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

TL;DR

This paper examines the theoretical limits of probabilistic rule-based expert systems, focusing on the syntax and calculus, and discusses implications for knowledge engineering in uncertain domains.

Contribution

It introduces an endomorphism theorem revealing limitations of the CF calculus due to independence assumptions and explores its implications for various probabilistic formalisms.

Findings

Endomorphism theorem highlights limitations of CF calculus

Implications for Bayesian and Dempster-Shafer theories

Discussion on rule-based knowledge engineering

Abstract

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.