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

Abstract

In presence of uncertainty, computation of certainty factor of a hypothesis requires, in general, availability of rules for combining evidence under chaining, disjunction and conjunction. The method described in this paper is based on 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 role of probabilities. For example, proposition 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, knowledge base of an expert system may be assumed to consist of propositions of general form QA's are B's. It is shown that six basic syllogisms are sufficient to provide a systematic framework for computation of certainty factors. A comparison with rules of combination of evidence in PROSPECTOR, MYCIN and other expert systems is presented and a connection between syllogistic reasoning and Dempster-Shafer theory is established. The syllogistic method of reasoning lends itself to a computationally efficient implementation and thus provides an effective tool for management of uncertainty in expert systems.