Abstract

The three most important theories of quantitative reasoning under uncertainty currently implemented in expert systems are reviewed: probability theory, belief functions theory, and possibility theory. They are compared with respect to the requirements of logical consistency they satisfy, and with respect to their adequacy in representing the process of belief updating or learning from new data. It is pointed out the difference between two different kinds of uncertainty, namely, uncertainty due to partial ignorance of the information sufficient to establish the truth-value of a statement, and uncertainty due to the vagueness of the meaning of a statement. The consequences of this difference are stressed. A final warning is given concerning the dangers of trusting too much the mathematical machinery disregarding the appropriateness of the framework in which the machinery has been put at work.

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