Probabilistic rules and their variants have recently supported several successful applications of expert systems, in spite of the difficulty of committing informants to particular conditional probabilities or ";certainty factors"; and in spite of the experimentally observed insensitivity of system performance to perturbations of the chosen values. Here we survey recent developments concerning reasoned assumptions which offer hope for avoiding the practical elusiveness of probabilistic rules while retaining theoretical power, for basing systems on the information unhesitatingly gained from expert informants, and reconstructing the entailed degrees of belief later.

Editors' Note: Many expert systems require some means criticisms of this approach from those steeped in the practical of handling heuristic rules whose conclusions are less than certain issues of constructing large rule-based expert systems. Abstract the expert system draws inferences in solving different problems. Doyle's paper argues that it is difficult for a human expert "certainty factors," and in spite of the experimentally observed insensitivity of system performance to perturbations of the chosen values Recent successes of "expert systems" stem from much Research Projects Agency (DOD), ARPA Order No. 3597, monitored In the following, we explain the modified approach together with its practical and theoretical attractions. The client's income bracket is 50%, can be found (Minsky, 1975; Shortliffe & Buchanan, 1975; and 2. The client carefully studies market trends, Duda, Hart, & Nilsson, 1976; Szolovits, 1978; Szolovits & THEN: 3. There is evidence (0.8) that the investment Pauker, 1978). Reasoned Assumptions (from Davis, 1979) and would use the rule to draw conclusions whose "certainty factors" depend on the observed certainty Although our approach usually approximates that of Bayesian probabilities, accommodates representational systems based on "frames" namely as subjective degrees of belief.

This article describes a theory of reasoning about uncertainly, based on a representation of states of certainly called endorsements. The theory of endorsements is an alternative to numerical methods for reasoning about uncertainly, such as subjective Bayesian methods (Shortliffe and Buchanan, 1975; Duda hart, and Nilsson, 1976) and Shafer-dempster theory (Shafer, 1976). The fundamental concern with numerical representations of certainty is that they hide the reasoning about uncertainty. While numbers are easy to propagate over inferences, what the numbers mean is unclear. The theory of endorsements provide a richer representation of the factors that affect certainty and supports multiple strategies for dealing with uncertainty.

Cambridge University Press

REVEREND BAYES ON INFERENCE ENGINES: A DISTRIBUTED HIERARCHICAL APPROACH(*)(**) Judea Pearl Cognitive Systems Laboratory School of Engineering and Applied Science University of California, Los Angeles 90024 ABSTRACT This paper presents generalizations of Bayes likelihood-ratio updating rule which facilitate an asynchronous propagation of the impacts of new beliefs and/or new evidence in hierarchically organized inference structures with multi-hypotheses variables. The computational scheme proposed specifies a set of belief parameters, communication messages and updating rules which guarantee that the diffusion of updated beliefs is accomplished in a single pass and complies with the tenets of Bayes calculus. Introduction This paper addresses the issue ofefficiently propagating the impact of new evidence and beliefs through a complex network of hierarchically organized inference rules. Such networks find wide applications in expert-systems Cl], [2],[3],speech recognition [4], situation assessment [5], the modelling of reading comprehension [6] and judicial reasoning [7]. Many AI researchers have accepted the myth that a respectable computational model of inexact reasoning must distort, modify or ignore at least some principles of probability calculus.

In J. E. Hayes, D. Michie, and L. I. Mikulich (Eds.), Machine Intelligence 9. Chichester, England: Ellis Horwood Ltd., 149-195

Knowledge about a particular type of ore deposit is encoded in a computational model representing observable geological features and the relative significance thereof.

How do practicing physicians make clinical decisions? What techniques can we use in the computer to produce programs that exhibit medical expertise?

The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable. More specifically, if F is a fuzzy subset of a universe of discourse U={u} which is characterized by its membership function μF, then a proposition of the form “X is F,” where X is a variable taking values in U, induces a possibility distribution ∏X which equates the possibility of X taking the value u to μF(u)—the compatibility of u with F. In this way, X becomes a fuzzy variable which is associated with the possibility distribution ∏x in much the same way as a random variable is associated with a probability distribution. In general, a variable may be associated both with a possibility distribution and a probability distribution, with the weak connection between the two expressed as the possibility/probability consistency principle. A thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is, in the main, possibilistic rather than probabilistic in nature. Thus, by employing the concept of a possibility distribution, a proposition, p, in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p. Several types of conditional translation rules are discussed and, in particular, a translation rule for propositions of the form “X is F is α-possible,” where α is a number in the interval [0, 1], is formulated and illustrated by examples.

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