This paper presents an application of the Dempster-Shafer evidence combination scheme in building a rule based expert system shell for diagnostic reasoning. Domain knowledge is stored as rules with associated belief functions. The reasoning component uses a combination of forward and backward inferencing mechanisms to interact with the user in a mixed initiative format.

Advanced Decision Systems Abstract We present a thorough integration of hierarchical Bayesian inference with comprehensive physical representation of objects and their relations in a system for reasoning with geometry in machine vision. Bayesian inference provides a framework (or accruing probabilities to rank order hypotheses. This is a preliminary version of visual interpretation in SUCCESSOR, an intelligent, model-based vision system integrating multiple sensors. Introduction Our design for machine vision uses an evidential accrual process, a. beginning from representation and database of a priori models o(physical objects and their photometric, geometric, and functional properties, together with their relationships and environment, b. predicting observables using models of sensors and perceptual measurement processes; c. making measurements of corresponding observables, measuring image evidence for features of objects and structures of features such as edges, vertices and regions; d. generating hypotheses of instances o(objects from those measurements and predictions; and In range imagery, measurements are 3d. There is still a difficult stage of segmenting and estimating 3d relations that disclose object structure. In 2d images, there is an additional inference from 2d projected image evidence to 3d interpretation of surfaces. System structure tends to break up into a natural hierarchy of representation and processing [Binford 80).

The domain of spare parts forecasting is examined, and is found to present unique uncertainty based problems in the architectural design of a knowledge-based system. A mixture of different uncertainty paradigms is required for the solution, with an intriguing combinatoric problem arising from an uncertain choice of inference engines. Thus, uncertainty in the system is manifested in two different meta-levels. The different uncertainty paradigms and meta-levels must be integrated into a functioning whole. FRED is an example of a difficult real-world domain to which no existing uncertainty approach is completely appropriate. This paper discusses the architecture of FRED, highlighting: the points of uncertainty and other interesting features of the domain, the specific implications of those features on the system design (including the combinatoric explosions), their current implementation & future plans,and other problems and issues with the architecture.

Dempster's rule of combination has been the most controversial part of the Dempster-Shafer (D-S) theory. In particular, Zadeh has reached a conjecture on the noncombinability of evidence from a relational model of the D-S theory. In this paper, we will describe another relational model where D-S masses are represented as conditional granular distributions. By comparing it with Zadeh's relational model, we will show how Zadeh's conjecture on combinability does not affect the applicability of Dempster's rule in our model.

This paper shows that the common method used for making predictions under uncertainty in A1 and science is in error. This method is to use currently available data to select the best model from a given class of models-this process is called abduction-and then to use this model to make predictions about future data. The correct method requires averaging over all the models to make a prediction-we call this method transduction. Using transduction, an AI system will not give misleading results when basing predictions on small amounts of data, when no model is clearly best. For common classes of models we show that the optimal solution can be given in closed form.

The apparent failure of individual probabilistic expressions to distinguish uncertainty about truths from uncertainty about probabilistic assessments have prompted researchers to seek formalisms where the two types of uncertainties are given notational distinction. This paper demonstrates that the desired distinction is already a built-in feature of classical probabilistic models, thus, specialized notations are unnecessary.

EXAMINATION OF SHAFER'S CANONICAL EXAMPLES Kathryn Blackmond Laskey Decision Science Consortium, Inc. 7700 Leesburg Pike, Suite 421 Falls Church, VA 22043 1 Abstract In the canonical examples underlying Shafer-Dempster theory, beliefs over the hypotheses of interest are derived from a probability model for a set of auxiliary hypotheses. Beliefs are derived via a compatibility relation connecting the auxiliary hypotheses to subsets of the primary hypotheses. A belief function differs from a Bayesian probability model in that one does not condition on those parts of the evidence for which no probabilities are specified. The significance of this difference in conditioning assumptions is illustrated with two examples giving rise to identical belief functions but different Bayesian probability distributions. Introduction The artificial intelligence community is in the midst of a lively debate over the representation and manipulation of uncertainty.

A number of writers have supposed that for the full specification of belief, higher order probabilities are required. Some have even supposed that there may be an unending sequence of higher order probabilities of probabilities of probabilities.... In the present paper we show that higher order probabilities can always be replaced by the marginal distributions of joint probability distributions. We consider both the case in which higher order probabilities are of the same sort as lower order probabilities and that in which higher order probabilities are distinct in character, as when lower order probabilities are construed as frequencies and higher order probabilities are construed as subjective degrees of belief. In neither case do higher order probabilities appear to offer any advantages, either conceptually or computationally.

For example, Nilsson in [6] and Grosof in [3] have considered methods for reasoning with sets of probability assignments generated by probabilistic equality and inequality constraints1. Following Nilsson, I use the expression "Probabilistic Logic" to denote the collection of such methods. The aim of these methods is to compute a set of possible probabilities for a given statement from the specified set of probability assignments. If the set of probability assignments is generated by probabilistic equality and inequality constraints, the possible probabilities for a given statement form an interval. Since Dempster-Shafer also associates an interval with each statement A, namely the interval bounded by Bel(A) and Pls(A), the question arises as to the connection between Dempster-Shafer belief functions and sets of probability assignments defined by equality and inequality constraints. Grosof [3] has shown that the latter is a generalization of the former: every Dempster-Shafer belief function is representable by a set of probability assignments arising from equality and inequality constraints, but not vice-versa. A related issue concerns the connection between Dempster's rule of combination and the combination of evidence statements in probabilistic logic. Grosof [2] states some results concerning conditions under which these two methods of combining evidence yield the same result. The aim of this paper is to generalize Grosof's results and to investigate how divergent the two

Modifiable combining functions are a synthesis of two general approaches to combining evidence. Because they facilitate the acquisition, representation, explanation, and modification of expert knowledge about combinations of evidence, they are presented as a device for knowledge engineers, not as a normative theory of evidence combination. The basic idea of modifiable combining functions is to acquire degrees of belief for a subset of all possible combinations of evidence, then infer degrees of belief for other combinations in the set.