We describe a new approach to default reasoning, based on a principle of indifference among possible worlds. We interpret default rules as extreme statistical statements, thus obtaining a knowledge base KB comprised of statistical and first-order statements. We then assign equal probability to all worlds consistent with KB in order to assign a degree of belief to a statement '. The degree of belief can be used to decide whether to defeasibly conclude '. Various natural patterns of reasoning, such as a preference for more specific defaults, indifference to irrelevant information, and the ability to combine independent pieces of evidence, turn out to follow naturally from this technique. Furthermore, our approach is not restricted to default reasoning; it supports a spectrum of reasoning, from quantitative to qualitative. It is also related to other systems for default reasoning. In particular, we show that the work of [ Goldszmidt et al., 1990 ] , which applies maximum entropy ideas t...

ost of today's commercial expert-system building tools use certainty or confidence factors to handle uncertainties in the knowledge or data. ' But they cannot cope with fuzzy concepts such as tall, good, or hot, which constitute a very significant part of a natural language. In fact, some of these fuzzy concepts have been incorporated into several expert systems, such as Cadiag-2 ' and Fault,j which are purposely built from a high-level language for a specific domain of application. In Cadiag-2 the knowledge representation of fuzzy concepts is designed specifically for medical diagnosis. In Fault some fuzzy reasoning is also supported. Several AI programming languages, such as FProlog, also provide mechanisms to handle fuzzy concepts. ' FProlog is similar to Prolog except that in FProlog a truth value expressed numerically is allowed in a fact. The uncertainty can then be handled automatically by the FProlog interpreter. This article presents a comprehensive expert-system building tool, called System Z-11, that can deal with exact, fuzzy (or inexact), and combined reasoning, allowing fuzzy and normal terms to be freely mixed in the rules and facts of an expert system. This fully implemented tool has been used to build several expert systems in the fields of student curriculum advisement, medical diagnosis, psychoanalysis, and risk analysis. System Z-I1 is a rule-

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