The Rational and Computational Scope of Probabilistic Rule-Based Expert Systems
This work addresses theoretical limitations in probabilistic rule-based expert systems for AI researchers and knowledge engineers, but it is incremental as it builds on existing formalisms.
The paper analyzes the rational scope of belief updating schemes in AI, focusing on syntax and calculus, and presents an endomorphism theorem that reveals limitations due to conditional independence assumptions in certainty factor calculus, with implications for Bayesian and Dempster-Shafer theories.
Belief updating schemes in artificial intelligence may be viewed as three dimensional languages, consisting of a syntax (e.g. probabilities or certainty factors), a calculus (e.g. Bayesian or CF combination rules), and a semantics (i.e. cognitive interpretations of competing formalisms). This paper studies the rational scope of those languages on the syntax and calculus grounds. In particular, the paper presents an endomorphism theorem which highlights the limitations imposed by the conditional independence assumptions implicit in the CF calculus. Implications of the theorem to the relationship between the CF and the Bayesian languages and the Dempster-Shafer theory of evidence are presented. The paper concludes with a discussion of some implications on rule-based knowledge engineering in uncertain domains.