Sebastian Bader, Technische Universität Dresden; Artur S. d'Avila Garcez, City University London; Pascal Hitzler, University of Karlsruhe
The integration of symbolic and neural-network-based artificial intelligence paradigms constitutes a very challenging area of research. The overall aim is to merge these two very different major approaches to intelligent systems engineering while retaining their respective strengths. For symbolic paradigms that use the syntax of some first-order language this appears to be particularly 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 network 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 interpretation I. As a result, the fibred network approximates the single-step operator TP of the logic program, thus capturing the semantics of the program.