Flexible Reasoning of Boolean Constraints in Recurrent Neural Networks with Dual Representation

In this paper, we propose a recurrent neural network that can flexibly make inferences to satisfy given Boolean constraints. In our proposed network, each Boolean variable is represented in dual representation by a pair of neurons, which can handle four states of true, false, unknown, and contradiction. We successfully import Blake’s classical Boolean reasoning algorithm to recurrent neural network with hidden neurons of Boolean product terms. For symmetric Boolean functions, we designed an extended model of Boolean reasoning which can drastically reduce the hardware cost. Since our network has only excitatory connections, it does not suffer from oscillation and we can freely combine multiple Boolean constraints.