Computation of Normal Logic Programs by Fibring Neural Networks

In this paper, we develop a theory of the integration of fibring neural networks (a generalization of conventional neural networks) into model-theoretic semantics for logic programming. We present some ideas and results about the approximate computation by fibring neural networks of semantic immediate consequence operators TP and TP , where TP denotes a generalization of TP relative to a many-valued logic analogous to Kleene’s strong logic. We establish a minimalfixed-point semantics for normal logic programs somewhat analogous to the leastfixed-point semantics for definite logic programs. We argue that the class of logic programs for which the approximation by fibring neural networks may be employed to compute minimal fixed points of TP and of TP is the class of normal programs. Our theorems on the approximation of TP and TP for normal programs extend recent results on approximation of these operators for definite programs by conventional neural networks.