Topological framework for representing and solving probabilistic inference problems in expert systems

The authors present the concept of influence diagrams for representing probabilistic dependence and independence between state variables in a given problem domain and a topological framework for solving probabilistic inference problems in expert systems. The mathematical basis for influence diagrams is explained and theorems for mathematical manipulation of them are presented, in a graph-theoretic framework. Topological transformation rules developed in previous research are formalized in an axiomatic manner based on a concept of consistency. A polynomial-time symbolic-level algorithm for solving probabilistic inference problems is developed. The algorithm involves searching through the diagram to answer any specific diagnostic query about the system