A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In particular, the method allows belief network algorithms to calculate general probabilistic propositions over nodes in the network. Although in the worst case the time complexity of the method is exponential in the size of a query, it is polynomial in the size of a number of common types of queries.

Reasoning under uncertainty in Al hats come to mean assessing the credibility of hypotheses inferred from evidence. But techniques for assessing credibility do not tell a problem solver what to do when it is uncertain. This is the focus of our current research. We have developed a medical expert system called MUM, for Managing Uncertainty in Medicine, that plans diagnostic sequences of questions, tests, and treatments. This paper describes the kinds of problems that MUM was designed to solve and gives a brief description of its architecture. More recently, we have built an empty version of MUM called MU, and used it to reimplement MUM and a small diagnostic system for plant pathology. The latter part of the paper describes the features of MU that make it appropriate for building expert systems that manage uncertainty.

A major aspect of human reasoning involves the use of approximations. Particularly in situations where the decision-making process is under stringent time constraints, decisions are based largely on approximate, qualitative assessments of the situations. Our work is concerned with the application of approximate reasoning to real-time control. Because of the stringent processing speed requirements in such applications, hardware implementations of fuzzy logic inferencing are being pursued. We describe a programming environment for translating fuzzy control rules into hardware realizations. Two methods of hardware realizations are possible. The First is based on a special purpose chip for fuzzy inferencing. The second is based on a simple memory chip. The ability to directly translate a set of decision rules into hardware implementations is expected to make fuzzy control an increasingly practical approach to the control of complex systems.

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and solution of probabilistic and decision-theoretic models for complex and uncertain domains. Given a query, a logical proof is produced if possible; if not, an influence diagram based on the query and the knowledge of the decision domain is produced and subsequently solved. A uniform declarative, first-order, knowledge representation is combined with a set of integrated inference procedures for logical, probabilistic, and decision-theoretic reasoning.

Our previous work on classifying complex ship images [1,2] has evolved into an effort to develop software tools for building and solving generic classification problems. Managing the uncertainty associated with feature data and other evidence is an important issue in this endeavor. Bayesian techniques for managing uncertainty [7,12,13] have proven to be useful for managing several of the belief maintenance requirements of classification problem solving. One such requirement is the need to give qualitative explanations of what is believed. Pearl [11] addresses this need by computing what he calls a belief commitment-the most probable instantiation of all hypothesis variables given the evidence available. Before belief commitments can be computed, the straightforward implementation of Pearl's procedure involves finding an analytical solution to some often difficult optimization problems. We describe an efficient implementation of this procedure using tensor products that solves these problems enumeratively and avoids the need for case by case analysis. The procedure is thereby made more practical to use in the general case.

In this paper, we present some results of evidential reasoning in understanding multispectral images of remote sensing systems. The Dempster-Shafer approach of combination of evidences is pursued to yield contextual classification results, which are compared with previous results of the Bayesian context free classification, contextual classifications of dynamic programming and stochastic relaxation approaches.

Heckerman (1], for example, shows that the equations that define MYCIN's certainty factors can be translated into probabilistic terms. Other studies, however, have attempted to use the answers provided by probability theory as a norm against which the accuracy of heuristic formalisms can be measured [2,3,4]. These studies differed somewhat in implementation, but each began with example inference networks. Next, new values were assigned to the evidence nodes, as though additional information were being supplied by a user. Finally, conclusion node values were calculated which reflected the new information, according to the heuristic formalisms under consideration and also according to a probablistic method which provided the minimum *This research was conducted under the McDonnell Douglas Independent Research and Development program.

Much of the controversy about methods for automated decision making has focused on specific calculi for combining beliefs or propagating uncertainty. We broaden the debate by (1) exploring the constellation of secondary tasks surrounding any primary decision problem, and (2) identifying knowledge engineering concerns that present additional representational tradeoffs. We argue on pragmatic grounds that the attempt to support all of these tasks within a single calculus is misguided. In the process, we note several uncertain reasoning objectives that conflict with the Bayesian ideal of complete specification of probabilities and utilities. In response, we advocate treating the uncertainty calculus as an object language for reasoning mechanisms that support the secondary tasks. Arguments against Bayesian decision theory are weakened when the calculus is relegated to this role. Architectures for uncertainty handling that take statements in the calculus as objects to be reasoned about offer the prospect of retaining normative status with respect to decision making while supporting the other tasks in uncertain reasoning.

In our previous series of studies to investigate the role of evidential reasoning in the RUBRIC system for full-text document retrieval (Tong et al., 1985; Tong and Shapiro, 1985; Tong and Appelbaum, 1987), we identified the important role that problem structure plays in the overall performance of the system. In this paper, we focus on these structural elements (which we now call "semantic structure") and show how explicit consideration of their properties reduces what previously were seen as difficult evidential reasoning problems to more tractable questions.

The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference, some extensions seem to be simply wrong and we use qualitative techniques to weed out the unwanted ones. In the area of diagnosis, however, the multiple explanations may all seem reasonable, however improbable. Choosing among them is a matter of quantitative preference. Quantitative preference works well in diagnosis when knowledge is modelled causally. Here we suggest a framework that combines probabilities and defaults in a single unified framework that retains the semantics of diagnosis as construction of explanations from a fixed set of possible hypotheses. We can then compute probabilities incrementally as we construct explanations. Here we describe a branch and bound algorithm that maintains a set of all partial explanations while exploring a most promising one first. A most probable explanation is found first if explanations are partially ordered.