Causal Compositional Models in Valuation-Based Systems

Abstract. This paper shows that Pearl’s causal networks can be de-scribed using compositional models in the valuation-based systems (VBS) framework. There are several advantages of using the VBS framework. First, VBS is a generalization of several uncertainty theories (e.g., prob-ability theory, a version of possibility theory where combination is the product t-norm, Spohn’s epistemic belief theory, and Dempster-Shafer belief function theory). This implies that causal compositional models, initially described in probability theory, are now described in all uncer-tainty calculi that fit in the VBS framework. Second, using the operators of VBS, we describe how causal inference can be made in causal compo-sitional models in an elegant and unifying algebraic way. This includes the computation of conditioning, and the computation of the effect of interventions