The belief network is a well-known graphical structure for representing independences in a joint probability distribution. The methods, which perform probabilistic inference in belief networks, often treat the conditional probabilities which are stored in the network as certain values. However, if one takes either a subjectivistic or a limiting frequency approach to probability, one can never be certain of probability values. An algorithm should not only be capable of reporting the probabilities of the alternatives of remaining nodes when other nodes are instantiated; it should also be capable of reporting the uncertainty in these probabilities relative to the uncertainty in the probabilities which are stored in the network. In this paper a method for determining the variances in inferred probabilities is obtained under the assumption that a posterior distribution on the uncertainty variables can be approximated by the prior distribution. It is shown that this assumption is plausible if their is a reasonable amount of confidence in the probabilities which are stored in the network. Furthermore in this paper, a surprising upper bound for the prior variances in the probabilities of the alternatives of all nodes is obtained in the case where the probability distributions of the probabilities of the alternatives are beta distributions. It is shown that the prior variance in the probability at an alternative of a node is bounded above by the largest variance in an element of the conditional probability distribution for that node.

When a planner must decide whether it has enough evidence to make a decision based on probability, it faces the sample size problem. Current planners using probabilities need not deal with this problem because they do not generate their probabilities from observations. This paper presents an event based language in which the planner's probabilities are calculated from the binomial random variable generated by the observed ratio of one type of event to another. Such probabilities are subject to error, so the planner must introspect about their validity. Inferences about the probability of these events can be made using statistics. Inferences about the validity of the approximations can be made using interval estimation. Interval estimation allows the planner to avoid making choices that are only weakly supported by the planner's evidence.

This paper outlines a methodology for analyzing the representational support for knowledge-based decision-modeling in a broad domain. A relevant set of inference patterns and knowledge types are identified. By comparing the analysis results to existing representations, some insights are gained into a design approach for integrating categorical and uncertain knowledge in a context sensitive manner.

A series of monte carlo studies were performed to compare the behavior of some alternative procedures for reasoning under uncertainty. The behavior of several Bayesian, linear model and default reasoning procedures were examined in the context of increasing levels of calibration error. The most interesting result is that Bayesian procedures tended to output more extreme posterior belief values (posterior beliefs near 0.0 or 1.0) than other techniques, but the linear models were relatively less likely to output strong support for an erroneous conclusion. Also, accounting for the probabilistic dependencies between evidence items was important for both Bayesian and linear updating procedures.

Any probabilistic model of a problem is based on assumptions which, if violated, invalidate the model. Users of probability based decision aids need to be alerted when cases arise that are not covered by the aid's model. Diagnosis of model failure is also necessary to control dynamic model construction and revision. This paper presents a set of decision theoretically motivated heuristics for diagnosing situations in which a model is likely to provide an inadequate representation of the process being modeled.

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzzy sets of interpretations, each fuzzy set representing a possibility distribution describing what is known about the state of the world. A possibilistic knowledge base is then viewed as a set of possibility distributions that satisfy it. The refutation method of automated deduction in possibilistic logic, based on previously introduced generalized resolution principle is proved to be sound and complete with respect to the proposed semantics, including the case of partial inconsistency.

The concept of movable evidence masses that flow from supersets to subsets as specified by experts represents a suitable framework for reasoning under uncertainty. The mass flow is controlled by specialization matrices. New evidence is integrated into the frame of discernment by conditioning or revision (Dempster's rule of conditioning), for which special specialization matrices exist. Even some aspects of non-monotonic reasoning can be represented by certain specialization matrices.

The categorial approach to evidential reasoning can be seen as a combination of the probability kinematics approach of Richard Jeffrey (1965) and the maximum (cross-) entropy inference approach of E. T. Jaynes (1957). As a consequence of that viewpoint, it is well known that category theory provides natural definitions for logical connectives. In particular, disjunction and conjunction are modelled by general categorial constructions known as products and coproducts. In this paper, I focus mainly on Dempster-Shafer theory of belief functions for which I introduce a category I call Dempster?s category. I prove the existence of and give explicit formulas for conjunction and disjunction in the subcategory of separable belief functions. In Dempster?s category, the new defined conjunction can be seen as the most cautious conjunction of beliefs, and thus no assumption about distinctness (of the sources) of beliefs is needed as opposed to Dempster?s rule of combination, which calls for distinctness (of the sources) of beliefs.

We motivate and describe a theory of belief in this paper. This theory is developed with the following view of human belief in mind. Consider the belief that an event E will occur (or has occurred or is occurring). An agent either entertains this belief or does not entertain this belief (i.e., there is no "grade" in entertaining the belief). If the agent chooses to exercise "the will to believe" and entertain this belief, he/she/it is entitled to a degree of confidence c (1 > c > 0) in doing so. Adopting this view of human belief, we conjecture that whenever an agent entertains the belief that E will occur with c degree of confidence, the agent will be surprised (to the extent c) upon realizing that E did not occur.

We discuss representing and reasoning with knowledge about the time-dependent utility of an agent's actions. Time-dependent utility plays a crucial role in the interaction between computation and action under bounded resources. We present a semantics for time-dependent utility and describe the use of time-dependent information in decision contexts. We illustrate our discussion with examples of time-pressured reasoning in Protos, a system constructed to explore the ideal control of inference by reasoners with limit abilities.