Extending Logical Neural Networks using First-Order Theories

TL;DR

This paper extends Logical Neural Networks to incorporate first-order theories, specifically equality, enhancing their reasoning capabilities without relying on the unique-names assumption.

Contribution

The paper introduces a method to integrate first-order theories into LNNs, broadening their applicability to more complex logical reasoning tasks.

Findings

Extended LNNs support equality and function symbols.

Enabled reasoning without the unique-names assumption.

Demonstrated improved problem-solving capabilities.

Abstract

Logical Neural Networks (LNNs) are a type of architecture which combine a neural network's abilities to learn and systems of formal logic's abilities to perform symbolic reasoning. LLNs provide programmers the ability to implicitly modify the underlying structure of the neural network via logical formulae. In this paper, we take advantage of this abstraction to extend LNNs to support equality and function symbols via first-order theories. This extension improves the power of LNNs by significantly increasing the types of problems they can tackle. As a proof of concept, we add support for the first-order theory of equality to IBM's LNN library and demonstrate how the introduction of this allows the LNN library to now reason about expressions without needing to make the unique-names assumption.