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, dis-junction 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 computation-ally efficient implementation and thus provides an effective tool for the management of uncertainty in expert systems. I. SYLLOGISTIC REASONING In the existing expert systems, the computation of certainty factors of hypotheses and conclusions is carried out through the use of probability-based methods (Barr and Feigenbaum, 1982). More recently, the use of belief functions in the context of the Dempster-Shafer theory has attracted increasing attention (Wesley, Lowrance and Garvey, 1984). In a different approach which is outlined in this paper, syllogistic reasoning is employed to provide a basis for the formulation of rules for combination of evidence. Classically, the major and minor premises in syllogistic reasoning are allowed to contain only the standard quantifiers all and some. For example, the paradigmatic syllogism Barbara is expressed by the rule where A, B and C are arbitrary predicates in two-valued logic. This syllogism expresses the transitivity of set containment and, as such, provides the basis for property inheritance in knowledge representation systems.