We present a logical relationship between a small number of intuitive properties for measures of belief and the axioms of probability theory. In this paper, we discuss the ramifications of a proof showing that the axioms of probability theory follow logically from a set of simple properties. It is useful to decompose the problem of reasoning under uncertainty in to three distinct components: problem formulation, initial belief assignment, and belief entailment. We refer to the use of' a single real number to represent continuous measures of belief as the Another assertion is that belief in the negation of a proposition Q, denoted -Q, should be determined by the belief in the proposition itself.
The certainty-factor (CF) model is a commonly used method for managing uncertainty in rule-based systems. We review the history and mechanics of the CF model, and delineate precisely its theoretical and practical limitations. In addition, we examine the belief network, a representation that is similar to the CF model but that is grounded firmly in probability theory. We show that the belief-network representation overcomes many of the limitations of the CF model, and provides a promising approach to the practical construction of expert systems.