We want to apply Funahashi's theorem in order to approximate the TP operator for first-order (normal) logic programs P via 3-layer feedforward networks. I.e. we need to understand TP as a continuous function on the reals.
We will need to study some preliminaries from set-theoretic topology first result from [HS00, HHS0x], which extends results from [HKS99]. We close with some further considerations about the methods and results.
(2004). Approximating First-Order Logic Programs by Feedforward Networks. .