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
postscript version (210kB) is available.
The paper builds on the following works:
- P.P. Shenoy: Conditional independence in valuation-based
systems. International Journal of Approximate Reasoning
10 (1994), n. 3, pp. 203-234.
- 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. 105-134.