A Connectionist Model for Constructive Modal Reasoning

We present a new connectionist model for constructive, intuitionistic modal reasoning. We use ensembles of neural networks to represent intuitionistic modal theories, and show that for each intuitionistic modal program there exists a corresponding neural network ensemble that computes the program. This provides a massively parallel model for intuitionistic modal reasoning, and sets the scene for integrated reasoning, knowledge representation, and learning of intuitionistic theories in neural networks, since the networks in the ensemble can be trained by examples using standard neural learning algorithms.