Functional dependencies restrict the potential interactions among variables connected in a probabilistic network. This restriction can be exploited in qualitative probabilistic reasoning by introducing deterministic variables and modifying the inference rules to produce stronger conclusions in the presence of functional relations. I describe how to accomplish these modifications in qualitative probabilistic networks by exhibiting the update procedures for graphical transformations involving probabilistic and deterministic variables and combinations. A simple example demonstrates that the augmented scheme can reduce qualitative ambiguity that would arise without the special treatment of functional dependency. Analysis of qualitative synergy reveals that new higher-order relations are required to reason effectively about synergistic interactions among deterministic variables.

Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a probabilistic logic with truth functional connectives. We propose an alternative mechanism, Incidence Calculus, which is based on a representation of uncertainty using sets of points, which might represent situations, models or possible worlds. Incidence Calculus does provide a probabilistic logic with truth functional connectives.

ABSTRACT 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 interpretation of any theory of confidence factors applied to Knowledge Based Systems and describes an empirical interpretation of DS theory suggesting that the theory-has been seriously misinterpreted. For the essentially syntactic DS theory, the empirical model developed is based on the semantics of sample spaces. 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 OS theory cannot be interpreted as frequency ratios. Since a number of proposed applications of OS theory use belief functions in situations with statistically derived evidence and seem to appeal to statistical intuition to provide an interpretation of the results, it is likely that OS theory has often been misapplied. CONFIDENCE FACTORS, EMPIRICISM AND THE DEMPSTER-SHAFER THEORY OF EVIDENCE 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.

Henru Hamburger George Mason University and Naval Research Laboratory In an expert system, it is necessary to supply the values of various parameters. Ideally, an absolutely reliable source is available to supply an exact value for any parameter. In reality, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. This paper is a consideration of how to represent and combine imperfect estimates. It is assumed that the knowledge from each source takes the form of an estimate of the parameter value, paired with an associated measure of uncertainty.

Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of association between any number of pieces of evidence and conclusions. (Simpler models may be required, however, if the number of pieces of evidence bearing on a conclusion is large.) This paper presents a method of using these tables to make uncertain inferences without assumptions of conditional independence among pieces of evidence or heuristic combining rules. As evidence is accumulated, new joint probabilities are calculated so as to maintain any dependencies among the pieces of evidence that are found in the contingency table. The new conditional probability of the conclusion is then calculated directly from these new joint probabilities and the conditional probabilities in the contingency table.

This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are generally applicable, this paper illustrates them in heuristic search, which demands noise management and incremental learning. In our approach, both task performance and learning are guided by probability. Probabilities are incrementally normalized and revised, and their errors are located and corrected.

This paper describes a machine induction program (WITT) that attempts to model human categorization. Properties of categories to which human subjects are sensitive includes best or prototypical members, relative contrasts between putative categories, and polymorphy (neither necessary or sufficient features). This approach represents an alternative to usual Artificial Intelligence approaches to generalization and conceptual clustering which tend to focus on necessary and sufficient feature rules, equivalence classes, and simple search and match schemes. WITT is shown to be more consistent with human categorization while potentially including results produced by more traditional clustering schemes. Applications of this approach in the domains of expert systems and information retrieval are also discussed.

The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the relevant probabilities in a decision problem are known only to the extent that they belong to a class K of probability distributions. The concept is a generalization of a frequent suggestion that uncertainty be represented by intervals or ranges on probabilities. To make the representation useful for decision making, an inductive rule can be formulated which determines, in a well-defined manner, a best approximation to the unknown probability, given the set K. In addition, the knowledge set notion entails a natural procedure for updating -- modifying the set K given new evidence. Several non-intuitive consequences of updating emphasize the differences between inference with complete and inference with incomplete information.

Several different uncertain inference systems (UISs) have been developed for representing uncertainty in rule-based expert systems. Some of these, such as Mycin's Certainty Factors, Prospector, and Bayes' Networks were designed as approximations to probability, and others, such as Fuzzy Set Theory and DempsterShafer Belief Functions were not. How different are these UISs in practice, and does it matter which you use? When combining and propagating uncertain information, each UIS must, at least by implication, make certain assumptions about correlations not explicily specified. The maximum entropy principle with minimum cross-entropy updating, provides a way of making assumptions about the missing specification that minimizes the additional information assumed, and thus offers a standard against which the other UISs can be compared. We describe a framework for the experimental comparison of the performance of different UISs, and provide some illustrative results.

This paper is concerned with two theories of probability judgment: the Bayesian theory and the theory of belief functions. It illustrates these theories with some simple examples and discusses some of the issues that arise when we try to implement them in expert systems. The Bayesian theory is well known; its main ideas go back to the work of Thomas Bayes (1702-1761). The theory of belief functions, often called the Dempster-Shafer theory in the artificial intelligence community, is less well known, but it has even older antecedents; belief-function arguments appear in the work of George Hooper (16401723) and James Bernoulli (1654-1705). For elementary expositions of the theory of belief functions, see Shafer (1976, 1985).