# Logic Tensor Networks: Deep Learning and Logical Reasoning from Data and Knowledge

arXiv: https://arxiv.org/abs/1606.04422 · HTML: https://mlsanity.com/paper/1606.04422/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2016.

## Built on by (most cited first, 5 of 5)

- [Unlocking the Potential of Generative AI through Neuro-Symbolic Architectures: Benefits and Limitations](https://mlsanity.com/paper/2502.11269/) (2025)
- [CLEVR-POC: Reasoning-Intensive Visual Question Answering in Partially Observable Environments](https://mlsanity.com/paper/2403.03203/) (2024)
- [Attention as Binding: A Vector-Symbolic Perspective on Transformer Reasoning](https://mlsanity.com/paper/2512.14709/) (2025)
- [Foundations of Multisensory Artificial Intelligence](https://mlsanity.com/paper/2404.18976/) (2024)
- [Neuro-Symbolic Graph Transformers for Hierarchical Intention Recognition from Multimodal Human Activity Sequences](https://mlsanity.com/paper/2610.18176/) (2026)

## Abstract (arXiv)

We propose Logic Tensor Networks: a uniform framework for integrating automatic learning and reasoning. A logic formalism called Real Logic is defined on a first-order language whereby formulas have truth-value in the interval [0,1] and semantics defined concretely on the domain of real numbers. Logical constants are interpreted as feature vectors of real numbers. Real Logic promotes a well-founded integration of deductive reasoning on a knowledge-base and efficient data-driven relational machine learning. We show how Real Logic can be implemented in deep Tensor Neural Networks with the use of Google's tensorflow primitives. The paper concludes with experiments applying Logic Tensor Networks on a simple but representative example of knowledge completion.