Parallel Formulation of Evidential-Reasoning Theories

There it no general consensus on how bett to attack evidential-reasoning (ER) problems, particularly in expert-system applications. Several approaches have evolved, but they have their roots in diverse fields, such as statistics and philosophy, and have neither a common terminology nor a common set of assumptions. The research reported here provides two useful results. First, it structures the evidential-reasoning problem in a general paradigm robust enough to be of practical use in design and construction of expert systems. Second, it uses this paradigm to formulate five important theoretical approaches in a parallel fashion in order to identify key assumptions, similarities, and differences. The five approaches discussed are classical Bayes, convex Bayes, Dempster-Shafer, Kyburg, and possibility. I. STRUCTURING THE PROBLEM The handling of evidence is a central element in such expert-system applications as diagnosis, integration, and control. In most tasks, evidence accumulates over time to dynamically affect uncertainties, so that the decision preferred earlier may differ from the one preferred later. However, delaying a decision is often not feasible, since this may foreclose opportunities or increase costs. Thus, it is important to understand how accumulating evidence will affect the decision process in the face of uncertainty. The evidential-reasoning (ER) problem may be expressed in the following way: given reports about the world, and a set of current beliefs about the world, how shall I revise my beliefs as new reports are received? Reports may range from the simple to the complex, referring to various objects and events, and may contain various uncertainties. Beliefs also range from the simple to the complex, and have a notoriously obscure structure. The fact that several different theoretical approaches to evidential rationing have evolved makes it difficult to formulate and answer important questions of application. For example, what are the rules for structuring the reports about the world that feed raw material into the updating schemes advocated by each theoretical approach? What are the constraints on ER that are implicit (and explicit) in application of each of the approaches? This leads us to seek a structured paradigm broad enough to encompass the models associated with each approach. Such a paradigm can be constructed in four parts as follows: Background Elements This portion of the paradigm contains a definition of the domain of discourse, that is, of the world-model to which we shall apply the ER process. It also contains current knowledge of that world including, possibly, knowledge of the cost of various actions in that world. Knowledge is described in terms of belief Observation Reports This portion of the paradigm describes the structure and content of reports about the external world that are the raw material for revision of the knowledge embedded in the background. Updating Mechanism This portion of the paradigm describes the assumptions, rules, and algorithms used to revise knowledge upon receipt of observation reports. Decision Mechanism This portion of the paradigm describes the assumptions, rules, and algorithms used to choose among various courses of action given revised knowledge of the world. We shall use this paradigm as a framework for the remainder of the I I . THEORETICAL APPROACHES We will discuss five major approaches to evidential reasoning: classical Bayes, convex Bayes, Dempster-Shafsr, Kyburg, and possibility. Each will be presented separately using the structured ER paradigm described above.