On the Rational Scope of Probabilistic Rulebased

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 C F 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.