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McCarthy has observed that the representational power of most connectionist systems is restricted to unary predicates applied to a fixed object. More recently, Fodor and Pylyshyn have made a sweeping claim that connectionist systems cannot incorporate systematicity and compositionality. These comments suggest that representing structured knowledge in a connectionist network and using this knowledge in a systematic way is considered difficult if not impossible. The work reported in this paper demonstrates that a connectionist system can not only represent structured knowledge and display systematic behavior, but it can also do so with extreme efficiency. The paper describes a connectionist system that can represent knowledge expressed as rules and facts involving multi-place predicates (i.e., n-ary relations), and draw limited, but sound, inferences based on this knowledge. The system is extremely efficient - in fact, optimal, as it draws conclusions in time proportional to the length of the proof. It is observed that representing and reasoning with structured knowledge requires a solution to the variable binding problem. A solution to this problem using a multi-phase clock is proposed. The solution allows the system to maintain and propagate an arbitrary number of variable bindings during the reasoning process. The work also identifies constraints on the structure of inferential dependencies and the nature of quantification in individual rules that are required for efficient reasoning. These constraints may eventually help in modelling the remarkable human ability of performing certain inferences with extreme efficiency.
Lokendra Shastri and Venkat Ajjanagadde, "A Connectionist System for Rule Based Reasoning With Multi-Place Predicates and Variables", . January 1989.
Date Posted: 06 December 2007