Neural-Symbolic Integration: The Road Ahead

In this book, we have seen that the integration of Connectionist Logic Systems (CLS) and Hybrid Systems by Translation (HST) may provide effective Neural-Symbolic Learning Systems. C-IL²P is an example of such a system. In order to enable effective learning from examples and background knowledge, the main insight was to keep the network structure as simple as possible, and try to find the best symbolic representation for it. We have done so by presenting a Translation Algorithm from logic programs to single hidden layer neural networks. It was essential, though, to show the equivalence between the symbolic representation and the neural network, in order to ensure a sound translation of the background knowledge into a connectionist representation. Such a theorem also rendered C-IL²P as a massively parallel model of symbolic computation, as in CLSs, with two corollaries showing that the neural network computes, respectively, the stable model semantics of the general logic program given as background knowledge, and the answer set semantics of the extended logic program given as background knowledge. An extension of the system to accommodate superiority relations between rules, finally provided the symbolic representation that best fits into single hidden layer networks; that of prioritised extended logic programming.