On the Rational Scope of Probabilistic Rule-Based Inference Systems

Belief updating schemes in artificial intelligence may be viewed as threedimensional languages, consisting of a syntax (e.g. probabilities or certaintyfactors), a calculus (e.g. Bayesian or CF combination rules), and a semantics(i.e. cognitive interpretations of competing formalisms). This paper studiesthe rational scope of those languages on the syntax and calculus grounds. Inparticular, the paper presents an endomorphism theorem which highlightsthe limitations imposed by the conditional independence assumptionsimplicit in the CF calculus. Implications of the theorem to the relationshipbetween the CF and the Bayesian languages and the Dempster-Shafer theoryof evidence are presented. The paper concludes with a discussion of someimplications on rule-based knowledge engineering in uncertain domains