Formal Properties of Conditional Independence in Diierent Calculi of Ai

Abstract

In this paper formal properties of CI in diierent frameworks are studied. The rst part is devoted to the comparison of three diierent frameworks for study CI: probability theory, theory of relational databases and Spohn's theory of ordinal conditional functions. Although CI{models arising in these frameworks are very similar (they satisfy semigraphoid axioms) we give examples showing that their formal properties still diier (each other). On the other hand, we nd that (within each of these frameworks) there exists no nite complete axiomatic characterization of CI{models by nding an innnite set of sound inference rules (the same in all three frameworks). In the second part further frameworks for CI are discussed: Dempster{Shafer theory, possibility theory and (general) Shenoy's theory of valuation{based systems.

Cite this paper

@inproceedings{Studen1993FormalPO, title={Formal Properties of Conditional Independence in Diierent Calculi of Ai}, author={Milan Studen}, year={1993} }