Survey of several forms of updating, with a practical illustrative example. We study several updating (conditioning) schemes that emerge naturally from a common scenarion to provide some insights into their meaning. Updating is a subtle operation and there is no single method, no single 'good' rule. The choice of the appropriate rule must always be given due consideration. Planchet (1989) presents a mathematical survey of many rules. We focus on the practical meaning of these rules. After summarizing the several rules for conditioning, we present an illustrative example in which the various forms of conditioning can be explained.

Irrelevance-based partial MAPs are useful constructs for domain-independent explanation using belief networks. We look at two definitions for such partial MAPs, and prove important properties that are useful in designing algorithms for computing them effectively. We make use of these properties in modifying our standard MAP best-first algorithm, so as to handle irrelevance-based partial MAPs.

This paper proposes a new method for solving Bayesian decision problems. The method consists of representing a Bayesian decision problem as a valuation-based system and applying a fusion algorithm for solving it. The fusion algorithm is a hybrid of local computational methods for computation of marginals of joint probability distributions and the local computational methods for discrete optimization problems.

The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without resorting to their numerical definition. This paper explores a representation for independence statements using multiple undirected graphs and some simple graphical transformations. The independence statements derivable in this system are equivalent to those obtainable by the graphoid axioms. Therefore, this is a purely graphical proof technique for conditional independence.

In this article we present two ways of structuring bodies of evidence, which allow us to reduce the complexity of the operations usually performed in the framework of evidence theory. The first structure just partitions the focal elements in a body of evidence by their cardinality. With this structure we are able to reduce the complexity on the calculation of the belief functions Bel, Pl, and Q. The other structure proposed here, the Hierarchical Trees, permits us to reduce the complexity of the calculation of Bel, Pl, and Q, as well as of the Dempster's rule of combination in relation to the brute-force algorithm. Both these structures do not require the generation of all the subsets of the reference domain.

This paper introduces conceptual relations that synthesize utilitarian and logical concepts, extending the logics of preference of Rescher. We define first, in the context of a possible worlds model, constraint-dependent measures that quantify the relative quality of alternative solutions of reasoning problems or the relative desirability of various policies in control, decision, and planning problems. We show that these measures may be interpreted as truth values in a multi valued logic and propose mechanisms for the representation of complex constraints as combinations of simpler restrictions. These extended logical operations permit also the combination and aggregation of goal-specific quality measures into global measures of utility. We identify also relations that represent differential preferences between alternative solutions and relate them to the previously defined desirability measures. Extending conventional modal logic formulations, we introduce structures for the representation of ignorance about the utility of alternative solutions. Finally, we examine relations between these concepts and similarity based semantic models of fuzzy logic.

During interactions with human consultants, people are used to providing partial and/or inaccurate information, and still be understood and assisted. We attempt to emulate this capability of human consultants; in computer consultation systems. In this paper, we present a mechanism for handling uncertainty in plan recognition during task-oriented consultations. The uncertainty arises while choosing an appropriate interpretation of a user?s statements among many possible interpretations. Our mechanism handles this uncertainty by using probability theory to assess the probabilities of the interpretations, and complements this assessment by taking into account the information content of the interpretations. The information content of an interpretation is a measure of how well defined an interpretation is in terms of the actions to be performed on the basis of the interpretation. This measure is used to guide the inference process towards interpretations with a higher information content. The information content for an interpretation depends on the specificity and the strength of the inferences in it, where the strength of an inference depends on the reliability of the information on which the inference is based. Our mechanism has been developed for use in task-oriented consultation systems. The domain that we have chosen for exploration is that of a travel agency.

Deliberation plays an important role in the design of rational agents embedded in the real-world. In particular, deliberation leads to the formation of intentions, i.e., plans of action that the agent is committed to achieving. In this paper, we present a branching time possible-worlds model for representing and reasoning about, beliefs, goals, intentions, time, actions, probabilities, and payoffs. We compare this possible-worlds approach with the more traditional decision tree representation and provide a transformation from decision trees to possible worlds. Finally, we illustrate how an agent can perform deliberation using a decision-tree representation and then use a possible-worlds model to form and reason about his intentions.

Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about the actual result of the experiment may be quantified, representing either the likelihood of the choice of :r_X or the degree to which any such X would be suitable as a description of the outcome. The former case corresponds to a probability distribution, while the latter gives a possibility assignment on X. The study of such assignments and their properties falls within the purview of possibility theory [DP88, Y80, Z783. It, like probability theory, assigns values between 0 and 1 to express likelihoods of outcomes. Here, however, the similarity ends. Possibility theory uses the maximum and minimum functions to combine uncertainties, whereas probability theory uses the plus and times operations. This leads to very dissimilar theories in terms of analytical framework, even though they share several semantic concepts. One of the shared concepts consists of expressing quantitatively the uncertainty associated with a given distribution. In probability theory its value corresponds to the gain of information that would result from conducting an experiment and ascertaining an actual result. This gain of information can equally well be viewed as a decrease in uncertainty about the outcome of an experiment. In this case the standard measure of information, and thus uncertainty, is Shannon entropy [AD75, G77]. It enjoys several advantages-it is characterized uniquely by a few, very natural properties, and it can be conveniently used in decision processes. This application is based on the principle of maximum entropy; it has become a popular method of relating decisions to uncertainty. This paper demonstrates that an equally integrated theory can be built on the foundation of possibility theory. We first show how to define measures of in formation and uncertainty for possibility assignments. Next we construct an information-based metric on the space of all possibility distributions defined on a given domain. It allows us to capture the notion of proximity in information content among the distributions. Lastly, we show that all the above constructions can be carried out for continuous distributions-possibility assignments on arbitrary measurable domains. We consider this step very significant-finite domains of discourse are but approximations of the real-life infinite domains. If possibility theory is to represent real world situations, it must handle continuous distributions both directly and through finite approximations. In the last section we discuss a principle of maximum uncertainty for possibility distributions. We show how such a principle could be formalized as an inference rule. We also suggest it could be derived as a consequence of simple assumptions about combining information. We would like to mention that possibility assignments can be viewed as fuzzy sets and that every fuzzy set gives rise to an assignment of possibilities. This correspondence has far reaching consequences in logic and in control theory. Our treatment here is independent of any special interpretation; in particular we speak of possibility distributions and possibility measures, defining them as measurable mappings into the interval [0, 1]. Our presentation is intended as a self-contained, albeit terse summary. Topics discussed were selected with care, to demonstrate both the completeness and a certain elegance of the theory. Proofs are not included; we only offer illustrative examples.

For high level path planning, environments are usually modeled as distance graphs, and path planning problems are reduced to computing the shortest path in distance graphs. One major drawback of this modeling is the inability to model uncertainties, which are often encountered in practice. In this paper, a new tool, called U-yraph, is proposed for environment modeling. A U-graph is an extension of distance graphs with the ability to handle a kind of uncertainty. By modeling an uncertain environment as a U-graph, and a navigation problem as a Markovian decision process, we can precisely define a new optimality criterion for navigation plans, and more importantly, we can come up with a general algorithm for computing optimal plans for navigation tasks.