Connectionist computations of intuitionistic reasoning

TY - JOUR

T1 - Connectionist computations of intuitionistic reasoning

AU - Garcez, A S D

AU - Lamb, L C

AU - Gabbay, D M

PY - 2006/7/31

Y1 - 2006/7/31

N2 - The construction of computational models with provision for effective learning and added reasoning is a fundamental problem in computer science. In this paper, we present a new computational model for integrated reasoning and learning that combines intuitionistic reasoning and neural networks. We use 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. In our model, 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. (C) 2006 Elsevier B.V. All rights reserved

AB - The construction of computational models with provision for effective learning and added reasoning is a fundamental problem in computer science. In this paper, we present a new computational model for integrated reasoning and learning that combines intuitionistic reasoning and neural networks. We use 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. In our model, 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. (C) 2006 Elsevier B.V. All rights reserved

U2 - 10.1016/j.tcs.2005.11.043

DO - 10.1016/j.tcs.2005.11.043

M3 - Article

VL - 358

SP - 34

EP - 55

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 1

ER -