Computing firstorder logic programs by fibring artificial neural network

The integration of symbolic and neural-network-based artificial intelligence paradigms constitutes a very chal-lenging area of research. The overall aim is to merge these two very different major approaches to intelli-gent systems engineering while retaining their respec-tive strengths. For symbolic paradigms that use the syn-tax of some first-order language this appears to be par-ticularly difficult. In this paper, we will extend on an idea proposed by Garcez and Gabbay (2004) and show how first-order logic programs can be represented by fibred neural networks. The idea is to use a neural net-work to iterate a global counter n. For each clause Ci in the logic program, this counter is combined (fibred) with another neural network, which determines whether Ci outputs an atom of level n for a given interpreta-tion I. As a result, the fibred network approximates the single-step operator TP of the logic program, thus cap-turing the semantics of the program