Syllogistic Reasoning as a Basis for Combination of Evidence in Expert Systems

In the presence of uncertainty, computation of the certainty factor of a hypothesis requires, in general, the availability of rules for combining evidence under chaining, disjunction and conjunction. The method described in this paper is based on the use of what may be viewed as a generalization of syllogistic reasoning in classical logic--a generalization in which numerical or, more generally, fuzzy quantifiers assume the role of probabilities. For example, the proposition QA's are B's, in which Q is a numerical or fuzzy quantifier, may be interpreted as "the conditional probability of B given A is Q." In this sense, the knowledge base of an expert system may be assumed to consist of propositions of the general form "QA's are B's." It is shown that six basic syllogisms are sufficient to provide a systematic framework for the computation of certainty factors. A comparison with the rules of combination of evidence in PROSPECTOR, MYCIN and other expert systems is presented and a connection between syllogistic reasoning and the Dempster-Shafer theory is established. The syllogistic method of reasoning lends itself to a computationally efficient implementation and thus provides an effective tool for the management of uncertainty in expert systems.