Connectionist Intuitionistic Reasoning

Abstract

In this chapter, we present a computational model combining intuitionistic reasoning and neural networks. We make use of ensembles of neural networks to represent intuitionistic theories, and show that for each intuitionistic theory and intuitionistic modal theory, there exists a corresponding neural-network ensemble that computes a fixed-point semantics of the theory. This provides a massively parallel model for intuitionistic reasoning. As usual, the neural networks can be trained from examples to adapt to new situations using standard neural learning algorithms, thus providing a unifying foundation for intuitionistic reasoning, knowledge representation, and learning.