Reasoning with uncertainty using Nilsson's probabilistic logic and the maximum entropy formalism

Abstract

An expert system must reason with certain and uncertain information. This thesis is concerned with the process of Reasoning with Uncertainty. Nilsson's elegant model of "Probabilistic Logic" has been chosen as the framework for this investigation, and the information theoretical aspect of the maximum entropy formalism as the inference engine. These two formalisms, although semantically compelling, offer major complexity problems to the implementor. Probabilistic Logic models the complete uncertainty space, and the maximum entropy formalism finds the least commitment probability distribution within the uncertainty space. The main finding in this thesis is that Nilsson's Probabilistic Logic can be successfully developed beyond the structure proposed by Nilsson. Some deficiencies in Nilsson's model have been uncovered in the area of probabilistic representation, making Probabilistic Logic less powerful than Bayesian Inference techniques. These deficiencies are examined and a new model of entailment is presented which overcomes these problems, allowing Probabilistic Logic the full representational power of Bayesian Inferencing. The new model also preserves an important extension which Nilsson's Probabilistic Logic has over Bayesian Inference: the ability to use uncertain evidence. Traditionally, the probabilistic, solution proposed by the maximum entropy formalism is arrived at by solving non-linear simultaneous equations for the aggregate factors of the non- linear terms. In the new model the maximum entropy algorithms are shown to have the highly desirable property of tractability. Although these problems have been solved for probabilistic entailment the problems of complexity are still prevalent in large databases of expert rules. This thesis also considers the use of heuristics and meta level reasoning in a complex knowledge base. Finally, a description of an expert system using these techniques is given.