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Nonmonotonic Inferences and Neural Networks

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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 non-monotonic 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 non-monotonic 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 non-monotonic 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.

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  1. Department of Philosophy, University of Amsterdam, Nieuwe Doelenstraat 15, Amsterdam, The Netherlands

    Reinhard Blutner

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  1. Reinhard Blutner
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Blutner, R. Nonmonotonic Inferences and Neural Networks. Synthese 142, 143–174 (2004). https://doi.org/10.1007/s11229-004-1929-y

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