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.Information Systems Working Papers Serie
