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Significant advances have recently been made concerning the integration of symbolic knowledge representation with artificial neural networks (also called connectionist systems). However, while the integration with propositional paradigms has resulted in applicable systems, the case of first-order knowledge representation has so far hardly proceeded beyond theoretical studies which prove the existence of connectionist systems for approximating first-order logic programs up to any chosen precision. Advances were hindered severely by the lack of concrete algorithms for obtaining the approximating networks which were known to exist: the corresponding proofs are not constructive in that they do not yield concrete methods for building the systems. In this paper, we will make the required advance and show how to obtain the structure and the parameters for different kinds of connectionist systems approximating covered logic programs.


Presented at the International Joint Conference on Artificial Intelligence workshop on Neural-Symbolic Learning and Resonance, Edinburgh, Scotland, August 1, 2005.