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.

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.

This paper analyzes the circumstances under which Bayesian networks can be pruned in order to reduce computational complexity without altering the computation for variables of interest. Given a problem instance which consists of a query and evidence for a set of nodes in the network, it is possible to delete portions of the network which do not participate in the computation for the query. Savings in computational complexity can be large when the original network is not singly connected. Results analogous to those described in this paper have been derived before [Geiger, Verma, and Pearl 89, Shachter 88] but the implications for reducing complexity of the computations in Bayesian networks have not been stated explicitly. We show how a preprocessing step can be used to prune a Bayesian network prior to using standard algorithms to solve a given problem instance. We also show how our results can be used in a parallel distributed implementation in order to achieve greater savings. We define a computationally equivalent subgraph of a Bayesian network. The algorithm developed in [Geiger, Verma, and Pearl 89] is modified to construct the subgraphs described in this paper with O(e) complexity, where e is the number of edges in the Bayesian network. Finally, we define a minimal computationally equivalent subgraph and prove that the subgraphs described are minimal.

The arc reversal/node reduction approach to probabilistic inference is extended to include the case of instantiated evidence by an operation called "evidence reversal." This not only provides a technique for computing posterior joint distributions on general belief networks, but also provides insight into the methods of Pearl [1986b] and Lauritzen and Spiegelhalter [1988]. Although it is well understood that the latter two algorithms are closely related, in fact all three algorithms are identical whenever the belief network is a forest.

A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have required, in the worst case, time exponential in the number of attributes of the system. In this paper a closed form solution to the probability of an attribute given the evidence is found. The closed form solution, however does not enforce the (non-linear) constraint that all terms in the underlying distribution be positive. The equation requires O(r^3) steps to evaluate, where r is the number of independent marginal constraints describing the system at the time of evaluation. Furthermore, a marginal constraint may be exchanged with a new constraint, and a new solution calculated in O(r^2) steps. This method is appropriate for calculating probabilities in a real time expert system

A learning algorithm is presented which given the structure of a causal tree, will estimate its link probabilities by sequential measurements on the leaves only. Internal nodes of the tree represent conceptual (hidden) variables inaccessible to observation. The method described is incremental, local, efficient, and remains robust to measurement imprecisions.

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].

The causal Bayesian approach is based on the assumption that effects (e.g., symptoms) that are not conditionally independent with respect to some causal agent (e.g., a disease) are conditionally independent with respect to some intermediate state caused by the agent, (e.g., a pathological condition). This paper describes the development of a causal Bayesian model for the diagnosis of appendicitis. The paper begins with a description of the standard Bayesian approach to reasoning about uncertainty and the major critiques it faces. The paper then lays the theoretical groundwork for the causal extension of the Bayesian approach, and details specific improvements we have developed. The paper then goes on to describe our knowledge engineering and implementation and the results of a test of the system. The paper concludes with a discussion of how the causal Bayesian approach deals with the criticisms of the standard Bayesian model and why it is superior to alternative approaches to reasoning about uncertainty popular in the Al community.

Bayesian Belief Networks have been largely overlooked by Expert Systems practitioners on the grounds that they do not correspond to the human inference mechanism. In this paper, we introduce an explanation mechanism designed to generate intuitive yet probabilistically sound explanations of inferences drawn by a Bayesian Belief Network. In particular, our mechanism accounts for the results obtained due to changes in the causal and the evidential support of a node.

The generalized fault diagram, a data structure for failure analysis based on the influence diagram, is defined. Unlike the fault tree, this structure allows for dependence among the basic events and replicated logical elements. A heuristic procedure is developed for efficient processing of these structures.