Skip to main content
SpringerLink
Log in

A Symbolic Approach To Uncertainty Management

  • Published:
Applied Intelligence Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Hern´andez, Qualitative Representation of Spatial Knowledge, Springer Verlag: Berlin, 1994.

  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.

  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.

  4. M. Chachoua, “Une Th´eorie Symbolique de l'Entropie pour le raitement des Informations Incertaines,” Ph.D Thesis, Universit´e d'Angers, 1998.

  5. A. Kaufmann, Les logiques humaines et artificielles, Editions Herm`es, 1988.

  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. 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. 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.

  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.

  10. L.J. Savage, The Foundations of Statistics, Wiley: New York, 1954.

  11. P. G¨ardenfors, “Qualitative probability as an intensional logic,” Philosophical Logic, vol. 4, pp. 177–185, 1975.

    Google Scholar 

  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.

  13. R. Aleliunas, “A new normative theory of probabilistic logic,” in Proceedings of CSCSI'88, 1988, pp. 67–74.

  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. 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.

  16. F. Bacchus, Representing and Reasoning with Probabilistic Knowledge: A Logical Approach to Probabilities, MIT Press: London, 1990.

    Google Scholar 

  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.

  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.

  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. 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.

  21. H. Farreny, Les Syst`emes experts: principes et exemples, CEPADUES, 1985.

  22. E. Kant, Logique, Librairie Philosophique J. Vrin: Paris, 1966.

  23. C.E. Shannon, “A mathematical theory of communication,” Bell System Technical, vol. 27, pp. 379–423, 1948.

    Google Scholar 

  24. C.E. Shannon and W.Weaver, The Mathematical Theory of Communication, University of Illinois Press: Urbana, 1949.

  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. G.J. Klir and T.A. Folger, Fuzzy Sets, Uncertainty and Information, Prentice-Hall: Upper Saddle River, NJ, 1988.

    Google Scholar 

  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.

  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.

  29. E.T. Jaynes, “On the rationale of maximum entropy methods,” IEEE, vol. 70, no. 9, pp. 939–952, 1982.

    Google Scholar 

  30. E.T. Jaynes, Probability Theory: The Logic of Science, Fragmentary Edition, 1995.

  31. W.V.O. Quine, Le mot et la chose, Editions Flammarion, 1977.

  32. N. Rescher, Many-Valued Logic, McGraw-Hill: New York, 1969.

    Google Scholar 

  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. D. Pacholczyk, “A new approach to vagueness and uncertainty,” CCAI, vol. 9, no. 4, pp. 395–435, 1992.

    Google Scholar 

  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. 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.

  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. 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.

  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. D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum: New York,1988.

  41. B. Bouchon-Menier, La Logique floue et ses applications, Addison Wesley: Reading, MA, 1995.

  42. L.A. Zadeh, “Fuzzy sets as a basis of a theory of possibility,” Fuzzy Sets and Systems, vol. 1, pp. 3–28, 1978.

    Article  Google Scholar 

  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. G. Shafer, A Mathematical Theory of Evidence, Princeton University Press: Princeton, NJ, 1976.

  45. L. Isra¨el, La d´ecision m´edicale, Calmann-L´evy, 1980.

  46. G. Tiberghien, Certitude et m´emoire, Les Editions du CNRS, 1971.

  47. A. Tarski, Logique, s´emantique, m´eta-math´ematique, Vol. 1, Librairie Armand Colin, 1972.

  48. M. De-Glas, “Knowledge representation in fuzzy setting,” Rapport interne, 89/48, LAFORIA, Paris, 1989.

  49. L.A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338–353, 1965.

    Google Scholar 

  50. G.Doyon and P.Talbot, “La logique du raisonnement: th´eorie de l'inf´erence propositionnelle et application,” Editions Le Griffond'Argile, 1986.

  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. M. Tribus, D´ecisions rationnelles dans l'incertain, Editions Masson et Cie, 1972.

  53. M. Goldszmidt, Qualitative probabilities: A normative framework for commonsense reasoning, Ph.D. Thesis, University ofCalifornia, Los Angeles, 1992.

  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. M. Schramm and S. Schultz, “Combining propositional logic with maximum entropy reasoning on probability models,” in Proceedings of ECAI96, 1996.

  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.

  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.

  58. C. Robert, Mod`eles statistiques pour l'IA: L'exemple du diagnostic m´edical, Editions Masson, 1991.

  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.

  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.

  61. J.B. Rosser and A.R. Turquette, Many-Valued Logics, North Holland: Amsterdam, 1958.

  62. D. Sperber and D. Wilson, La pertinence: Communication et cognition, Les Editions de Minuit, 1989.

  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.

  64. E. Morin, La M´ethode: 1. La nature de la nature, Editions du Seuil, 1977.

  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.

Download references

Author information

Authors and Affiliations

  1. Laboratoire d'informatique LERIA, Université d'ANGERS, U.F.R Sciences, 2, Boulevard Lavoisier, F-49045, Angers Cedex 01, France

    Mohamed Chachoua

  2. Laboratoire d'informatique LERIA, Université d'ANGERS, U.F.R Sciences, 2, Boulevard Lavoisier, F-49045, Angers Cedex 01, France

    Daniel Pacholczyk

Authors
  1. Mohamed Chachoua
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Pacholczyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chachoua, M., Pacholczyk, D. A Symbolic Approach To Uncertainty Management. Applied Intelligence 13, 265–283 (2000). https://doi.org/10.1023/A:1026572211922

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026572211922

Search

Navigation