As the technology for building knowledge based systems has matured, important lessons have been learned about the relationship between the architecture of a system and the nature of the problems it is intended to solve. We are implementing a knowledge engineering tool called BART that is designed with these lessons in mind. BART is a Bayesian reasoning tool that makes belief networks and other probabilistic techniques available to knowledge engineers building classificatory problem solvers. BART has already been used to develop a decision aid for classifying ship images, and it is currently being used to manage uncertainty in systems concerned with analyzing intelligence reports. This paper discusses how state-of-the-art probabilistic methods fit naturally into a knowledge based approach to classificatory problem solving, and describes the current capabilities of BART.

This extended abstract presents a logic, called Lp, that is capable of representing and reasoning with a wide variety of both qualitative and quantitative statistical information. The advantage of this logical formalism is that it offers a declarative representation of statistical knowledge; knowledge represented in this manner can be used for a variety of reasoning tasks. The logic differs from previous work in probability logics in that it uses a probability distribution over the domain of discourse, whereas most previous work (e.g., Nilsson [2], Scott et al. [3], Gaifinan [4], Fagin et al. [5]) has investigated the attachment of probabilities to the sentences of the logic (also, see Halpern [6] and Bacchus [7] for further discussion of the differences). The logic Lp possesses some further important features. First, Lp is a superset of first order logic, hence it can represent ordinary logical assertions. This means that Lp provides a mechanism for integrating statistical information and reasoning about uncertainty into systems based solely on logic. Second, Lp possesses transparent semantics, based on sets and probabilities of those sets. Hence, knowledge represented in Lp can be understood in terms of the simple primative concepts of sets and probabilities. And finally, the there is a sound proof theory that has wide coverage (the proof theory is complete for certain classes of models). The proof theory captures a sufficient range of valid inferences to subsume most previous probabilistic uncertainty reasoning systems. For example, the linear constraints like those generated by Nilsson's probabilistic entailment [2] can be generated by the proof theory, and the Bayesian inference underlying belief nets [8] can be performed. In addition, the proof theory integrates quantitative and qualitative reasoning as well as statistical and logical reasoning. In the next section we briefly examine previous work in probability logics, comparing it to Lp. Then we present some of the varieties of statistical information that Lp is capable of expressing. After this we present, briefly, the syntax, semantics, and proof theory of the logic. We conclude with a few examples of knowledge representation and reasoning in Lp, pointing out the advantages of the declarative representation offered by Lp. We close with a brief discussion of probabilities as degrees of belief, indicating how such probabilities can be generated from statistical knowledge encoded in Lp. The reader who is interested in a more complete treatment should consult Bacchus [7].

After a brief introduction to causal probabilistic networks and the HUGIN approach, the problem of conflicting data is discussed. A measure of conflict is defined, and it is used in the medical diagnostic system MUNIN. Finally, it is discussed how to distinguish between conflicting data and a rare case.

A scientific reasoning system makes decisions using objective evidence in the form of independent experimental trials, propositional axioms, and constraints on the probabilities of events. As a first step towards this goal, we propose a system that derives probability intervals from objective evidence in those forms. Our reasoning system can manage uncertainty about data and rules in a rule based expert system. We expect that our system will be particularly applicable to diagnosis and analysis in domains with a wealth of experimental evidence such as medicine. We discuss limitations of this solution and propose future directions for this research. This work can be considered a generalization of Nilsson's "probabilistic logic" [Nil86] to intervals and experimental observations.

We analyzed the convergence properties of likelihood- weighting algorithms on a two-level, multiply connected, belief-network representation of the QMR knowledge base of internal medicine. Specifically, on two difficult diagnostic cases, we examined the effects of Markov blanket scoring, importance sampling, demonstrating that the Markov blanket scoring and self-importance sampling significantly improve the convergence of the simulation on our model.

In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived reflecting the uncertainty of the input probabilities. The algorithm is based on an approximate sample representation of the basic probabilities. This sample is continuously modified by a stochastic simulation procedure, the Metropolis algorithm, such that the sequence of successive samples corresponds to the desired posterior distribution. The procedure is able to combine inconsistent probabilities according to their reliability and is applicable to general inference networks with arbitrary structure. Dempster-Shafer probability mass functions may be included using specific measurement distributions. The properties of the approach are demonstrated by numerical experiments.

In almost all situation assessment problems, it is useful to dynamically contract and expand the states under consideration as assessment proceeds. Contraction is most often used to combine similar events or low probability events together in order to reduce computation. Expansion is most often used to make distinctions of interest which have significant probability in order to improve the quality of the assessment. Although other uncertainty calculi, notably Dempster-Shafer [Shafer, 1976], have addressed these operations, there has not yet been any approach of refining and coarsening state spaces for the Bayesian Network technology. This paper presents two operations for refining and coarsening the state space in Bayesian Networks. We also discuss their practical implications for knowledge acquisition.

A major difficulty in developing and maintaining very large knowledge bases originates from the variety of forms in which knowledge is made available to the KB builder. The objective of this research is to bring together two complementary knowledge representation schemes: term subsumption languages, which represent and reason about defining characteristics of concepts, and proximate reasoning models, which deal with uncertain knowledge and data in expert systems. Previous works in this area have primarily focused on probabilistic inheritance. In this paper, we address two other important issues regarding the integration of term subsumption-based systems and approximate reasoning models. First, we outline a general architecture that specifies the interactions between the deductive reasoner of a term subsumption system and an approximate reasoner. Second, we generalize the semantics of terminological language so that terminological knowledge can be used to make plausible inferences. The architecture, combined with the generalized semantics, forms the foundation of a synergistic tight integration of term subsumption systems and approximate reasoning models.

This paper derives a formula for computing the conditional probability of a set of candidates, where a candidate is a set of disorders that explain a given set of positive findings. Such candidate sets are produced by a recent method for multidisorder diagnosis called symptom clustering. A symptom clustering represents a set of candidates compactly as a cartesian product of differential diagnoses. By evaluating the probability of a candidate set, then, a large set of candidates can be validated or pruned simultaneously. The probability of a candidate set is then specialized to obtain the probability of a single candidate. Unlike earlier results, the equation derived here allows the specification of positive, negative, and unknown symptoms and does not make assumptions about disorders not in the candidate.

One of the most important aspects in any treatment of uncertain information is the rule of combination for updating the degrees of uncertainty. The theory of belief functions uses the Dempster rule to combine two belief functions defined by independent bodies of evidence. However, with limited dependency information about the accumulated belief the Dempster rule may lead to unsatisfactory results. The present study suggests a method to determine the accumulated belief based on the premise that the information gain from the combination process should be minimum. This method provides a mechanism that is equivalent to the Bayes rule when all the conditional probabilities are available and to the Dempster rule when the normalization constant is equal to one. The proposed principle of minimum information gain is shown to be equivalent to the maximum entropy formalism, a special case of the principle of minimum cross-entropy. The application of this principle results in a monotonic increase in belief with accumulation of consistent evidence. The suggested approach may provide a more reasonable criterion for identifying conflicts among various bodies of evidence.