M. Studeny: Formal properties of conditional independence in different calculi of AI. In Symbolic and Quantitative Approaches to Reasoning and Uncertainty (M. Clarke, R. Kruse, S. Moral eds.), Springer-Verlag, Berlin - Heidelberg 1993, pp. 341-348.

The paper is maily a survey with several examples, the main results are proved in references, in particular in the papers:
M. Studeny: Conditional independence and natural conditional functions. International Journal of Approximate Reasoning 12 (1995), n. 1, pp. 43-68.
M. Studeny: Conditional independence relations have no finite complete characterization. In Information Theory, Statistical Decision Functions and Random Processes. Transactions of the 11th Prague Conference vol. B (S. Kubik, J.A. Visek eds.), Kluwer, Dordrecht - Boston - London (also Academia, Prague) 1992, pp. 377-396.
Y. Sagiv and S.F. Walecka: Subset dependencies and completeness result for a subclass of embedded multivalued dependencies. Journal of the Association for Computing Machinery 29 (1982), n. 1, pp. 103-117.

The first part is devoted to the comparison of three different frameworks for study of conditional independence: probability theory, theory of relational databases and Spohn's theory of ordinal conditional functions. The given examples show that the formal properties of conditional independence arising in these areas differ each other. On the other hand, the same method can be used to show that there exists no finite complete axiomatic characterization of conditional independence models (within each of these frameworks). In the second part further frameworks for conditional independence are discussed: Dempster-Shafer's theory, possibility theory and (general) Shenoy's theory of valuation-based systems.

AMS classification 68T30, 68P15, 94D05

conditional independence
database relation
natural conditional function
possibility theory
Dempster Shafer's theory

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The paper builds on the following works: