Nonmonotonic Inferences and Neural Networks
Reinhard Blutner

Abstract:
There is a gap between two different modes of computation: the
symbolic mode and the subsymbolic (neuron-like) mode. The aim of this
paper is to overcome this gap by viewing symbolism as a high-level
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 (a) that certain activities of
connectionist networks can be interpreted as nonmonotonic inferences,
and (b) 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 show the usefulness of
nonmonotonic logic as a descriptive and analytic tool for analyzing
emerging properties of connectionist networks. Assuming an exponential
development of the weight function, the present account relates to
optimality theory - a general framework that aims to integrate
insights from symbolism and connectionism. The paper concludes with
some speculations about extending the present ideas.