This research develops computer systems for representing knowledge, particularly by rule-based systems, and for reasoning with that knowledge by many processors operating in parallel. Target machines to support these parallel reasoning systems, such as the NCUBE hypercube, will be tested. The importance of this research is that rule based systems are the core of many "expert system" applications in artificial intelligence. These systems however are very demanding on the resources of a single-processor computer. In order to improve their performance, the theory and practice of their implementation on multiprocessor systems must be developed.