Valuation Networks and Conditional Independence

Valuation networks have been proposed as graph� ical representations of valuation�based systems (VBSs). The VBS framework is able to capture many uncertainty calculi including probability theory, Dempster�Shafer's belief�function theory, Spohn's epistemic belief theory, and Zadeh's possibility theory. In this paper, we show how valuation networks encode conditional indepen� dence relations. For the probabilistic case, the class of probability models encoded by valuation networks includes undirected graph models, di� rected acyclic graph models, directed balloon graph models, and recursive causal graph models.