The Rational and Computational Scope of Probabilistic Rule-Based Expert Systems

Belief consolidation schemes in AI can be viewed as three dimensional languages, consisting of a syntax (e.g. probabilities or certainty Factors), a calculus (e.g. Bayesian rules or CF combination rules), and a semantics (i.e. cognitive interpretations of competing formalisms). This paper studies the underlying rationality of those languages on the syntax and calculus grounds. In particular, the paper presents the CF-Bayesian Endomorphism Theorem, which explicitly defines the class of real-life problems of expertise that have a rational CF interpretation. Some implications of the theorem to the relationship between the CF and the Bayesian languages and the Dempster-Shafer Theory of Evidence are presented. Finally, the paper discusses the implications of the theorem on the science and practice of rule-based knowledge engineering.