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.

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.

Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete normative analysis impossible. We attempt to move discussion beyond the debate over the scope of problems that can be handled effectively to cases where it is clear that there are insufficient computational resources to perform an analysis deemed as complete. Under these conditions, we stress the importance of considering the expected costs and benefits of applying alternative approximation procedures and heuristics for computation and knowledge acquisition. We discuss how knowledge about the structure of user utility can be used to control value tradeoffs for tailoring inference to alternative contexts. We address the notion of real-time rationality, focusing on the application of knowledge about the expected timewise-refinement abilities of reasoning strategies to balance the benefits of additional computation with the costs of acting with a partial result. We discuss the benefits of applying decision theory to control the solution of difficult problems given limitations and uncertainty in reasoning resources.

We propose a norm of consistency for a mixed set of defeasible and strict sentences, based on a probabilistic semantics. This norm establishes a clear distinction between knowledge bases depicting exceptions and those containing outright contradictions. We then define a notion of entailment based also on probabilistic considerations and provide a characterization of the relation between consistency and entailment. We derive necessary and sufficient conditions for consistency, and provide a simple decision procedure for testing consistency and deciding whether a sentence is entailed by a database. Finally, it is shown that if al1 sentences are Horn clauses, consistency and entailment can be tested in polynomial time.

The purpose of this paper is to report on the most recent developments in our ongoing investigation of the representation and manipulation of uncertainty in automated reasoning systems. In our earlier studies (Tong and Shapiro, 1985) we described a series of experiments with RUBRIC (Tong et al., 1985), a system for full-text document retrieval, that generated some interesting insights into the effects of choosing among a class of scalar valued uncertainty calculi. [n order to extend these results we have begun a new series of experiments with a larger class of representations and calculi, and to help perform these experiments we have developed a general purpose inference engine.

Current approaches to expert systems' reasoning under uncertainty fail to capture the iterative revision process characteristic of intelligent human reasoning. This paper reports on a system, called the Non-monotonic Probabilist, or NMP (Cohen, et al., 1985). When its inferences result in substantial conflict, NMP examines and revises the assumptions underlying the inferences until conflict is reduced to acceptable levels. NMP has been implemented in a demonstration computer-based system, described below, which supports threat correlation and in-flight route replanning by Air Force pilots.

The issue of confidence factors in Knowledge Based Systems has become increasingly important and Dempster-Shafer (DS) theory has become increasingly popular as a basis for these factors. This paper discusses the need for an empirical lnterpretatlon of any theory of confidence factors applied to Knowledge Based Systems and describes an empirical lnterpretatlon of DS theory suggesting that the theory has been extensively misinterpreted. For the essentially syntactic DS theory, a model is developed based on sample spaces, the traditional semantic model of probability theory. This model is used to show that, if belief functions are based on reasonably accurate sampling or observation of a sample space, then the beliefs and upper probabilities as computed according to DS theory cannot be interpreted as frequency ratios. Since many proposed applications of DS theory use belief functions in situations with statistically derived evidence (Wesley [1]) and seem to appeal to statistical intuition to provide an lnterpretatlon of the results as has Garvey [2], it may be argued that DS theory has often been misapplied.

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.

Fuzzy logic is an important technique for modeling uncertainty in expert systems (i.e., in cases where inferencing of conclusion from given evidence is difficult to ascertain). This paper proposes a fuzzy expert system framework that combines case-based and rule-based reasoning effectively to produce a usable tool for Type 2 Diabetes Mellitus (T2DM) management. The major targets are on combined therapies (i.e., lifestyle and pharmacologic), and the recognition of management data dynamics (trends) during reasoning. The Knowledge base (KB) is constructed using fuzzified input values which are subsequently de-fuzziffied after reasoning, to produce crisp outputs to patients in the form of low-risk advice. The extended framework features a combined reasoning approach for simplified output in the form of decision support for clinicians. With seven operational input variables and two additional pre-set variables for testing, the results of the proposed work will be compared with other methods using similarity to expert’s decision as metrics.

We present a general architecture for the monitoring and diagnosis of large scale sensor-based systems with real time diagnostic constraints. This architecture is multileveled, combining a single monitoring level based on statistical methods with two model based diagnostic levels. At each level, sources of uncertainty are identified, and integrated methodologies for uncertainty management are developed. The general architecture was applied to the monitoring and diagnosis of a specific nuclear physics detector at Lawrence Berkeley National Laboratory that contained approximately 5000 components and produced over 500 channels of output data. The general architecture is scalable, and work is ongoing to apply it to detector systems one and two orders of magnitude more complex.