge: A Logical Approach to Probabilities, MIT Press: London, 1990.Google Scholar
  17. 17.
    D. Pacholczyk, “Contribution au traitement logico-symbolique de la connaissance,” Th`ese d'´etat, Universit´e Pierre et Marie Curie, Paris, 6 April 1992.Google Scholar
  18. 18.
    A.Y. Darwiche and M.L. Ginsberg, “A symbolic generalization of probability theory,” in Proceedings of the American Association for Artificial Intelligence, 1992, pp. 622–627.Google Scholar
  19. 19.
    J. Pearl and M. Goldszmidt, “Qualitative probabilities for default reasoning, belief revision, and causal modeling,” Artificial Intelligence Journal, vol. 84, no. 2, pp. 57–112, 1996.Google Scholar
  20. 20.
    D. Lehmann, “Generalized qualitative probability: Savage revisited,” in Proceedings of the Twelfth Annual Conference on Uncertainty in Artificial Intelligence (UAI-96), Portland,Oregon, 1996, pp. 381–388.Google Scholar
  21. 21.
    H. Farreny, Les Syst`emes experts: principes et exemples, CEPADUES, 1985.Google Scholar
  22. 22.
    E. Kant, Logique, Librairie Philosophique J. Vrin: Paris, 1966.Google Scholar
  23. 23.
    C.E. Shannon, “A mathematical theory of communication,” Bell System Technical, vol. 27, pp. 379–423, 1948.Google Scholar
  24. 24.
    C.E. Shannon and W.Weaver, The Mathematical Theory of Communication, University of Illinois Press: Urbana, 1949.Google Scholar
  25. 25.
    A. De-Luca and S. Termini, “A definition of non-probabilistic entropy in the setting of fuzzy sets theory,” Information and Control, vol. 20, pp. 301–312, 1972.Google Scholar
  26. 26.
    G.J. Klir and T.A. Folger, Fuzzy Sets, Uncertainty and Information, Prentice-Hall: Upper Saddle River, NJ, 1988.Google Scholar
  27. 27.
    M. Chachoua and D. Pacholczyk, “Qualitative reasoning under uncertainty,” in 11th International FLAIRS Conference, Special Track Uncertain Reasoning, Florida, USA, 1998, pp. 415–419.Google Scholar
  28. 28.
    M. Chachoua and D. Pacholczyk, “Qualitative reasoning under uncertain knowledge,” in Volume 1: Methodology and Tools in Knowledge-Based Systems, IEA-98–AIE, edited by A.P. DelPobil, J. Mira, and M. Ali. Number 1415 in Lecture Notes in Computer Science, Spinger-Verlag: Berlin, 1998, pp. 377–386.Google Scholar
  29. 29.
    E.T. Jaynes, “On the rationale of maximum entropy methods,” IEEE, vol. 70, no. 9, pp. 939–952, 1982.Google Scholar
  30. 30.
    E.T. Jaynes, Probability Theory: The Logic of Science, Fragmentary Edition, 1995.Google Scholar
  31. 31.
    W.V.O. Quine, Le mot et la chose, Editions Flammarion, 1977.Google Scholar
  32. 32.
    N. Rescher, Many-Valued Logic, McGraw-Hill: New York, 1969.Google Scholar
  33. 33.
    H. Akdag, M. De-Glas, and D. Pacholczyk, “A qualitative theory of uncertainty,” Fundamenta Informaticae, vol. 17, no. 4, pp. 333–362, 1992.Google Scholar
  34. 34.
    D. Pacholczyk, “A new approach to vagueness and uncertainty,” CCAI, vol. 9, no. 4, pp. 395–435, 1992.Google Scholar
  35. 35.
    D. Pacholczyk, “A logico-symbolic probability theory for the management of uncertainty,” CCAI, vol. 11, no. 4, pp. 417–484, 1994.Google Scholar
  36. 36.
    V.S. Subrahmanian, “On the semantics of quantitative logic programs,” in Proceedings of 4th IEEE Symposium on Logic Programming, Computer Society Press, 1987, pp. 173–182.Google Scholar
  37. 37.
    M. Kifer and V.S. Subrahmanian, “Theory of generalized annotated logic,” Journal of Logic Programming, vol. 12, pp. 335–367, 1992.Google Scholar
  38. 38.
    F.S. Corrêa-Da-Silva and D.V. Carbogim, “A Two-sorted interpretation for annotated logic,” Technical Report RT-MAC-9801, Instituto de Matemàtica e Estat´stica da Universidade de Sâo Paulo, Brasil, February 1998.Google Scholar
  39. 39.
    D.V. Carbogim and F.S. Corrêa-Da-Silva, “Annotated logic: Applications for imperfect information,” Applied Intelligence, vol. 9, no. 2, pp. 163–172, 1998.Google Scholar
  40. 40.
    D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum: New York,1988.Google Scholar
  41. 41.
    B. Bouchon-Menier, La Logique floue et ses applications, Addison Wesley: Reading, MA, 1995.Google Scholar
  42. 42.
    L.A. Zadeh, “Fuzzy sets as a basis of a theory of possibility,” Fuzzy Sets and Systems, vol. 1, pp. 3–28, 1978.CrossRefGoogle Scholar
  43. 43.
    A.P. Dempster, “Upper and lower probabilities induced by a multivalued mapping,” Annals of Mathematical Statistics, vol. 38, pp. 325–339, 1967.Google Scholar
  44. 44.
    G. Shafer, A Mathematical Theory of Evidence, Princeton University Press: Princeton, NJ, 1976.Google Scholar
  45. 45.
    L. Isra¨el, La d´ecision m´edicale, Calmann-L´evy, 1980.Google Scholar
  46. 46.
    G. Tiberghien, Certitude et m´emoire, Les Editions du CNRS, 1971.Google Scholar
  47. 47.
    A. Tarski, Logique, s´emantique, m´eta-math´ematique, Vol. 1, Librairie Armand Colin, 1972.Google Scholar
  48. 48.
    M. De-Glas, “Knowledge representation in fuzzy setting,” Rapport interne, 89/48, LAFORIA, Paris, 1989.Google Scholar
  49. 49.
    L.A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338–353, 1965.Google Scholar
  50. 50.
    G.Doyon and P.Talbot, “La logique du raisonnement: th´eorie de l'inf´erence propositionnelle et application,” Editions Le Griffond'Argile, 1986.Google Scholar
  51. 51.
    G.J. Klir, “Measures of uncertainty in the Dempster-Shafer Theory of evidence,” in Advances in the Dempster-Shafer Theory of Evidence, edited by R.R. Yager, J. Kacprzyk, and M. Fedrizzi, J. Wiley: New York, pp. 35–49, 1994.Google Scholar
  52. 52.
    M. Tribus, D´ecisions rationnelles dans l'incertain, Editions Masson et Cie, 1972.Google Scholar
  53. 53.
    M. Goldszmidt, Qualitative probabilities: A normative framework for commonsense reasoning, Ph.D. Thesis, University ofCalifornia, Los Angeles, 1992.Google Scholar
  54. 54.
    A.J. Grove, J.Y. Halpern, and D. Koller, “Random world and maximum entropy,” Artificial Intelligence Research, vol. 2, pp. 33–88, 1994.Google Scholar
  55. 55.
    M. Schramm and S. Schultz, “Combining propositional logic with maximum entropy reasoning on probability models,” in Proceedings of ECAI96, 1996.Google Scholar
  56. 56.
    E. Weydert, “Qualitative entropy maximisation: A preliminary report,” in Proceedings of the Third Dutch/German Workshop on Nonmonotonic Reasoning Techniques and their Applications,Germany, February 1997, pp. 63–72.Google Scholar
  57. 57.
    P.C. Rhodes and G.R. Garside, “Maximum entropy for expert systems: The horns of a dilemma,” Technical Report CS-13–19, Internal Research Report, Department of Computing, University of Bradford, 1991.Google Scholar
  58. 58.
    C. Robert, Mod`eles statistiques pour l'IA: L'exemple du diagnostic m´edical, Editions Masson, 1991.Google Scholar
  59. 59.
    W. R¨odder and C.H. Meyer, “Coherent knowledge processing at maximum entropy by spirit,” in Proceedings of the Twelfth Annual Conference on Uncertainty in Artificial Intelligence (UAI-96), Portland, Oregon, 1996, pp. 470–476.Google Scholar
  60. 60.
    F.S. Corrêa-Da-Silva, “On reasoning with and reasoning about uncertainty in artificial intelligence,” in European Summer Meeting of the Association of Symbolic Logic, Spain, 1996.Google Scholar
  61. 61.
    J.B. Rosser and A.R. Turquette, Many-Valued Logics, North Holland: Amsterdam, 1958.Google Scholar
  62. 62.
    D. Sperber and D. Wilson, La pertinence: Communication et cognition, Les Editions de Minuit, 1989.Google Scholar
  63. 63.
    M.P. Wellman, “Some varieties of qualitative probability,” in Fifth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, July1994, pp.437–442.Google Scholar
  64. 64.
    E. Morin, La M´ethode: 1. La nature de la nature, Editions du Seuil, 1977.Google Scholar
  65. 65.
    J.P. Haton, N. Bouzid, F. Chapillet, B. Lâasri, M.C. Haton, H. Lâasri, P. Marquis, T. Mondot, and A. Napoli, Le raisonnement en intelligence artificielle: Mod`eles, techniques et rchitecture pour les syst`emes `a base de connaissances, Inter-Editions, 1991.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Mohamed Chachoua
    • 1
  • Daniel Pacholczyk
    • 2
  1. 1.Laboratoire d'informatique LERIAUniversité d'ANGERS, U.F.R SciencesAngers Cedex 01France
  2. 2.Laboratoire d'informatique LERIAUniversité d'ANGERS, U.F.R SciencesAngers Cedex 01France

Personalised recommendations