# LTNtorch: PyTorch Implementation of Logic Tensor Networks

arXiv: https://arxiv.org/abs/2409.16045 · HTML: https://mlsanity.com/paper/2409.16045/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 2 of its 5 references that are in the map.
- First posted on arXiv 24 Sep 2024.

## Placed in

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

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

- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)

## Built on by (most cited first, 4 of 4)

- [Integrating Background Knowledge in Medical Semantic Segmentation with Logic Tensor Networks](https://mlsanity.com/paper/2509.22399/) (2025)
- [Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models](https://mlsanity.com/paper/2605.18202/) (2026)
- [sLTN: Structural Logic Tensor Networks](https://mlsanity.com/paper/2608.11136/) (2026)
- [SymDQN: Symbolic Knowledge and Reasoning in Neural Network-based Reinforcement Learning](https://mlsanity.com/paper/2504.02654/) (2025)

## Abstract (arXiv)

Logic Tensor Networks (LTN) is a Neuro-Symbolic framework that effectively incorporates deep learning and logical reasoning. In particular, LTN allows defining a logical knowledge base and using it as the objective of a neural model. This makes learning by logical reasoning possible as the parameters of the model are optimized by minimizing a loss function composed of a set of logical formulas expressing facts about the learning task. The framework learns via gradient-descent optimization. Fuzzy logic, a relaxation of classical logic permitting continuous truth values in the interval [0,1], makes this learning possible. Specifically, the training of an LTN consists of three steps. Firstly, (1) the training data is used to ground the formulas. Then, (2) the formulas are evaluated, and the loss function is computed. Lastly, (3) the gradients are back-propagated through the logical computational graph, and the weights of the neural model are changed so the knowledge base is maximally satisfied. LTNtorch is the fully documented and tested PyTorch implementation of Logic Tensor Networks. This paper presents the formalization of LTN and how LTNtorch implements it. Moreover, it provides a basic binary classification example.