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.), SpringerVerlag, Berlin 
Heidelberg 1993, pp. 341348.
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. 4368.
 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. 377396.
 Y. Sagiv and S.F. Walecka: Subset dependencies and
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 Abstract
 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: DempsterShafer's theory, possibility theory
and (general) Shenoy's theory of valuationbased systems.
 AMS classification 68T30, 68P15, 94D05
 Keywords
 conditional independence
 database relation
 natural conditional function
 possibility theory
 Dempster Shafer's theory

A
pdf copy (converted postscript version) (272kB) is available.
The paper builds on the following works:
 P.P. Shenoy: Conditional independence in valuationbased
systems. International Journal of Approximate Reasoning
10 (1994), n. 3, pp. 203234.
 W. Spohn:
Ordinal conditional functions: a dynamic theory of epistemic
states. In Causation in Decision, Belief Change, and Statistics
volume II. (W.L. Harper, B. Skyrms eds.), Kluwer, Dordrecht
1988, pp. 105134.