We are interested in creating an automated or semi-automated system with the capability of taking a set of radar imagery, collection parameters and a priori map and other tactical data, and producing likely interpretations of the possible military situations given the available evidence. This paper is concerned with the problem of the interpretation and computation of certainty or belief in the conclusions reached by such a system. For example, if we consider the problem of confirming or denying the presence of a battalion in a given area, we should include in our decision making process the prior likelihood of military presence based on tactical objectives, the evidence of military vehicles in radar image data, the spatial and tactical clustering and patterns of the vehicles extracted from the imagery, etc. Furthermore, if the user of the system has particular interests such as knowing specific deployments, location of battalion headquarters, etc., then these interests should also be responded to

Current approaches to expert systems' reasoning under uncertainty fail to capture the iterative revision process characteristic of intelligent human reasoning. This paper reports on a system, called the Non-monotonic Probabilist, or NMP (Cohen, et al., 1985). When its inferences result in substantial conflict, NMP examines and revises the assumptions underlying the inferences until conflict is reduced to acceptable levels. NMP has been implemented in a demonstration computer-based system, described below, which supports threat correlation and in-flight route replanning by Air Force pilots.

This paper describes the incorporation of uncertainty in diagnostic reasoning based on the set covering model of Reggia et. al. extended to what in the Artificial Intelligence dichotomy between deep and compiled (shallow, surface) knowledge based diagnosis may be viewed as the generic form at the compiled end of the spectrum. A major undercurrent in this is advocating the need for a strong underlying model and an integrated set of support tools for carrying such a model in order to deal with uncertainty.

We describe a viewpoint on the Dempster/Shafer 'Theory of Evidence', and provide an interpretation which regards the combination formulas as statistics of the opinions of "experts". This is done by introducing spaces with binary operations that are simpler to interpret or simpler to implement than the standard combination formula, and showing that these spaces can be mapped homomorphically onto the Dempster/Shafer theory of evidence space. The experts in the space of "opinions of experts" combine information in a Bayesian fashion. We present alternative spaces for the combination of evidence suggested by this viewpoint.

In the 1940's, a physicist named Cox provided the first formal justification for the axioms of probability based on the subjective or Bayesian interpretation. He showed that if a measure of belief satisfies several fundamental properties, then the measure must be some monotonic transformation of a probability. In this paper, measures of change in belief or belief updates are examined. In the spirit of Cox, properties for a measure of change in belief are enumerated. It is shown that if a measure satisfies these properties, it must satisfy other restrictive conditions. For example, it is shown that belief updates in a probabilistic context must be equal to some monotonic transformation of a likelihood ratio. It is hoped that this formal explication of the belief update paradigm will facilitate critical discussion and useful extensions of the approach.

In this paper, we examine the concept of modularity, an often cited advantage of the ruled-based representation methodology. We argue that the notion of modularity consists of two distinct concepts which we call syntactic modularity and semantic modularity. We argue that when reasoning under certainty, it is reasonable to regard the rule-based approach as both syntactically and semantically modular. However, we argue that in the case of plausible reasoning, rules are syntactically modular but are rarely semantically modular. To illustrate this point, we examine a particular approach for managing uncertainty in rule-based systems called the MYCIN certainty factor model. We formally define the concept of semantic modularity with respect to the certainty factor model and discuss logical consequences of the definition. We show that the assumption of semantic modularity imposes strong restrictions on rules in a knowledge base. We argue that such restrictions are rarely valid in practical applications. Finally, we suggest how the concept of semantic modularity can be relaxed in a manner that makes it appropriate for plausible reasoning.

We start by defining an approach to non-monotonic probabilistic reasoning in terms of non-monotonic categorical (true-false) reasoning. We identify a type of non-monotonic probabilistic reasoning, akin to default inheritance, that is commonly found in practice, especially in "evidential" and "Bayesian" reasoning. We formulate this in terms of the Maximization of Conditional Independence (MCI), and identify a variety of applications for this sort of default. We propose a formalization using Pointwise Circumscription. We compare MCI to Maximum Entropy, another kind of non-monotonic principle, and conclude by raising a number of open questions

To develop an approach to utilizing continuous statistical information within the Dempster- Shafer framework, we combine methods proposed by Strat and by Shafero We first derive continuous possibility and mass functions from probability-density functions. Then we propose a rule for combining such evidence that is simpler and more efficiently computed than Dempster's rule. We discuss the relationship between Dempster's rule and our proposed rule for combining evidence over continuous frames.

There currently exists a gap between the theories proposed by the probability and uncertainty and the needs of Artificial Intelligence research. These theories primarily address the needs of expert systems, using knowledge structures which must be pre-compiled and remain static in structure during runtime. Many Al systems require the ability to dynamically add and remove parts of the current knowledge structure (e.g., in order to examine what the world would be like for different causal theories). This requires more flexibility than existing uncertainty systems display. In addition, many Al researchers are only interested in using "probabilities" as a means of obtaining an ordering, rather than attempting to derive an accurate probabilistic account of a situation. This indicates the need for systems which stress ease of use and don't require extensive probability information when one cannot (or doesn't wish to) provide such information. This paper attempts to help reconcile the gap between approaches to uncertainty and the needs of many AI systems by examining the control issues which arise, independent of a particular uncertainty calculus. when one tries to satisfy these needs. Truth Maintenance Systems have been used extensively in problem solving tasks to help organize a set of facts and detect inconsistencies in the believed state of the world. These systems maintain a set of true/false propositions and their associated dependencies. However, situations often arise in which we are unsure of certain facts or in which the conclusions we can draw from available information are somewhat uncertain. The non-monotonic TMS 12] was an attempt at reasoning when all the facts are not known, but it fails to take into account degrees of belief and how available evidence can combine to strengthen a particular belief. This paper addresses the problem of probabilistic reasoning as it applies to Truth Maintenance Systems. It describes a belief Maintenance System that manages a current set of beliefs in much the same way that a TMS manages a set of true/false propositions. If the system knows that belief in fact is dependent in some way upon belief in fact2, then it automatically modifies its belief in facts when new information causes a change in belief of fact2. It models the behavior of a TMS, replacing its 3-valued logic (true, false, unknown) with an infinite valued logic, in such a way as to reduce to a standard TMS if all statements are given in absolute true/false terms. Belief Maintenance Systems can, therefore, be thought of as a generalization of Truth Maintenance Systems, whose possible reasoning tasks are a superset of those for a TMS.

Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are: games-against nature [5, 6] varieties of maximum-entropy methods [7, 8, 9], and the author's min-score induction [10]. In the modeling approach, the basic issue is manageability, with respect to data elicitation and computation. Thus, it is assumed that the pertinent set of users in some sense knows the relevant probabilities, and the problem is to format that knowledge in a way that is convenient to input and store and that allows computation of the answers to current questions in an expeditious fashion. The basic issue for the inductive approach appears at first sight to be very different. In this approach it is presumed that the relevant probabilities are only partially known, and the problem is to extend that incomplete information in a reasonable way to answer current questions. Clearly, this approach requires that some form of induction be invoked. Of course, manageability is an important additional concern. Despite their seeming differences, the two approaches have a fair amount in common, especially with respect to the structural framework they employ. Roughly speaking, this framework involves identifying clusters of variables which strongly interact, establishing marginal probability distributions on the clusters, and extending the subdistributions to a more complete distribution, usually via a product formalism. The product extension is justified on the modeling approach in terms of assumed conditional independence; in the inductive approach the product form arises from an inductive rule.