Abstract
In [9] we have shown how to construct a 3-layer recurrent neural network (RNN) 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 paper we define a notion of approximation for interpretations and prove that there exists a feed forward neural network (FNN) that approximates the calculation of T p for a given (first order) acceptable logic program with an injective level mapping arbitrarily well. By extending the FNN by recurrent connections we get a RNN whose iteration approximates the fixed point of T p .
The proof is found by taking advantage of the fact that for acceptable 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 the real valued function f p corresponding to T p turns out to be continuous and a contraction and for this reason can be approximated by an indicated class of FNN.
The author acknowledge support from the German Academic Exchange Service (DAAD) under grant no. D/97/29570.
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Hölldobler, S., Kalinke, Y., Störr, HP. (1998). Recurrent neural networks to approximate the semantics of acceptable logic programs. In: Antoniou, G., Slaney, J. (eds) Advanced Topics in Artificial Intelligence. AI 1998. Lecture Notes in Computer Science, vol 1502. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095050
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DOI: https://doi.org/10.1007/BFb0095050
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