Many expert systems make use of some form of confidence factors in order to deal with uncertain information. However, the methods used to combine these factors in the process of reasoning are usually ad hoc and devoid of any theoretical justification. Nilsson creates a theoretical framework for dealing with such uncertainty factors. He assigns probabilities instead of truth values to propositions. The method is exemplified with the “probabilistic entailment problem”: Given P and P :6WWN Q with their respective uncertainty factors, what is a reasonable uncertainty factor for Q?

The described method computes a range of possible uncertainties, an advantage over any ad hoc system which might create an inconsistent(]) uncertainty factor for Q. The given algorithm is based on the solution of a matrix equation with one row for every relevant proposition in the system. To avoid large matrices resulting from a large knowledge base, the author introduces an approximation method.

Considering the current interest in expert systems, this paper constitutes an important theoretical underpinning for much of the heuristic work done in this area. The author mentions mathematical literature on probabilistic inference, but provides little comparison with these approaches. This makes the paper fairly “self-contained,” but it leaves a reader not familiar with the subject in the dark about the essential differences between the different existing approaches. Large parts of the paper are easy to read; only near the end does the mathematics involved become more advanced. I look forward to an expert system based on the presented theory.