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.
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
Fagin, R. (1977): Multivalued Dependencies and a new Normal Form for relational Databases. ACM Transactions on Database Systems, 2, pp. 262–278.
Fagin, R. (1983): Degrees of Acyclicity for Hypergraphs and Relational Database Schemes. Journ. ACM, 30 (3), pp. 514–550.
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.
Kahneman, D., Slovic, P., Tversky, A. (eds., 1982): Judgment under Uncertainty: Heuristics and Biases. New York, Cambridge University Press.
Kohlas, J., Monney, M. (1990): Propagating Belief Functions through Constraint Systems. FAW, U. Ulm, Tech. Rep. TR-90002.
Kong, A. (1986): Multivariate Belief Functions and graphical Models; Diss., Dept. of Statistics, Harvard University.
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.
Mellouli,K. (1987): On the Propagation of beliefs in networks using the Dempster/Shafer theory of evidence; Diss., Sch. of. Business, U. of Kansas.
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.
Ozsoyoglu, Z.M., Yuan, L.-Y. (1987): A new normal Form for Nested Relations. ACM Transactions on Database Systems, 12, pp. 111–136.
Pearl, J. (1988): Probabilistic Reasoning in intelligent Systems: Networks of Plausible Inference. Morgan Kaufman, San Mateo, CA.
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.
Shafer, G. (1976): A mathematical Theory of Evidence. Princeton, Princeton University Press.
Shafer, G., Shenoy, P., Mellouli, K. (1987): Propagating Belief Functions in Qualitative Markov Trees. Int. Journ. of Approximate Reasoning, 1 (4), pp. 349–400.
Shenoy, P. (1989): A valuation-based language for expert systems, Int. Journ. of Approximate Reasoning, 3 (5), pp. 383–411.
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.
Smets, P. (1986): Belief Functions and Generalized Bayes Theorem. Preprints of the 2nd IFSA Congress, Gakushuin University, Tokyo, pp. 404–407.
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.
Spies, M. (1991): Evidential Reasoning with Conditional Events (submitted).
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).
Zadeh, L. (1978): Fuzzy Sets as a basis of a theory of possibility, Fuzzy Sets and Systems, 1, pp. 3–28.
Author information
Authors and Affiliations
Editor information
Rights 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