Structural semigraphoids

International Journal of General Systems

Volumn 22, Issue 2, 1993, Pages 207-217

  Studený, Milan ^a  

^a INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Conditional independence; dependency model; semigraphoid; skeletal imsct; structural face; structural semigraphoid

Indexed keywords

GRAPH THEORY; INFERENCE ENGINES; KNOWLEDGE BASED SYSTEMS; LOGIC PROGRAMMING; PROBABILITY; RANDOM PROCESSES;

CONDITIONALLY INDEPENDENT STRUCTURES; INFERENCE RULES; PROBABILISTIC EXPERT SYSTEMS; STOCHASTIC CONDITIONAL INDEPENDENCE; STRUCTURAL SEMIGRAPHOIDS;

EXPERT SYSTEMS;

EID: 0028018647     PISSN: 03081079     EISSN: 15635104     Source Type: Journal    
DOI: 10.1080/03081079308935207     Document Type: Article

References (20)

1. Aigner, M. [1979], Combinatorial Theory. Springer-Verlag, Berlin-Heidelberg-New York.
2. Dawid, A. P. [1979], “Conditional independence in statistical theory ” Journal of the Royal Statistical Society B, 41, pp. 1-31.
3. Geiger, D. and Pearl, J. [1989], “Logical and algorithmic properties of conditional independence.” Proceedings of 2nd International Workshop on Artificial Intelligence and Statistics, January 4-7, 1989, Fort Lauderdale, Florida.
4. Geiger. D. and Pearl, J. [1993], “Logical and algorithmic properties of conditional independence and graphical models.”, to appear in Annals of Statistics.
5. Matüš, F. [1993], “Probabilistic conditional independence structures and matroid theory: backgrounds.” International Journal of General Systems, 4, pp. 95-106.
6. Mouchart, M. and Rolin, J.-M. [1984], “A note on conditional independence with statistical application.” Statistica XLIV (4), pp, 557-584.
7. Pearl, J. and Paz, A. [1985], “Graphoids, a graph-based logic for reasoning about relevance relations.” technical report 850038, R-53 UCLA Computer Science Department, October 1985 also in Advances in Artificial Intelligence-II, edited by B. Du Boulay at al. Amsterdam, North-Holland 1986.
8. Pearl, J. [1986], “Markov and Bayes networks: a comparison of two graphical representations of probabilistic knowledge.” technical report CSD 860024, R-46-1, University of California, Los Angeles 1986.
9. Shapley, L. S. [1972], “Cores.of convex games.” international Journal of Game Theory, 1, pp. II-26.
10. Smith J. Q. [1989], “Influence diagrams for statistical modelling.” The annals of Statistics, 17 (2), pp. 654-672.
11. Spiegelhalter, D. J. and Lauritzen, S. L. [1990], “Sequential updating of conditional probabilities on directed graphical structures.” Networks, 20 (5), pp. 579-605.
12. Studenya, M. [1989a]. “Multiinformation and the problem of characterization of conditional independence relations.” Problems of control and Information Theory, 18 (1), pp. 3-16
13. Studenya, M. [1989b], “Attempts at axiomatic descriptions of conditional independence.” Kybernetika, 25 (supplement to n. 3), pp. 72-79.
14. Studenya, M. [1991], “Convex set functions II.” research report n. 1734, Institute if Information Theory and Automation, November 1991.
15. Studenya, M. [1992], “Conditional independence relations have no finite complete characterization.” Trans. of 11th Prague Conference on Information Theory. Statistical Functions and Random Processes col. B, pp. 377-396, Academia, Prague.
16. Studenya, M. [1993a], “Description of conditional independence structures by means of imsets: a connection with product formula validity.” in B. Bouchon-Meunier, L. Valverde, R.R. Yager eds.: Uncertainty in Intelligent Systems, Elsevier, pp. 179-194.
17. Studenya, M. [1993b], “Description of structures of stochastic conditional independence by means of face and imsets 1st part: introduction and basic concepts.” submitted to International Journal of General Systems.
18. Studenya, M. [1993c], Description of structures of stochastic conditional independence by means of face and imsets 2nd part: basic theory,” submitted to International Journal of General Systems.
19. Studenya, M. [1993d], Description of structures of stochastic conditional independence by means of face and imsets 3rd part: example os use and appendices.” submitted to International Journal of General Systems.
20. Ui, S. Paz, A. [1993], “The representation power of probabilistic knowledge by undirected graphs and directed acyclic graphs: a comparison.” International Journal of General Systems. 4, pp. 129-141