A Connectionist Solution to the Multiple Instantiation Problem using Temporal Synchrony

Shastri and Ajjanagadde have described a neurally plausible system for knowledge representation and reasoning that can represent systematic knowledge involving n-ary predicates and variables, and perform a broad class of reasoning with extreme eeciency. The system maintains and propagates variable bindings using temporally synchronous|i.e., in-phase | ring of appropriate nodes. This paper extends the reasoning system to incorporate multiple instantia-tion of predicates, so that any predicate can be instantiated up to k times, k being a system parameter. The ability to accommodate multiple instantiations of a predicate allows the system to handle a much broader class of rules, including bounded transitiv-ity and recursion. The time and space requirements increase only by a constant factor, and the extended system can still answer queries in time proportional to the length of the shortest derivation of the query.