Learning models of predicate logical theories with neural networks based on topos theory

Abstract

This chapter presents an approach to learn first-order logical theories with neural networks. We discuss representation issues for this task in terms of a variable-free representation of predicate logic using topos theory and the possibility to use automatically generated equations (induced by the topos) as input for a neural network. Besides the translation of first-order logic into a variable-free representation, a programming language fragment for representing variable-free logic, the structure of the used neural network for learning, and the overall architecture of the system are discussed. Finally, an evaluation of the approach is presented by applying the framework to theorem proving problems. © 2007 Springer-Verlag Berlin Heidelberg.