Axioms for Probability and Belief-Function Propagation

Machine Intelligence and Pattern Recognition

Volumn 9, Issue C, 1990, Pages 169-198

  Shenoy, Prakash P ^a   Shafer, Glenn ^a  

^a UNIVERSITY OF KANSAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85012737234     PISSN: 09230459     EISSN: None     Source Type: Book Series    
DOI: 10.1016/B978-0-444-88650-7.50019-6     Document Type: Chapter

References (39)

1. Arnborg, S., Corneil, D.G., Proskurowski, A., Complexity of finding embeddings in a k-tree. SIAM Journal of Algebraic and Discrete Methods 8 (1987), 277–284.
2. Berge, C., Minieka, E., (eds.) Graphs and Hypergraphs, 1973, North-Holland.
3. Bertele, U., Brioschi, F., Nonserial Dynamic Programming, 1972, Academic Press.
4. Brownston, L.S., Farrell, R.G., Kant, E., Martin, N., Programming Expert Systems in OPS5: An Introduction to Rule-Based Programming, 1985, Addison-Wesley.
5. Buchanan, B.G., Shortliffe, E.H., (eds.) Rule-based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project, 1984, Addison-Wesley.
6. Cannings, C., Thompson, E.A., Skolnick, M.H., Probability functions on complex pedigrees. Advances in Applied Probability 10 (1978), 26–61.
7. Darroch, J.N., Lauritzen, S.L., Speed, T.P., Markov fields and log-linear models for contingency tables. Annals of Statistics 8 (1980), 522–539.
8. Davis, R., and King, J. J. (1984), The origin of rule-based systems in AI, in Buchanan and Shortliffe [1984, 20–52].
9. Dempster, A.P., New methods for reasoning toward posterior distributions based on sample data. Annals of Mathematical Statistics 37 (1966), 355–374.
10. Dempster, A.P., Kong, A., Uncertain evidence and artificial analysis, 1986, Department of Statistics, Harvard University Research Report S-108.
11. Golumbic, M.C., Algorithmic Graph Theory and Perfect Graphs, 1980, Academic Press.
12. Hsia, Y., Shenoy, P.P., An evidential language for expert systems. Ras, Z., (eds.) Methodologies for Intelligent Systems, 4, 1989, North-Holland, 9–16.
13. Hsia, Y., Shenoy, P.P., MacEvidence: A visual evidential language for knowledge-based systems, 1989, School of Business, University of Kansas Working Paper No. 211.
14. Kelly, C.W. III, Barclay, S., A general Bayesian model for hierarchical inference. Organizational Behavior and Human Performance 10 (1973), 388–403.
15. Kong, A. (1986), Multivariate belief functions and graphical models, doctoral dissertation, Department of Statistics, Harvard University.
16. Lauritzen, S.L., Speed, T.P., Vijayan, K., Decomposable graphs and hypergraphs. Journal of the Australian Mathematical Society 36 (1984), 12–29 series A.
17. Lauritzen, S.L., Spiegelhalter, D.J., Local computations with probabilities on graphical structures and their application to expert systems (with discussion). Journal of the Royal Statistical Society 50:2 (1988), 157–224 series B.
18. Maier, D., The Theory of Relational Databases, 1983, Computer Science Press.
19. Mellouli, K. (1987), On the propagation of beliefs in networks using the Dempster-Shafer theory of evidence, doctoral dissertation, School of Business, University of Kansas.
20. Pearl, J., Fusion, propagation and structuring in belief networks. Artificial Intelligence 29 (1986), 241–288.
21. Rose, D.J., Triangulated graphs and the elimination process. Journal of Mathematical Analysis and Applications 32 (1970), 597–609.
22. Shachter, R.D., Heckerman, D., A backwards view for assessment. AI Magazine 8:3 (1987), 55–61.
23. Shafer, G., A Mathematical Theory of Evidence, 1976, Princeton University Press.
24. Shafer, G., Logan, R., Implementing Dempster's rule for hierarchical evidence. Artificial Intelligence 33 (1987), 271–298.
25. Shafer, G., Shenoy, P.P., Local computation in hypertrees, 1988, School of Business, University of Kansas Working Paper No. 201.
26. Shafer, G., Shenoy, P.P., Mellouli, K., Propagating belief functions in qualitative Markov trees. International Journal of Approximate Reasoning 1:4 (1987), 349–400.
27. Shafer, G., Shenoy, P. P. and Srivastava, R. P. (1988), AUDITOR'S ASSISTANT: A knowledge engineering tool for audit decisions, Auditing Symposium IX: Proceedings of the 1988 Touche Ross/University of Kansas Symposium on Auditing Problems, 61–84.
28. Shenoy, P.P., A valuation-based language for expert systems. International Journal of Approximate Reasoning 3:5 (1989), 383–411.
29. Shenoy, P.P., On Spohn's rule for revision of beliefs, 1989, School of Business, University of Kansas Working Paper No. 213.
30. Shenoy, P.P., Shafer, G., Propagating belief functions using local computations. IEEE Expert 1:3 (1986), 43–52.
31. Shenoy, P.P., Shafer, G., Axioms for discrete optimization using local computation, 1988, School of Business, University of Kansas Working Paper No. 207.
32. Shenoy, P.P., Shafer, G., Constraint propagation, 1988, School of Business, University of Kansas Working Paper No. 208.
33. Shenoy, P.P., Shafer, G., Mellouli, K., Propagation of belief functions: A distributed approach. Lemmer, J.F., Kanal, L.N., (eds.) Uncertainty in Artificial Intelligence 2, 1988, North-Holland, 325–336.
34. Spohn, W., Ordinal conditional functions: A dynamic theory of epistemic states. Harper, W.L., Skyrms, B., (eds.) Causation in Decision, Belief Change, and Statistics, II, 1988, D. Reidel Publishing Company, 105–134.
35. Spohn, W. (1990), A general non-probabilistic theory of inductive reasoning, this volume.
36. Tarjan, R.E., Yannakakis, M., Simple linear time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal of Computing 13 (1984), 566–579.
37. Zarley, D.K., An evidential reasoning system, 1988, School of Business, University of Kansas Working Paper No. 206.
38. Zarley, D.K., Hsia, Y. and Shafer, G. (1988), Evidential reasoning using DELIEF, Proceedings of the Seventh National Conference on Artificial Intelligence (AAAI-88), 1, 205–209, Minneapolis, MN.
39. Zhang, L., Studies on finding hypertree covers for hypergraphs, 1988, School of Business, University of Kansas Working Paper No. 198.