Conditioning in Decomposable Compositional Models in Valuation-Based Systems

Valuation-based systems (VBS) can be considered as a generic uncertainty framework that has many uncertainty calculi, such as probability theory, a version of possibility theory where combination is the product t-norm, Spohn’s epistemic belief theory, and DempsterShafer belief function theory, as special cases. In this paper, we focus our attention on conditioning, which is defined using the combination, marginalization, and removal operators of VBS. We show that conditioning can be expressed using the composition operator. We define decomposable compositional models in the VBS framework. Finally, we show that conditioning in decomposable compositional models can be done using local computation. Since all results are obtained in the VBS framework, they hold in all calculi that fit in the VBS framework.