On the implication problem for probabilistic conditional independency

IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans.

Volumn 30, Issue 6, 2000, Pages 785-805

  Wong, S K M ^a   Butz, C J ^b   Wu, D ^a  

^a UNIVERSITY OF REGINA   (Canada)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER NETWORKS; EMBEDDED SYSTEMS; MARKOV PROCESSES; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; THEOREM PROVING;

BAYESIAN NETWORKS; EMBEDDED MULTIVALUED DEPENDENCY; PROBABILISTIC CONDITIONAL INDEPENDENCE;

RELATIONAL DATABASE SYSTEMS;

EID: 0034313525     PISSN: 10834427     EISSN: None     Source Type: Journal    
DOI: 10.1109/3468.895901     Document Type: Article

References (47)

1. S. Abiteboul, P. Fischer, and H. Schek, Nested Relations and Complex Objects in Databases. New York: Springer-Verlag, 1989, vol. 361.
2. W. W. Armstrong, "Dependency structures of database relationships," in Proc. IFIP 74. Amsterdam, The Netherlands, 1974, pp. 580-583.
3. C. Beeri, R. Fagin, and J. H. Howard, "A complete axiomatization for functional and multivalued dependencies in database relations," in Proc. ACM-SIGMOD Int. Conf. Management of Data, 1977, pp. 47-61.
4. C. Beeri, R. Fagin, D. Maier, and M. Yannakakis, "On the desirability of acyclic database schemes," J. ACM, vol. 30, no. 3, pp. 479-513, July 1983.
5. C. Berge, Graphs and Hypergraphs. Amsterdam, The Netherlands: North-Holland, 1976.
6. C. Boutiliere, N. Friedman, M. Goldszmidt, and D. Koller, "Context-specific independence inbayesian networks," in 12th Conf. Uncertainty in Artificial Intelligence. San Mateo, CA, 1996, pp. 115-123.
7. C. J. Butz and S. K. M. Wong, "Recovery protocols in multi-agent probabilistic reasoning systems," in Int. Database Engineering and Applications Symp.. Piscataway, NJ, 1999, pp. 302-310.
8. S. Ceri and G. Pelagatti, Distributed Databases: Principles & Systems. New York: McGraw-Hill, 1984.
9. E. F. Codd, "A relational model of data for large shared data banks," Commun. ACM, vol. 13, no. 6, pp. 377-387, June 1970.
10. A. P. Dawid and S. L. Lauritzen, "Hyper markov laws in the statistical analysis of decomposable graphical models," Ann. Stat., vol. 21, pp. 1272-1317, 1993.
11. R. Fagin, "Normal forms and relational database operators," in Proc. ACM-SIGMOD Int. Conf. Management of Data, 1979, pp. 153-160.
12. R. Fagin and M. Y Vardi, "The theory of data dependencies: A survey," in Mathematics of Information Processing: Proc. Symposia in Applied Mathematics, vol. 34, 1986, pp. 19-71.
13. D. Geiger and J. Pearl, "Logical and algorithmic properties of conditional independence," Univ. California, Tech. Rep. R-97-II-L, 1989.
14. _, "Logical and algorithmic properties of conditional independence and graphical models," Ann. Stat., vol. 21, no. 4, pp. 2001-2021, 1993.
15. D. Geiger, T. Verma, and J. Pearl, "Identifying independence in bayesian networks," Univ. California, Tech. Rep. R-116, 1988.
16. P. Hajek, T. Havranek, and R. Jirousek, Uncertain Information Processing in Expert Systems. Boca Raton, FL: CRC, 1992.
17. C. Herrmann, "On the undecidability of implications between embedded multivalued database dependencies," Inf. Comput., vol. 122, no. 2, pp. 221-235, 1995.
18. G. Jaeschke and H. J. Schek, "Remarks on the algebra on non first normal form relations," in Proc. 1st ACM SIGACT-SIGMOD Symp. Principles of Database Systems, 1982, pp. 124-138.
19. F. V. Jensen, S. L. Lauritzen, and K. G. Olesen, "Bayesian updating in causal probabilistic networks by local computation," Comput. Stat. Quarterly, vol. 4, pp. 269-282, 1990.
20. D. Koller and A. Pfeffer, "Object-oriented bayesian networks," in 13th Conf. Uncertainty in Artificial Intelligence. San Mateo, CA, 1997, pp. 302-313.
21. T. T. Lee, "An information-theoretic analysis of relational databases - Part I: Data dependencies and information metric," IEEE Trans. Software Eng., vol. SE-13, no. 10, pp. 1049-1061, 1987.
22. Y. E. Lien, "On the equivalence of database models," J. ACM, vol. 29, no. 2, pp. 336-362, Oct. 1982.
23. D. Maier, The Theory of Relational Databases. Rockville, MD: Principles of Computer Science, Computer Science, 1983.
24. D. Maier, A. O. Mendelzon, and Y. Sagiv, "Testing implications of data dependencies, "ACM Trans. Database Syst., vol. 4, no. 4, pp. 455-469, 1979.
25. F. Malvestuto, "A unique formal system for binary decompositions of database relations, probability distributions and graphs," Inf. Sci., vol. 59, pp. 21-52, 1992.
26. _, "A complete axiomatization of full acyclic join dependencies," Inf. Process. Lett., vol. 68, no. 3, pp. 133-139, 1998.
27. A. Mendelzon, "On axiomatizing multivalued dependencies in relational databases," Journal of the ACM, vol. 26, no. 1, pp. 37-44, 1979.
28. R. E. Neapolitan, Probabilistic Reasoning in Expert Systems. New York: Wiley, 1990.
29. D. Parker and K. Parsaye-Ghomi, "Inference involving embedded multivalued dependencies and transitive dependencies," in Proc. ACM-SIGMOD Int. Conf. Management of Data, 1980, pp. 52-57.
30. A. Paz, Membership algorithm for marginal independencies," Univ. California, Tech. Rep. CSD-880095, 1988.
31. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, CA: Morgan Kaufmann , 1988.
32. J. Pearl, D. Geiger, and T. Verma, "Conditional independence and its representations," Kybernetica, vol. 25, no. 2, pp. 33-44, 1989.
33. J. Pearl and A. Paz, "Graphoids: Graph-based logic for reasoning about relevance relations," Univ. California, Tech. Rep. R-53-L, 1985.
34. Y. Sagiv and F. Walecka, "Subset dependencies and a complete result for a subclass of embedded multivalued dependencies," J. ACM, vol. 20, no. 1, pp. 103-117, 1982.
35. G. Shafer, An axiomatic study of computation in hypertrees, , School of Business Working Papers 232, Univ. Kansas, 1991.
36. M. Studeny, "Multiinformation and the problem of characterization of conditional-independence relations," Problems of Control and Information Theory, vol. 18, no. 1, pp. 3-16, 1989.
37. _, "Conditional independence relations have no finite complete characterization," in 11th Prague Conf. Information Theory, Statistical Decision Foundation and Random Processes. Norwell, MA, 1990, pp. 377-396.
38. K. Tanaka, Y. Kambayashi, and S. Yajima, "Properties of embedded multivalued dependencies in relational databases," Trans. IECE Jpn., vol. E62, no. 8, pp. 536-543, 1979.
39. T. Verma and J. Pearl, "Causal networks: Semantics and expressiveness," in 4th Conf. Uncertainty in Artificial Intelligence, St. Paul, MN, 1988, pp. 352-359.
40. W. X. Wen, "From relational databases to belief networks," in 7th Conf. Uncertainty in Artificial Intelligence. San Mateo, CA, 1991, pp. 406-413.
41. S. K. M. Wong, "Testing implication of probabilistic dependencies," in 12th Conf. Uncertainty in Artificial Intelligence. San Mateo, CA, 1996, pp. 545-553.
42. _, "An extended relational data model for probabilistic reasoning," J. Intell Inf. Syst., vol. 9, pp. 181-202, 1997.
43. S. K. M. Wong and C. J. Butz, "Probabilistic reasoning in a distributed multi-agent environment," in 3rd Int. Conf. Multi-Agent Systems. Piscataway, NJ, 1998, pp. 341-348.
44. _, "Contextual weak independence in bayesian networks," in 15th Conf. Uncertainty in Artificial Intelligence. San Mateo, CA, 1999, pp. 670-679.
45. S. K. M. Wong, C. J. Butz, and Y. Xiang, "A method for implementing a probabilistic model as a relational database," in 11th Conf. Uncertainty in Artificial Intelligence. San Mateo, CA, 1995, pp. 556-564.
46. S. K. M. Wong and Z. W. Wang, "On axiomatization of probabilistic conditional independence," in 10th Conf. Uncertainty in Artificial Intelligence. San Mateo, CA, 1994, pp. 591-597.
47. Y. Xiang, "A probabilistic framework for cooperative multi-agent distributed interpretation and optimization of communication," Artif. Intell., vol. 87, pp. 295-342, 1996.