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This chapter introduced the models of belief propagation and belief revision for approximate reasoning in acyclic and cyclic networks respectively. The analysis of deadlock freedom of the belief propagation algorithm ensures that the algorithm does not terminate pre-maturely. The belief revision algorithm on the other hand may undergo limit cyclic behaviors. The principles of the limit cycle elimination technique may then be undertaken to keep the reasoning free from getting stuck into limit cycles. Possible sources of entry of nonmonotonicity into the reasoning space and their elimination by a special voting arrangement has also been undertaken.

Unlike the existing methodology of reasoning on FPN, the most important aspect of the chapter lies in the representation of the belief updating policy by a single vector-matrix equation. Thus, if the belief revision does not get trapped into limit cycles and nonmonotonicity, the steady state solution of the reasoning system can be obtained by recurrently updating the belief vector until the vector converges to a stable state.