Conditional Inference and Logic for Intelligent Systems: A Theory of Measure-Free Conditioning

Abstract

Approved for public release; distribution is unlimited. ABSTRACT (Maximum 200 words)This work addresses an anomaly involving probability and logic relative to thtu interprutation of irni.., .ti,,e statements, and the evaluation of those btateamunts compatible wvith _unditionarl probability. One of our cieuf motivrations 1s thle need to for..,alize rigorously the connections betwecen conditional probablity and the "hidden" logit. Uf Implicative statements, such as production rules in expert systemb and defaults in CommoI~I-n uns reasoning. The pjurpove Is to provide theoretica! results for probabilistic reasoning that will be useful in the design and evaluation of inference rules of such systems.f -L Published by North-Holland, 1991 Publishes, Amsterdam, New York, Oxford, and Tokyo. PREFACE 1.This book is concerned with a systematic investigation of the concept of "measure-free" conditioning and its associated logic for intelligent systems. Its purpose is to provide a foundation for inference in such systems. The basic problem is the representation and evaluation of implicative statements in natural language, in a way compatible with conditional probability. This longstanding problem involves three distinct disciplines: natural language, logic, and probability. [The situation is different today. The problem is before us because of the need to provide a firm foundation for probabilistic reasoning in intelligent systems; in particular, V how to combine conditional information arising from disparate sources in expert systems and how to compute it probabilistically. This is in line with the Bayesian approach to probabilistic reasoning in intelligent systems (Pearl, 1988). Probability not only has a firm mathematical foundation, but also the conditional probability operator captures a form of non-monotonicity of common sense reasoning.Our goal is a more complete and satisfactory theory of "measure-free" conditioning.If the concept of "conditional event" can be formalized and a suitable algebra of operators between such events be developed, then the resulting structure will have use in designing inference rules in expert systems. With probability being the method of choice for handling uncertainty despite the plethora of non-probabilistic procedures such as example, Dubois and Prade (1988)). This development is not to be confused with other "conditional logics", such as that of Nute (1980) and Appiah (1985), which are not j ~ compatible with conditional probability, nor with non-commutative extensions of Boolean logic (Guzman and Squier, 1990). Our approach differs also from that of Adams (1975),[who takes conditionals as primitives in natural language, while ours are mathematical entities.[1 This book is primarily concerned with theory. The reader is expected to be familiar with basic probability theory, elementary logic, and elementary facts from ring theory.However, the text is largely self-contained. The hope is that this book will trigger further JI interest in both the theory and applications of this topic.In c...

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