Logic programming is being used extensively by Artificial Intelligence researchers to solve problems including natural language processing and expert systems. These languages, of which Prolog is the most widely used, promise to revolutionize software engineering, but much greater performance is needed. Researchers have demonstrated the applicability of neural network models to the solution of certain NP-complete problems, but these methods are not obviously applicable to the execution of logic programs. This paper outlines the use of neural networks in four aspects of the logic program execution cycle, and discusses results of a simulation of three of these. Four neural network functional units are described, called the substitution agent, the clause filter, the structure processor, and the heuristics generator, respectively. Simulation results suggest that the system described may provide several orders of magnitude improvement in execution speed for large logic programs. However, practical implementation of the proposed architecture will require the application of optical computing techniques due to the large number of neurons required, and the need for massive, adaptive connectivity.