Nonmonotonic Logic and Neural Networks

Abstract

A puzzle in the philosophy of mind concerns the gap between symbolic and subsymbolic (neuron-like) modes of processing (e.g. Smolensky 1988). The aim of this paper is to overcome this gap by viewing symbolism as a highlevel description of the properties of (a class of) neural networks. Combining methods of algebraic semantics and nonmonotonic logic, the possibility of integrating both modes of viewing cognition is demonstrated. The main results are (I) that certain activities of connectionist networks can be interpreted as nonmonotonic inferences, and (II) that there is a strict correspondence between the coding of knowledge in Hopfield networks and the knowledge representation in weight-annotated Poole systems. These results (a) show the usefulness of nonmonotonic logic as a descriptive and analytic tool for analyzing emerging properties of connectionist networks, (b) single out certain logical systems by giving them a "deeper justification", and (c) pave the way for using connectionist methods (e.g. "simulated annealing") in order to perform nonmonotinic inferences.