During the past two years, the Dempster-Shafer theory of evidence has attracted considerable attention within the AI community as a promising method of dealing with uncertainty in expert systems. As presented in the literature, the theory is hard to master. In a simple approach that is outlined in this paper, the Dempster-Shafer theory is viewed in the context of relational databases as the application of familiar retrieval techniques to second-order relations in first normal form. The relational viewpoint clarifies some of the controversial issues in the Dempster-Shafer theory and facilities its use in AI-oriented applications.

In fact, such a pattern can itself be considered a frame, where the position of each pixel is a slot, and the shade or A recent article by Ronald Brachman (Brachman, color at each pixel is then the attached value. It should 1985) points out some philosophical or semantic problems then be possible to represent this pattern as I have just in using the notion of a prototype, which is described by described it-z.e., by a frame representing the background, using default properties. The problem arises since default partially obscured or covered by a frame representing the properties can be overridden or cancelled in representing object of interest, partially obscured or covered by some particular instances, and therefore lack definitional power: other objects. The fact that some part of the object of interest is obscured does not mean that it is no longer there, nor As an example, Brachman presents an elephant joke: that it is not intrinsic to the object's definition. Q: What's big and gray, has a trunk, and lives in the trees?

Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to represent the generic knowledge of a domain expert, and it turns into a computational architecture if the links are used not merely for storing factual knowledge but also for directing and activating the data flow in the computations which manipulate this knowledge. The first part of the paper deals with the task of fusing and propagating the impacts of new information through the networks in such a way that, when equilibrium is reached, each proposition will be assigned a measure of belief consistent with the axioms of probability theory. It is shown that if the network is singly connected (e.g. The second part of the paper deals with the problem of finding a tree-structured representation for a collection of probabilistically coupled propositions using auxiliary (dummy) variables, colloquially called “hidden causes.”

We present a logical relationship between a small number of intuitive properties for measures of belief and the axioms of probability theory. The relationship was first demonstrated several decades ago but has remained obscure. We introduce the proof and discuss its relevance to research on reasoning under uncertainty in artificial intelligence. In particular, we demonstrate that the logical relationship can facilitate the identification of differences among alternative plausible reasoning methodologies. Finally, we make use of the relationship to examine popular non-probabilistic strategies.

See also: Evaluating influence diagrams with decision circuits. In Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence (UAI2007)Operations Research, 34, 871-882

The choice of implication as a representation for empirical associations and for deduction as a model of inference requires a mechanism extraneous to deduction to manage uncertainty associated with inference. Consequently, the interpretation of representations of uncertainty is unclear. Representativeness, or degree of fit, is proposed as an interpretation of degree of belief for classification tasks. The calculation of representativeness depends on the nature of the associations between evidence and conclusions. Patterns of associations are characterized as endorsements of conclusions. We discuss an expert system that uses endorsements to control the search for the most representative conclusion, given evidence.

Two topics are treated here. Second, we present an inference machine. This machine treats uncertain knowledge in the form of evidence for and against the accuracy of a proposition. The connection between these two topics is established by implementation of the user model on the inference machine.

In Defense of Probability Peter Cheeseman SRI International 333 Ravenswood Ave., Menlo Park, California 94025 Abstract In this paper, it is argued that probability theory, when used correctly, is suffrcient for the task of reasoning under uncertainty. Since numerous authors have rejected probability as inadequate for various reasons, the bulk of the paper is aimed at refuting these claims and indicating the scources of error. In particular, the definition of probability as a measure of belief rather than a frequency ratio is advocated, since a frequency interpretation of probability drastically restricts the domain of applicability. Other sources of error include the confusion between relative and absolute probability, the distinction between probability and the uncertainty of that probability. Also, the interaction of logic and probability is discusses and it is argued that many extensions of logic, such as "default logic" are better understood in a probabilistic framework. The main claim of this paper is that the numerous schemes for representing and reasoning about uncertainty that have appeared in the AI literature are unnecessary--probability is all that is needed. 1 Introduction A glance through any major AI publication shows that an overwhelming proportion of papers are concerned with what might be described as the logical approach to inference and knowledge representation. It now widely accepted that many knowledge representations can be mapped into (first order) predicate calculus, and the corresponding inference procedures can be reduced to a type of controlled logical deduction. However, examples of human reasoning (judgements) are full of such terms as "probably", "most", "usually" etc., showing that many patterns of human reasoning are not logical in form, but intrinsically probabilistic. The claim that many patterns of human reasoning are probabilistic does not mean that the underlying "logic" of such patterns cannot be axiomatized. On the contrary, a basis for such an axiomatization is given in section 3. The claim is that when such an exercise is performed, the resulting patterns of inference are different in form from those found in analogous logical deductions.

Proceedings of the 7th Conference of the Cognitive Science Society, University of California, Irvine, CA. pp. 329–334

It may be argued that this, in principle, is a more realistic approach because it addresses, rather than finesses, the problem of incomplete information in the knowledge base. On the other hand, the Dempster-Shafer theory provides a basis-at least at present-for only a small subset of the rules of combination which are needed for inferencing in expert systems. In particular, the theory does not address the issue of chaining, nor does it come to grips with the fuzziness of probabilities and certainty factors. Thus, although the theory is certainly a step in the right direction, for it provides a framework for dealing with granular data, it does require a great deal of further development to become a broadly useful tool for the management of uncertainty in expert systems. Although not easy to understand, Shafer's book contains a wealth of significant results, and is a must for anyone who wants to do serious research on problems relating to the rules of combination of evidence in expert systems. Indeed, there is no doubt that, in the years to come, the Dempster-Shafer theory and its extensions will become an integral part of the theory of such systems and will certainly occupy an important place in knowledge engineering and related fields.