Neural networks and rational Lukasiewicz logic

We describe a correspondence between rational Lukasiewicz formulas and neural networks in which the activation function is the truncated identity and synaptic weights are rational numbers. On one hand, having a logical representation (in a given logic) of neural networks could widen the interpretability, amalgamability and reuse of these objects. On the other hand, neural networks could be used to learn formulas from data and as circuital counterparts of (functions represented by) formulas.