A Connectionist Framework for Reasoning: Reasoning with Examples
We present a connectionist architecture that supports almost instantaneous deductive and abductive reasoning. The deduction algorithm responds in few steps for single rule queries and in general, takes time that is linear with the number of rules in the query. The abduction algorithm produces an explanation in few steps and the best explanation in time linear with the size of the assumption set. The size of the network is polynomially related to the size of other representations of the domain, and may even be smaller. 
 
We base our connectionist model on Valiant's Neuroidal model (Val94) and thus make minimal assumptions about the computing elements, which are assumed to be classical threshold elements with states. Within this model we develop a reasoning framework that utilizes a model-based approach to reasoning (KKS93; KR94b). In particular, we suggest to interpret the connectionist architecture as encoding examples of the domain we reason about and show how to perform various reasoning tasks with this interpretation. We then show that the representations used can be acquired efficiently from interactions with the environment and discuss how this learning process influences the reasoning performance of the network.