The Boltzmann Machine: a Connectionist Model for Supra-Classical Logic

Abstract

This thesis moves towards reconciliation of two of the major paradigms of artificial intelligence: by exploring the representation of symbolic logic in an artificial neural network. Previous attempts at the machine representation of classical logic are reviewed. We however, consider the requirements of inference in the broader realm of supra-classical, non-monotonic logic. This logic is concerned with the tolerance of exceptions, thought to be associated with common-sense reasoning. Biological plausibility extends these requirements in the context of human cognition.

The thesis identifies the requirements of supra-classical, non-monotonic logic in relation to the properties of candidate neural networks. Previous research has theoretically identified the Boltzmann machine as a potential candidate. We provide experimental evidence supporting a version of the Boltzmann machine as a practical representation of this logic.

The theme is pursued by looking at the benefits of utilising the relationship between the logic and the Boltzmann machine in two areas. We report adaptations to the machine architecture which select for different information distributions. These distributions correspond to state preference in traditional logic versus the concept of atomic typicality in contemporary approaches to logic. We also show that the learning algorithm of the Boltzmann machine can be adapted to implement pseudo-rehearsal during retraining. The results of machine retraining are then utilised to consider the plausibility of some current theories of belief revision in logic. Furthermore, we propose an alternative approach to belief revision based on the experimental results of retraining the Boltzmann machine.