Abstract
Probabilistic methods provide a formalism for reasoning aboutpartial beliefs under conditions of uncertainty. This paper suggests a newrepresentation of probabilistic knowledge. This representation encompassesthe traditional relational database model. In particular, it is shown thatprobabilistic conditional independence is equivalent to the notion of generalized multivalued dependency. More importantly,a Markov network can be viewed as a generalized acyclic joindependency. This linkage between these two apparently different butclosely related knowledge representations provides a foundation fordeveloping a unified model for probabilistic reasoning and relationaldatabase systems.
Similar content being viewed by others
References
D. Barbará, H. Garcia-Molina and Daryl Porter, "The management of probabilistic data," IEEE Transactions on Knowledge and Data Engineering, vol. 4, no.5, pp. 487–502, 1992.
C. Beeri, R. Fagin, D. Maier and M. Yannakakis, "On the desirability of acyclic database schemes," Journal of the Association for Computing Machinery, vol. 30, no.3, pp. 479–513, 1983.
C. Berge, Graphs and Hypergraphs. North Holland, 1973.
G.F. Cooper, "The computational complexity of probabilistic inference using Bayesian belief networks," Artificial Intelligence, vol. 42, no.2-3, pp. 393–402, 1990.
R. Dechter, "Decomposing a Relation into a Tree of Binary Relations," Journal of Computer and System Sciences, vol. 41, pp. 2–24, 1990.
C. Delobel, "Normalization and hierarchical dependencies in the relational data model," ACM Transactions on Database Systems, vol. 3, no.3, pp. 201–222, 1978.
R. Fagin, A.O. Mendelzon and J.D. Ullman, "A simplified universal relation assumption and its properties," ACM Transactions on Database Systems, vol. 7, no.3, pp. 343–360, 1982.
R. Fagin, "Multivalued dependencies and a new normal form for relational databases," ACM Transactions on Database Systems, vol. 2, no.3, pp. 262–278, 1977.
P. Hajek, T. Havranek and R. Jirousek, Uncertain Information Processing in Expert Systems. CRC Press, 1992.
J. Hill, "Comment," Statistical Science, vol. 8, no.3, pp. 258–261, 1993.
F.V. Jensen, "Junction trees-a new characterization of decomposable hypergraphs," Research Report, JUDEX, Aalborg, Denmark, 1988.
R. Kruse, E. Schwecke and J. Heinsohn, Uncertainty and Vagueness in Knowledge Based Systems. Springer-Verlag, 1988.
S. Lauritzen and D. Spiegelhalter, "Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems," Journal of the Royal Statistical Society, B, vol. 50, No.2, pp. 157–224, 1988.
T.T. Lee, "An Algebraic Theory of Relational Databases," The Bell System Technical Journal, vol. 62, no.10, pp. 3159–3204, 1983.
T.T. Lee, "An information-theoretic analysis of relational databases-Part 1: data dependencies and information metric," IEEE Transactions on Software Engineering, vol. SE-13, no.10, pp. 1049–1061, 1987.
D. Maier, The Theory of Relational Databases. Computer Science Press, 1983.
R.E. Neapolitan, Probabilistic Reasoning in Expert Systems. John Wiley & sons, Inc., 1990.
J. Pearl, "Fusion, propagation and structuring in belief networks," Artificial Intelligence, vol. 29, no.3, pp. 241–288, 1986.
J. Pearl and T. Verma, "The Logic of Representing Dependencies by Directed Graphs," AAAI87 Sixth National Conference on Artificial Intelligence, vol. 1, pp. 374–379, 1987.
J. Pearl, Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, 1988.
G. Shafer, P. Shenoy and K. Mellouli, "Propagating Belief Functions in Qualitative Markov Trees," International Journal of Approximate Reasoning, vol. 1, pp. 349–400, 1987.
G. Shafer, "An axiomatic study of computation in hypertrees," School of Business Working Paper Series, (No. 232), University of Kansas, Lawrence, 1991.
S.K.M. Wong, C.J. Butz and Y. Xiang, "A method for implementing a probabilistic model as a relational database," Eleventh Conference on Uncertainty in Artificial Intelligence, pp. 556–564, 1995.
S.K.M. Wong, "Testing implication of probabilistic dependencies," Twelfth Conference on Uncertainty in Artificial Intelligence, pp. 545–553, 1996.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wong, S. An Extended Relational Data Model For Probabilistic Reasoning. Journal of Intelligent Information Systems 9, 181–202 (1997). https://doi.org/10.1023/A:1008603515938
Issue Date:
DOI: https://doi.org/10.1023/A:1008603515938