Rules and Variables in a Connectionist Reasoning System

[Lokendra Shastri]

Technical report announcement, please send requests to glenda at cis.upenn.edu


	A Connectionist System for Rule Based Reasoning with Multi-Place 
			Predicates and Variables

		 Lokendra Shastri and Venkat Ajjanagadde
		Computer and Information Science Department
			University of Pennsylvania
			Philadelphia, PA  19104

				MS-CIS-8906
				LINC LAB 141

				Abstract

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 modeling the remarkable human ability of performing certain inferences
with extreme efficiency.