Causal Compositional Models in Valuation-Based Systems

Abstract

This paper shows that Pearl’s causal networks can be described 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., probability 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 uncertainty calculi that fit in the VBS framework. Second, using the operators of VBS, we describe how causal inference can be made in causal compositional models in an elegant and unifying algebraic way. This includes the computation of conditioning, and the computation of the effect of interventions.