The Weak Completion Semantics is a novel cognitive theory which has been successfully applied -- among others -- to the suppression task, the selection task and syllogistic reasoning. It is based on logic programming with skeptical abduction. Each weakly completed program admits a least model under the three-valued Lukasiewicz logic which can be computed as the least fixed point of an appropriate semantic operator. The operator can be represented by a three-layer feed-forward network using the Core method. Its least fixed point is the unique stable state of a recursive network which is obtained from the three-layer feed-forward core by mapping the activation of the output layer back to the input layer. The recursive network is embedded into a novel network to compute skeptical abduction. This extended abstract outlines a fully connectionist realization of the Weak Completion Semantics.