A note on the relationships between logic programs and neural networks

Authors:
Pascal Hitzler;Anthony Karel Seda
Affiliations:
Department of Mathematics, University College, Cork, Ireland;Department of Mathematics, University College, Cork, Ireland
Venue:
IW-FM'00 Proceedings of the 4th Irish conference on Formal Methods
Year:
2000

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Abstract

Several recent publications have exhibited relationships between the theories of logic programming and of neural networks. We consider a general approach to representing normal logic programs via feedforward neural networks. We show that the immediate consequence operator associated with each logic program, which can be understood as implicitly determining its declarative semantics, can be approximated by 3-layer feedforward neural networks arbitrarily well in a certain measure-theoretic sense. If this operator is continuous in a topology known as the atomic topology, then the approximation is uniform in all points.