A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In particular, the method allows belief network algorithms to calculate general probabilistic propositions over nodes in the network. Although in the worst case the time complexity of the method is exponential in the size of a query, it is polynomial in the size of a number of common types of queries.

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and solution of probabilistic and decision-theoretic models for complex and uncertain domains. Given a query, a logical proof is produced if possible; if not, an influence diagram based on the query and the knowledge of the decision domain is produced and subsequently solved. A uniform declarative, first-order, knowledge representation is combined with a set of integrated inference procedures for logical, probabilistic, and decision-theoretic reasoning.

Our previous work on classifying complex ship images [1,2] has evolved into an effort to develop software tools for building and solving generic classification problems. Managing the uncertainty associated with feature data and other evidence is an important issue in this endeavor. Bayesian techniques for managing uncertainty [7,12,13] have proven to be useful for managing several of the belief maintenance requirements of classification problem solving. One such requirement is the need to give qualitative explanations of what is believed. Pearl [11] addresses this need by computing what he calls a belief commitment-the most probable instantiation of all hypothesis variables given the evidence available. Before belief commitments can be computed, the straightforward implementation of Pearl's procedure involves finding an analytical solution to some often difficult optimization problems. We describe an efficient implementation of this procedure using tensor products that solves these problems enumeratively and avoids the need for case by case analysis. The procedure is thereby made more practical to use in the general case.

Much of the controversy about methods for automated decision making has focused on specific calculi for combining beliefs or propagating uncertainty. We broaden the debate by (1) exploring the constellation of secondary tasks surrounding any primary decision problem, and (2) identifying knowledge engineering concerns that present additional representational tradeoffs. We argue on pragmatic grounds that the attempt to support all of these tasks within a single calculus is misguided. In the process, we note several uncertain reasoning objectives that conflict with the Bayesian ideal of complete specification of probabilities and utilities. In response, we advocate treating the uncertainty calculus as an object language for reasoning mechanisms that support the secondary tasks. Arguments against Bayesian decision theory are weakened when the calculus is relegated to this role. Architectures for uncertainty handling that take statements in the calculus as objects to be reasoned about offer the prospect of retaining normative status with respect to decision making while supporting the other tasks in uncertain reasoning.

The comparisons of uncertainty calculi from the last two Uncertainty Workshops have all used theoretical probabilistic accuracy as the sole metric. While mathematical correctness is important, there are other factors which should be considered when developing reasoning systems. These other factors include, among other things, the error in uncertainty measures obtainable for the problem and the effect of this error on the performance of the resulting system. There are some domains in which many of the interesting conditional probabilities can be objectively estimated. For example, census data allows various characterizations of individuals with a reasonable degree of confidence.

In an earlier paper, a new theory of measurefree "conditional" objects was presented. In this paper, emphasis is placed upon the motivation of the theory. The central part of this motivation is established through an example involving a knowledge-based system. In order to evaluate combination of evidence for this system, using observed data, auxiliary at tribute and diagnosis variables, and inference rules connecting them, one must first choose an appropriate algebraic logic description pair (ALDP): a formal language or syntax followed by a compatible logic or semantic evaluation (or model). Three common choices- for this highly non-unique choice - are briefly discussed, the logics being Classical Logic, Fuzzy Logic, and Probability Logic. In all three,the key operator representing implication for the inference rules is interpreted as the often-used disjunction of a negation (b => a) = (b'v a), for any events a,b. However, another reasonable interpretation of the implication operator is through the familiar form of probabilistic conditioning. But, it can be shown - quite surprisingly - that the ALDP corresponding to Probability Logic cannot be used as a rigorous basis for this interpretation! To fill this gap, a new ALDP is constructed consisting of "conditional objects", extending ordinary Probability Logic, and compatible with the desired conditional probability interpretation of inference rules. It is shown also that this choice of ALDP leads to feasible computations for the combination of evidence evaluation in the example. In addition, a number of basic properties of conditional objects and the resulting Conditional Probability Logic are given, including a characterization property and a developed calculus of relations.

This paper describes a heuristic Bayesian method for computing probability distributions from experimental data, based upon the normal distribution form of the influence diagram. An example illustrates its use in medical technology assessment. This approach facilitates the integration of results from different studies, and permits a medical expert to make proper assessments without considerable statistical training. There has been extensive research on the construction and manipulation of expert systems using probabilities as a measure for uncertainty. These systems are capable of recognizing considerable dependence and of learning from unreliable observations.

Poly-trees are singly connected causal networks in which variables may arise from multiple causes. This paper develops a method of recovering ply-trees from empirically measured probability distributions of pairs of variables. The method guarantees that, if the measured distributions are generated by a causal process structured as a ply-tree then the topological structure of such tree can be recovered precisely and, in addition, the causal directionality of the branches can be determined up to the maximum extent possible. The method also pinpoints the minimum (if any) external semantics required to determine the causal relationships among the variables considered.

Decision tree induction systems are being used for knowledge acquisition in noisy domains. This paper develops a subjective Bayesian interpretation of the task tackled by these systems and the heuristic methods they use. It is argued that decision tree systems implicitly incorporate a prior belief that the simpler (in terms of decision tree complexity) of two hypotheses be preferred, all else being equal, and that they perform a greedy search of the space of decision rules to find one in which there is strong posterior belief. A number of improvements to these systems are then suggested.

This paper demonstrates a methodology for examining the accuracy of uncertain inference systems (UIS), after their parameters have been optimized, and does so for several common UIS's. This methodology may be used to test the accuracy when either the prior assumptions or updating formulae are not exactly satisfied. Surprisingly, these UIS's were revealed to be no more accurate on the average than a simple linear regression. Moreover, even on prior distributions which were deliberately biased so as give very good accuracy, they were less accurate than the simple probabilistic model which assumes marginal independence between inputs. This demonstrates that the importance of updating formulae can outweigh that of prior assumptions. Thus, when UIS's are judged by their final accuracy after optimization, we get completely different results than when they are judged by whether or not their prior assumptions are perfectly satisfied.