Neural networks and logical reasoning systems. A translation table

TL;DR

This paper establishes a detailed correspondence between logical reasoning systems and neural network operations, aiming to bridge symbolic and network-based representations for learning systems.

Contribution

It introduces a translation dictionary linking logic elements to neural network components, facilitating bidirectional conversion between symbolic and neural formulations.

Findings

Atomic propositions correspond to nodes with n-th order synapses.

Rules are represented as synaptic intensity constraints.

Forward chaining maps to synaptic dynamics.

Abstract

A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general translation dictionary which, hopefully, will allow to go back and forth between symbolic and network formulations, a desirable step in learning-oriented systems and multicomputer networks. In the framework of Horn clause logics it is found that atomic propositions with n arguments correspond to nodes with n-th order synapses, rules to synaptic intensity constraints, forward chaining to synaptic dynamics and queries either to simple node activation or to a query tensor dynamics.