This paper discusses the semantics and proof theory of Nilsson's probabilistic logic, outlining both the benefits of its well-defined model theory and the drawbacks of its proof theory. Within Nilsson's semantic framework, we derive a set of inference rules which are provably sound. The resulting proof system, in contrast to Nilsson's approach, has the important feature of convergence - that is, the inference process proceeds by computing increasingly narrow probability intervals which converge from above and below on the smallest entailed probability interval. Thus the procedure can be stopped at any time to yield partial information concerning the smallest entailed interval.

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.

More precisely, given an evaluation of certain evidences, an evidential reasoning scheme generates an evaluation of certain hypotheses. When the evaluation of the evidences Is a binary one, that Is, we either have an evidence or do not have that evidence, the scheme acts as a set function for each hypothesis: a value as an evaluation of the hypothesis Is assigned to each subset of evidences. When the evaluation of hypotheses is also a binary one, the scheme can be represented by a collection of boolean "If-then" rules. Various approaches may be used to mak e this collection more compact. Intermediate concepts, default rules, and other Inventions I Ik e the "choice components" in SEEK2 are among these approaches. The problem becomes more compl lcated when the evaluation of hypotheses uses values from a I inearly ordered set (Integers, real numbers, or I lngulstlc quantifiers) or a partially ordered set (Intervals or property hierarchies). It becomes even more complex when hypotheses are related to each other (Shafer's theory Is an example when hypotheses are subsets of a set), or when the evaluation of evidences are not binary (systems where hypotheses can serve as evidences to other hypothese are examp I es).

RUM (Reasoning with Uncertainty Module), is an integrated software tool based on a KEE, a frame system implemented in an object oriented language. RUM's architecture is composed of three layers: representation, inference, and control. The representation layer is based on frame-like data structures that capture the uncertainty information used in the inference layer and the uncertainty meta-information used in the control layer. The inference layer provides a selection of five T-norm based uncertainty calculi with which to perform the intersection, detachment, union, and pooling of information. The control layer uses the meta-information to select the appropriate calculus for each context and to resolve eventual ignorance or conflict in the information. This layer also provides a context mechanism that allows the system to focus on the relevant portion of the knowledge base, and an uncertain-belief revision system that incrementally updates the certainty values of well-formed formulae (wffs) in an acyclic directed deduction graph. RUM has been tested and validated in a sequence of experiments in both naval and aerial situation assessment (SA), consisting of correlating reports and tracks, locating and classifying platforms, and identifying intents and threats. An example of naval situation assessment is illustrated. The testbed environment for developing these experiments has been provided by LOTTA, a symbolic simulator implemented in Flavors. This simulator maintains time-varying situations in a multi-player antagonistic game where players must make decisions in light of uncertain and incomplete data. RUM has been used to assist one of the LOTTA players to perform the SA task.

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.

When creating an expert system, the most difficult and expensive task is constructing a knowledge base. This is particularly true if the problem involves noisy data and redundant measurements. This paper shows how to modify the MACIE process for generating connectionist expert systems from training examples so that it can accommodate noisy and redundant data. The basic idea is to dynamically generate appropriate training examples by constructing both a 'deep' model and a noise model for the underlying problem. The use of winner-take-all groups of variables is also discussed. These techniques are illustrated with a small example that would be very difficult for standard expert system approaches.

An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such systems. It is not complete for information systems with more than two hypotheses, but applies to a subset of such systems. The logic is inductive in that conclusions are more informative than premises. Inferences using the formalism have a strong justification in terms of the expected value of the derived information system.

The use of numerical uncertainty representations allows better modeling of some aspects of human evidential reasoning. It also makes knowledge acquisition and system development, test, and modification more difficult. We propose that where possible, the assignment and/or refinement of rule weights should be performed automatically. We present one approach to performing this training - numerical optimization - and report on the results of some preliminary tests in training rule bases. We also show that truth maintenance can be used to make training more efficient and ask some epistemological questions raised by training rule weights.

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.