An algebra of bayesian belief universes for knowledge‐based systems

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Abstract
Causal probabilistic networks (CPNs) have proved to be a useful knowledge representation tool for modeling domains where causal relations‐in a broad sense‐are a natural way of relating domain concepts and where uncertainty is inherited in these relations. The domain is modeled in a CPN by use of a directed graph where the nodes represent concepts in the domain and the arcs represent causal relations. Furthermore, the quantitative relation between a node and its immediate causes is expressed as conditional probabilities. During the last few years, several schemes based on probability theory for incorporating and propagating new information throughout a CPN has emerged. As long as the domain can be modeled by use of a singly connected CPN (i. e., no more than one path between any pair of nodes), the schemes operate directly in the CPN and perform conceptually simple operations in this structure. When it comes to more complicated structures such as multiply connected CPNs (i. e., more than one path is allowed between pairs of nodes), the schemes operate in derived structures where the embedded domain knowledge no longer is as explicit and transparent as in the CPN. Furthermore, the simplicity in the operations is lost also. This report outlines a scheme‐the algebra ofBayesian belief universes‐for absorbing and propagating evidence in multiply connected CPNs. The scheme provides a secondary structure,a junction tree, and a simple set of algebraic operations between objects in this structure,Collect EvidenceandDistribute Evidence.These are the basic tools for making inference in a CPN domain model and yield a calculus as simple as in the case of singly connected CPNs.