# Extending Logical Neural Networks using First-Order Theories

arXiv: https://arxiv.org/abs/2207.02978 · HTML: https://mlsanity.com/paper/2207.02978/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 2 of its 4 references that are in the map.
- First posted on arXiv 6 Jul 2022.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 2 of 2)

- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Can Neural Networks Understand Logical Entailment?](https://mlsanity.com/paper/1802.08535/) (2018)

## Abstract (arXiv)

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.