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.

This paper describes a natural framework for rules, based on belief functions, which includes a repre- sentation of numerical rules, default rules and rules allowing and rules not allowing contraposition. In particular it justifies the use of the Dempster-Shafer Theory for representing a particular class of rules, Belief calculated being a lower probability given certain independence assumptions on an underlying space. It shows how a belief function framework can be generalised to other logics, including a general Monte-Carlo algorithm for calculating belief, and how a version of Reiter's Default Logic can be seen as a limiting case of a belief function formalism.

Decision-theoretic control of search has previously used as its basic unit. of computation the generation and evaluation of a complete set of successors. Although this simplifies analysis, it results in some lost opportunities for pruning and satisficing. This paper therefore extends the analysis of the value of computation to cover individual successor evaluations. The analytic techniques used may prove useful for control of reasoning in more general settings. A formula is developed for the expected value of a node, k of whose n successors have been evaluated. This formula is used to estimate the value of expanding further successors, using a general formula for the value of a computation in game-playing developed in earlier work. We exhibit an improved version of the MGSS* algorithm, giving empirical results for the game of Othello.

This note is concerned with a formal analysis of the problem of nonmonotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is established by introducing conditioning notions by means of formal structures that do not rely on quantitative measures. The associated conditional logic, compatible with conditional probability evaluations, is nonmonotonic relative to additional evidence. Computational aspects of conditional probability logic are mentioned. The importance of this development lies on its role to provide a conceptual basis for various forms of evidence combination and on its significance to unify multi-valued and nonmonotonic logics. Introduction Consider the case of automated reasoning under uncertainty in which we wish to take into account the uncertainty in a quantitative way.

A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge. This knowledge is used to build a set of second-level arguments, which are structured for efficient recapture of the knowledge used to construct them. Finally, at the top level is a Bayesian network constructed from the arguments. The system is designed to facilitate not just propagation of beliefs and assimilation of evidence, but also the dynamic process of constructing a belief network, evaluating its adequacy, and revising it when necessary.

We point out the need to use probability amplitudes rather than probabilities to model evidence accumulation in decision processes involving real physical sensors. Optical information processing systems are given as typical examples of systems that naturally gather evidence in this manner. We derive a new, amplitude-based generalization of the Hough transform technique used for object recognition in machine vision. We argue that one should use complex Hough accumulators and square their magnitudes to get a proper probabilistic interpretation of the likelihood that an object is present. Finally, we suggest that probability amplitudes may have natural applications in connectionist models, as well as in formulating knowledge-based reasoning problems.

While concept-based methods for information retrieval can provide improved performance over more conventional techniques, they require large amounts of effort to acquire the concepts and their qualitative and quantitative relationships. This paper discusses an architecture for probabilistic concept-based information retrieval which addresses the knowledge acquisition problem. The architecture makes use of the probabilistic networks technology for representing and reasoning about concepts and includes a knowledge acquisition component which partially automates the construction of concept knowledge bases from data. We describe two experiments that apply the architecture to the task of retrieving documents about terrorism from a set of documents from the Reuters news service. The experiments provide positive evidence that the architecture design is feasible and that there are advantages to concept-based methods.

This paper describes recent work on an ongoing project in medical diagnosis at the University of Guelph. A domain on which experts are not very good at pinpointing a single disease outcome is explored. On-line medical data is available over a relatively short period of time. Belief Functions (Dempster-Shafer theory) are first extracted from data and then modified with expert opinions. Several methods for doing this are compared and results show that one formulation statistically outperforms the others, including a method suggested by Shafer. Expert opinions and statistically derived information about dependencies among symptoms are also compared. The benefits of using uncertainty management techniques as methods for knowledge acquisition from data are discussed.

Incidence Calculus and Dempster-Shafer Theory of Evidence are both theories to describe agents' degrees of belief in propositions, thus being appropriate to represent uncertainty in reasoning systems. This paper presents a straightforward equivalence proof between some special cases of these theories.