Skip to main content

Application aspects of qualitative conditional independence

  • 1. Mathematical Theory Of Evidence
  • Conference paper
  • First Online:
Uncertainty in Knowledge Bases (IPMU 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 521))

  • 150 Accesses

Abstract

Axiomatic properties of qualitative conditional independence are compared to those of a Bayesian belief network approach, and judged as to their applicational relevance. It is found that qualitative conditional independence uses weaker axioms and has a clear interpretation in terms of the algebra of non-first normal form relations, and that it can be extended to the recently defined conditional event reasoning.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beeri, C., Fagin, R., Howard, J. (1977): A complete Axiomatization for functional and Multivalued Dependencies in Database Relations. Int. Conf. Mgmt. od Data, ACM, NY, pp. 47–61.

    Google Scholar 

  2. Dubois, D., Prade, H. (1988): Conditioning in Possibility and Evidence Theories — A logical Viewpoint. In: B. Bouchon, L. Saitta, R. Yager (eds.): Uncertainty and Intelligent Systems (Proc. Second IPMU, Urbino 1988), 401–408.

    Google Scholar 

  3. Fagin, R. (1977): Multivalued Dependencies and a new Normal Form for relational Databases. ACM Transactions on Database Systems, 2, pp. 262–278.

    Article  Google Scholar 

  4. Fagin, R. (1983): Degrees of Acyclicity for Hypergraphs and Relational Database Schemes. Journ. ACM, 30 (3), pp. 514–550.

    Article  Google Scholar 

  5. Fagin, R., Mendelzon, A.O., Ullman, J. (1982): A simplified universal Relation Assumption and Its Properties. ACM Transactions on Database Systems, 7 (3), pp. 343–360.

    Article  Google Scholar 

  6. Kahneman, D., Slovic, P., Tversky, A. (eds., 1982): Judgment under Uncertainty: Heuristics and Biases. New York, Cambridge University Press.

    Google Scholar 

  7. Kohlas, J., Monney, M. (1990): Propagating Belief Functions through Constraint Systems. FAW, U. Ulm, Tech. Rep. TR-90002.

    Google Scholar 

  8. Kong, A. (1986): Multivariate Belief Functions and graphical Models; Diss., Dept. of Statistics, Harvard University.

    Google Scholar 

  9. Lauritzen, S., Spiegelhalter, D. (1988): Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems. J. R. Statistical Society, 50, 2, pp. 157–224.

    Google Scholar 

  10. Mellouli,K. (1987): On the Propagation of beliefs in networks using the Dempster/Shafer theory of evidence; Diss., Sch. of. Business, U. of Kansas.

    Google Scholar 

  11. Goodman, I., Nguyen, H.: Conditional Objects and the Modeling of Uncertainties. In: M. Gupta, T. Yamakawa (eds.): Fuzzy Computing, North Holland, Amsterdam, pp. 119–138.

    Google Scholar 

  12. Ozsoyoglu, Z.M., Yuan, L.-Y. (1987): A new normal Form for Nested Relations. ACM Transactions on Database Systems, 12, pp. 111–136.

    Article  Google Scholar 

  13. Pearl, J. (1988): Probabilistic Reasoning in intelligent Systems: Networks of Plausible Inference. Morgan Kaufman, San Mateo, CA.

    Google Scholar 

  14. Sagiv, Y., Walecka, S. (1982): Subset Dependencies and a Completeness Result for a Subclas of Embedded Multivalued Dependencies. J. ACM, 29 (1), pp. 103–117.

    Article  Google Scholar 

  15. Shafer, G. (1976): A mathematical Theory of Evidence. Princeton, Princeton University Press.

    Google Scholar 

  16. Shafer, G., Shenoy, P., Mellouli, K. (1987): Propagating Belief Functions in Qualitative Markov Trees. Int. Journ. of Approximate Reasoning, 1 (4), pp. 349–400.

    Article  Google Scholar 

  17. Shenoy, P. (1989): A valuation-based language for expert systems, Int. Journ. of Approximate Reasoning, 3 (5), pp. 383–411.

    Article  Google Scholar 

  18. Shenoy, P., Shafer, G. (1990): Axioms for Probability and Belief-function Propagation. In: R.D. Shachter, T.S. Levitt, L.N. Kanal, J.F. Lemmer (eds.): Uncertainty in Artificial Intelligence, Vol. 4, pp. 169–198.

    Google Scholar 

  19. Smets, P. (1986): Belief Functions and Generalized Bayes Theorem. Preprints of the 2nd IFSA Congress, Gakushuin University, Tokyo, pp. 404–407.

    Google Scholar 

  20. Spies, M. (1988): A Model for the Management of imprecise Queries in relational Databases. in: B. Bouchon, L. Saitta, R. Yager (eds.): Uncertainty and Intelligent Systems. Springer Lecture Notes on Computer Science, vol. 313, Heidelberg; pp. 146–153.

    Google Scholar 

  21. Spies, M. (1991): Evidential Reasoning with Conditional Events (submitted).

    Google Scholar 

  22. Spies, M. (1990): Combination of Evidence with conditional objects and its application to cognitive modeling. In: I. Goodman, H. Nguyen, G., Rogers, M. Gupta (eds.): Conditional Logic in Expert Systems. North Holland (to appear).

    Google Scholar 

  23. Zadeh, L. (1978): Fuzzy Sets as a basis of a theory of possibility, Fuzzy Sets and Systems, 1, pp. 3–28.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Bernadette Bouchon-Meunier Ronald R. Yager Lotfi A. Zadeh

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Spies, M. (1991). Application aspects of qualitative conditional independence. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Uncertainty in Knowledge Bases. IPMU 1990. Lecture Notes in Computer Science, vol 521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028124

Download citation

  • DOI: https://doi.org/10.1007/BFb0028124

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54346-6

  • Online ISBN: 978-3-540-47580-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics