We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude of disbelief, which impose constraints over possible rankings of worlds. It was shown that, once we compute a priority function Z+ on the rules, the degree to which a given query is confirmed or denied can be computed in O(log n`) propositional satisfiability tests, where n is the number of rules in the knowledge base. In this paper, we show that computing Z+ requires O(n2 X log n) satisfiability tests, not an exponential number as was conjectured in [18], which reduces to polynomial complexity in the case of Horn expressions. We also show how reasoning with imprecise observations can be incorporated in our formalism and how the popular notions of belief revision and epistemic entrenchment are embodied naturally and tractably.

To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference algorithms operate over the network to answer queries. Recognizing the inflexibility of fixed models has led researchers to develop automated network construction procedures that use an expressive knowledge base to generate a network that can answer a query. Although more flexible than fixed model approaches, these construction procedures separate construction and evaluation into distinct phases. In this paper we develop an approach to combining incremental construction and evaluation of a partial probability model. The combined method holds promise for improved methods for control of model construction based on a trade-off between fidelity of results and cost of construction.

In the probabilistic approach to uncertainty management the input knowledge is usually represented by means of some probability distributions. In this paper we assume that the input knowledge is given by two discrete conditional probability distributions, represented by two stochastic matrices P and Q. The consistency of the knowledge base is analyzed. Coherence conditions and explicit formulas for the extension to marginal distributions are obtained in some special cases.

This article offers a modification of Chow and Liu's learning algorithm in the context of handwritten digit recognition. The modified algorithm directs the user to group digits into several classes consisting of digits that are hard to distinguish and then constructing an optimal conditional tree representation for each class of digits instead of for each single digit as done by Chow and Liu (1968). Advantages and extensions of the new method are discussed. Related works of Wong and Wang (1977) and Wong and Poon (1989) which offer a different entropy-based learning algorithm are shown to rest on inappropriate assumptions.

Data fusion allows the elaboration and the evaluation of a situation synthesized from low level informations provided by different kinds of sensors. The fusion of the collected data will result in fewer and higher level informations more easily assessed by a human operator and that will assist him effectively in his decision process. In this paper we present the suitability and the advantages of using a Possibilistic Assumption based Truth Maintenance System (0-ATMS) in a data fusion military application. We first describe the problem, the needed knowledge representation formalisms and problem solving paradigms. Then we remind the reader of the basic concepts of ATMSs, Possibilistic Logic and Il-ATMSs. Finally we detail the solution to the given data fusion problem and conclude with the results and comparison with a non-possibilistic solution.

We report on an experimental investigation into opportunities for parallelism in beliefnet inference. Specifically, we report on a study performed of the available parallelism, on hypercube style machines, of a set of randomly generated belief nets, using factoring (SPI) style inference algorithms. Our results indicate that substantial speedup is available, but that it is available only through parallelization of individual conformal product operations, and depends critically on finding an appropriate factoring. We find negligible opportunity for parallelism at the topological, or clustering tree, level.

We describe how we selectively reformulate portions of a belief network that pose difficulties for solution with a stochastic-simulation algorithm. With employ the selective conditioning approach to target specific nodes in a belief network for decomposition, based on the contribution the nodes make to the tractability of stochastic simulation. We review previous work on BNRAS algorithms- randomized approximation algorithms for probabilistic inference. We show how selective conditioning can be employed to reformulate a single BNRAS problem into multiple tractable BNRAS simulation problems. We discuss how we can use another simulation algorithm-logic sampling-to solve a component of the inference problem that provides a means for knitting the solutions of individual subproblems into a final result. Finally, we analyze tradeoffs among the computational subtasks associated with the selective conditioning approach to reformulation.

Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical formulas. Uncertain information is expressed by means of parameterized modal operators. We propose a semantics for this multimodal logic and give a sound and complete axiomatization. We study the links with related approaches and suggest how this framework might be used to manage both uncertain and incomplere knowledge.

Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and structural observability theorems are developed and algorithms are formulated. Controllability and observability are fundamental concepts in dynamic systems (Luenberger 1979). Controllability corresponds to the ability to control a system while observability analyzes the inferability of its variables. Both properties can be determined by the ranks of the system matrices. Structural controllability and observability, on the other hand, analyze the property of a system with its structure only, without the specific knowledge of the values of its elements (tin 1974, Shields and Pearson 1976). The structural analysis explores the connection between the structure of a model and the functional dependence among its elements. It is useful in comprehending problem and formulating solution by challenging the underlying intuitions and detecting inconsistency in a model. This type of qualitative reasoning can sometimes provide insight even when there is insufficient numerical information in a model.

Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and modal logics. We present two modal logics that can be used to represent and reason with qualitative statements of possibility and necessity. Within this modal framework, we are able to identify interesting relationships between possibilistic logic, beliefs and conditionals. In particular, the most natural conditional definable via possibilistic means for default reasoning is identical to Pearl's conditional for e-semantics.