A Computational Approach to Approximate and Plausible Reasoning with Applications to Expert Systems

Abstract

The intended purpose of this paper is twofold: proposing a common basis for the modeling of uncertainty and imprecision, and discussing various kinds of approximate and plausible reasoning schemes in this framework. Together with probability, different kinds of uncertainty measures (credibility and plausibility functions in the sense of Shafer, possibility measures in the sense of Zadeh and the dual measures of necessity, Sugeno's gλ-fuzzy measures) are introduced in a unified way. The modeling of imprecision in terms of possibility distribution is then presented, and related questions such as the measure of the uncertainty of fuzzy events, the probability and possibility qualification of statements, the concept of a degree of truth, and the truth qualification of propositions, are discussed at length. Deductive inference from premises weighted by different kinds of measures by uncertainty, or by truth-values in the framework of various multivalued logics, is fully investigated. Then, deductive inferences from imprecise or fuzzy premises are dealt with; patterns of reasoning where both uncertainty and imprecision are present are also addressed. The last section is devoted to the combination of uncertain or imprecise pieces of information given by different sources. On the whole, this paper is a tentative survey of quantitative approaches in the modeling of uncertainty and imprecision including recent theoretical proposals as well as more empirical techniques such as the ones developed in expert systems such as MYCIN or PROSPECTOR, the management of uncertainty and imprecision in reasoning patterns being a key issue in artificial intelligence.