The Probablistic Belief System with Confidence Factor

Abstract

To represent human knowledge in a formal system, we have to deal with vagueness, which is further divided into vagueness of the knowledge holder and vagueness of the knowledge itself. We call the former confidence factor and the latter subjective probability of the knowledge. Traditionally, these are represented as a single parameter, called an uncertainity factor, in most of expert systems. We introduce a Probability Belief Operator (PBO) which is the combination of two factors. PBO represents higher order probabilistic belief. By providing axioms on PBO, we show that the system is a generalization of certainity factors such as used in MYCIN. We will provide inference rules over PBO so as to use the system for inference dealing with belief and uncertainity. We show some examples of probablistic inductive inferernce. We then show that PBO is a generalization of belief axiom. The formalism is also applicable to knowledge acquisition.