Approximating the Semantics of Logic Programs by RecurrentNeural

; Abstract. In 8] we have shown how to construct a 3{layer recurrent neural network that computes the iteration of the meaning function T P of a given propositional logic program, what corresponds to the computation of the semantics of the program. In this article we deene a notion of approximation for interpretations and prove that there exists a 3{layer feed forward neural network that approximates the calculation of T P for a given ((rst order) recurrent logic program with an injective level mapping arbitrarily well. Extending the feed forward network by recurrent connections one obtains an recurrent neural network whose iteration approximates the xed point of T P. This result is proved by taking advantage of the fact that for recurrent logic programs T P is a contraction mapping on the complete metric space of the interpretations for the program. Mapping this metric space to the metric space IR a real valued function f P can be found which corresponds to T P , is continuous as well a contraction, and | for this reason | can be approximated by an appropriately chosen class of feed forward neural networks.