A NOTE OF CAUTION ON COMBINING CERTAINTIES

Abstract
In the case of expert systems, when premises from two different rules argue for the same conclusion, there exist a number of methods for combining the certainties in the conclusion, obtained from each premise individually, to yield a total certainty in the conclusion. When these certainties are interpreted as probability values, it is necessary in all these methods to make assumptions of independence concerning the premises and conclusion. It is proven here that there does not exist a procedure which yields, for all probability functions, meaningful bounds for the probability of the conclusion based on two premises in terms of the probabilities of the conclusion based on each premise individually. Additionally, it is proven that there does not even exist a procedure which yields, for all probability functions, meaningful bounds for the probability of the conclusion based on two premises in terms of the probabilities of all one- and two-member combinations of the premises and the conclusion. Finally, suggestions are made as to when to make assumptions of independence and when to take other alternatives.

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