Kutato is a system that takes as input a database of cases and produces a belief network that captures many of the dependence relations represented by those data. This system incorporates a module for determining the entropy of a belief network and a module for constructing belief networks based on entropy calculations. Kutato constructs an initial belief network in which all variables in the database are assumed to be marginally independent. The entropy of this belief network is calculated, and that arc is added that minimizes the entropy of the resulting belief network. Conditional probabilities for an arc are obtained directly from the database. This process continues until an entropy-based threshold is reached. We have tested the system by generating databases from networks using the probabilistic logic-sampling method, and then using those databases as input to Kutato. The system consistently reproduces the original belief networks with high fidelity.

Within diagnostic reasoning there have been a number of proposed definitions of a diagnosis, and thus of the most likely diagnosis, including most probable posterior hypothesis, most probable interpretation, most probable covering hypothesis, etc. Most of these approaches assume that the most likely diagnosis must be computed, and that a definition of what should be computed can be made a priori, independent of what the diagnosis is used for. We argue that the diagnostic problem, as currently posed, is incomplete: it does not consider how the diagnosis is to be used, or the utility associated with the treatment of the abnormalities. In this paper we analyze several well-known definitions of diagnosis, showing that the different definitions of the most likely diagnosis have different qualitative meanings, even given the same input data. We argue that the most appropriate definition of (optimal) diagnosis needs to take into account the utility of outcomes and what the diagnosis is used for.

We propose an abductive diagnosis theory that integrates probabilistic, causal and taxonomic knowledge. Probabilistic knowledge allows us to select the most likely explanation; causal knowledge allows us to make reasonable independence assumptions; taxonomic knowledge allows causation to be modeled at different levels of detail, and allows observations be described in different levels of precision. Unlike most other approaches where a causal explanation is a hypothesis that one or more causative events occurred, we define an explanation of a set of observations to be an occurrence of a chain of causation events. These causation events constitute a scenario where all the observations are true. We show that the probabilities of the scenarios can be computed from the conditional probabilities of the causation events. Abductive reasoning is inherently complex even if only modest expressive power is allowed. However, our abduction algorithm is exponential only in the number of observations to be explained, and is polynomial in the size of the knowledge base. This contrasts with many other abduction procedures that are exponential in the size of the knowledge base.

Comprehensible explanations of probabilistic reasoning are a prerequisite for wider acceptance of Bayesian methods in expert systems and decision support systems. A study of human reasoning under uncertainty suggests two different strategies for explaining probabilistic reasoning: The first, qualitative belief propagation, traces the qualitative effect of evidence through a belief network from one variable to the next. This propagation algorithm is an alternative to the graph reduction algorithms of Wellman (1988) for inference in qualitative probabilistic networks. It is based on a qualitative analysis of intercausal reasoning, which is a generalization of Pearl's "explaining away", and an alternative to Wellman's definition of qualitative synergy. The other, Scenario-based reasoning, involves the generation of alternative causal "stories" accounting for the evidence. Comparing a few of the most probable scenarios provides an approximate way to explain the results of probabilistic reasoning. Both schemes employ causal as well as probabilistic knowledge. Probabilities may be presented as phrases and/or numbers. Users can control the style, abstraction and completeness of explanations.

Several different uncertain inference systems (UISs) have been developed for representing uncertainty in rule-based expert systems. Some of these, such as Mycin's Certainty Factors, Prospector, and Bayes' Networks were designed as approximations to probability, and others, such as Fuzzy Set Theory and DempsterShafer Belief Functions were not. How different are these UISs in practice, and does it matter which you use? When combining and propagating uncertain information, each UIS must, at least by implication, make certain assumptions about correlations not explicily specified. The maximum entropy principle with minimum cross-entropy updating, provides a way of making assumptions about the missing specification that minimizes the additional information assumed, and thus offers a standard against which the other UISs can be compared. We describe a framework for the experimental comparison of the performance of different UISs, and provide some illustrative results.

This paper is concerned with two theories of probability judgment: the Bayesian theory and the theory of belief functions. It illustrates these theories with some simple examples and discusses some of the issues that arise when we try to implement them in expert systems. The Bayesian theory is well known; its main ideas go back to the work of Thomas Bayes (1702-1761). The theory of belief functions, often called the Dempster-Shafer theory in the artificial intelligence community, is less well known, but it has even older antecedents; belief-function arguments appear in the work of George Hooper (16401723) and James Bernoulli (1654-1705). For elementary expositions of the theory of belief functions, see Shafer (1976, 1985).

Judea Pearl Computer Science Department, Univenity of California, Loa Angelea The paper demonstrates that strict adherence to probability theory does not preclude the use of concurrent, self-activated constraint-propagation mechanisms for managing uncer tainty. Maintaining local records of sources-of-belief allows both predictive and diagnostic inferences to be activated simultanously and propagate harmoniously towards a stable equillibrium.

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.