This paper examines the quantities used by MYCIN to reason with uncertainty, called certainty factors. It is shown that the original definition of certainty factors is inconsistent with the functions used in MYCIN to combine the quantities. This inconsistency is used to argue for a redefinition of certainty factors in terms of the intuitively appealing desiderata associated with the combining functions. It is shown that this redefinition accommodates an unlimited number of probabilistic interpretations. These interpretations are shown to be monotonic transformations of the likelihood ratio p(EIH)/p(El H). The construction of these interpretations provides insight into the assumptions implicit in the certainty factor model. In particular, it is shown that if uncertainty is to be propagated through an inference network in accordance with the desiderata, evidence must be conditionally independent given the hypothesis and its negation and the inference network must have a tree structure. It is emphasized that assumptions implicit in the model are rarely true in practical applications. Methods for relaxing the assumptions are suggested.

We propose an inequality paradigm for probabilistic reasoning based on a logic of upper and lower bounds on conditional probabilities. We investigate a family of probabilistic logics, generalizing the work of Nilsson [14]. We develop a variety of logical notions for probabilistic reasoning, including soundness, completeness justification; and convergence: reduction of a theory to a simpler logical class. We argue that a bound view is especially useful for describing the semantics of probabilistic knowledge representation and for describing intermediate states of probabilistic inference and updating. We show that the Dempster-Shafer theory of evidence is formally identical to a special case of our generalized probabilistic logic. Our paradigm thus incorporates both Bayesian "rule-based" approaches and avowedly non-Bayesian "evidential" approaches such as MYCIN and DempsterShafer. We suggest how to integrate the two "schools", and explore some possibilities for novel synthesis of a variety of ideas in probabilistic reasoning.

Box 516, St. Louis, MO 63166 ABSTRACT This paper examines the accuracy of the PROSPECTOR model for uncertain reasoning. PROSPECTOR's solutions for a large number of computer·generated inference networks were compared to those obtained from probe· bility theory and minimum cross-entropy calculations. PROSPECTOR's answers were generally accurate for a restricted subset of problems that are consistent with its assumptions. However, even within this subset, we identified conditions under which PROSPECTOR's perfor· mance deteriorates. I NTRCOUCT I ON Researchers in artificial Intelligence have proposed or implemented several approaches to uncertain reason· in-- for knowledge-based systems.

In this paper, we describe a scheme for propagating belief functions in certain kinds of trees using only local computations. This scheme generalizes the computational scheme proposed by Shafer and Logan1 for diagnostic trees of the type studied by Gordon and Shortliffe, and the slightly more general scheme given by Shafer for hierarchical evidence. It also generalizes the scheme proposed by Pearl for Bayesian causal trees (see Shenoy and Shafer). Pearl's causal trees and Gordon and Shortliffe's diagnostic trees are both ways of breaking the evidence that bears on a large problem down into smaller items of evidence that bear on smaller parts of the problem so that these smaller problems can be dealt with one at a time. This localization of effort is often essential in order to make the process of probability judgment feasible, both for the person who is making probability judgments and for the machine that is combining them. The basic structure for our scheme is a type of tree that generalizes both Pearl's and Gordon and Shortliffe's trees. Trees of this general type permit localized computation in Pearl's sense. They are based on qualitative judgments of conditional independence. We believe that the scheme we describe here will prove useful in expert systems. It is now clear that the successful propagation of probabilities or certainty factors in expert systems requires much more structure than can be provided in a pure production-system framework. Bayesian schemes, on the other hand, often make unrealistic demands for structure. The propagation of belief functions in trees and more general networks stands on a middle ground where some sensible and useful things can be done. We would like to emphasize that the basic idea of local computation for propagating probabilities is due to Judea Pearl. It is a very innovative idea; we do not believe that it can be found in the Bayesian literature prior to Pearl's work. We see our contribution as extending the usefulness of Pearl's idea by generalizing it from Bayesian probabilities to belief functions. In the next section, we give a brief introduction to belief functions. The notions of qualitative independence for partitions and a qualitative Markov tree are introduced in Section III. Finally, in Section IV, we describe a scheme for propagating belief functions in qualitative Markov trees.

Influence diagrams are a directed graph representation for uncertainties as probabilities. Influence diagrams have been used for the last ten years as a model structuring and elicitation device in the practical field of decision analysis. They have been a powerful communication tool during the initial discussion about a problem, as well as when explaining results after analysis. Because the diagrams are heirarchical, with the numbers "hidden" within the nodes Within the last few years, a number of theoretical results allow for the analysis to be performed directly on the influence diagram-- as assessed. In general, these techniques apply a sequence of transformations to different influence diagrams, to solve either probabilistic inference or decision analysis problems.

Much artificial intelligence research focuses on the problem of deducing the validity of unobservable propositions or hypotheses from observable evidence.! Many of the knowledge representation techniques designed for this problem encode the relationship between evidence and hypothesis in a directed manner. Moreover, the direction in which evidence is stored is typically from evidence to hypothesis.

The causal Bayesian approach is based on the assumption that effects (e.g., symptoms) that are not conditionally independent with respect to some causal agent (e.g., a disease) are conditionally independent with respect to some intermediate state caused by the agent, (e.g., a pathological condition). This paper describes the development of a causal Bayesian model for the diagnosis of appendicitis. The paper begins with a description of the standard Bayesian approach to reasoning about uncertainty and the major critiques it faces. The paper then lays the theoretical groundwork for the causal extension of the Bayesian approach, and details specific improvements we have developed. The paper then goes on to describe our knowledge engineering and implementation and the results of a test of the system. The paper concludes with a discussion of how the causal Bayesian approach deals with the criticisms of the standard Bayesian model and why it is superior to alternative approaches to reasoning about uncertainty popular in the Al community.

This paper studies the underlying rationality of those languages on the syntax and calculus grounds. Some implications of the theorem to the relationship between the CF and the Bayesian languages and the Dempster-Shafer Theory of Evidence are presented. In order for a computer program to be a plausible --odel of a (mora or less) rational process of human expertise, the program should be capable of representing beliefs in a language that is (more or less) calibrated with a well-specified normative criterion, e.g. the axioms of Subjective Probability [15], the Theory of Confir.nation Tversky, the building blocks· of a probabilistic language are syntax, calculus, and semantics [18]. The-- is a set of numbers, co--only referred to as Degrees of Belief (e.g. standard probabilities or Certainty Factors), which are used to parameterize uncertain facts, inexact rules, and competing hypotheses.

A learning algorithm is presented which given the structure of a causal tree, will estimate its link probabilities by sequential measurements on the leaves only. Internal nodes of the tree represent conceptual (hidden) variables inaccessible to observation. The method described is incremental, local, efficient, and remains robust to measurement imprecisions.

We are interested in creating an automated or semi-automated system with the capability of taking a set of radar imagery, collection parameters and a priori map and other tactical data, and producing likely interpretations of the possible military situations given the available evidence. This paper is concerned with the problem of the interpretation and computation of certainty or belief in the conclusions reached by such a system. For example, if we consider the problem of confirming or denying the presence of a battalion in a given area, we should include in our decision making process the prior likelihood of military presence based on tactical objectives, the evidence of military vehicles in radar image data, the spatial and tactical clustering and patterns of the vehicles extracted from the imagery, etc. Furthermore, if the user of the system has particular interests such as knowing specific deployments, location of battalion headquarters, etc., then these interests should also be responded to