Representation and Learning of Propositional Knowledge in Symmetric Connectionist Networks

The goal of this article is to construct a connectionist inference engine that is capable of representing and learning nonmotonic knowledge. An extended version of propositional calculus is developed and is demonstrated to be useful for nonmonotonic reasoning and for coping with inconsistency that may be a result of noisy, unreliable sources of knowledge. Formulas of the extended calculus (called penalty logic) are proved to be equivalent in a very strong sense to symmetric networks (like Hopfield networks and Boltzmann machines), and efficient algorithms are given for translating back and forth between the two forms of knowledge representation. The... Read complete abstract on page 2.