# LogicENN: A Neural Based Knowledge Graphs Embedding Model with Logical Rules

arXiv: https://arxiv.org/abs/1908.07141 · HTML: https://mlsanity.com/paper/1908.07141/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2019.

## Built on by (most cited first, 8 of 8)

- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [Learning Representations of Bi-level Knowledge Graphs for Reasoning beyond Link Prediction](https://mlsanity.com/paper/2302.02601/) (2023)
- [Reason-Align-Respond: Aligning LLM Reasoning with Knowledge Graphs for KGQA](https://mlsanity.com/paper/2505.20971/) (2025)
- [Rule Induction in Knowledge Graphs Using Linear Programming](https://mlsanity.com/paper/2110.08245/) (2021)
- [Knowledge Reasoning via Jointly Modeling Knowledge Graphs and Soft Rules](https://mlsanity.com/paper/2301.02781/) (2023)
- [Current and Future Challenges in Knowledge Representation and Reasoning](https://mlsanity.com/paper/2308.04161/) (2023)
- [Improving TCM Question Answering through Tree-Organized Self-Reflective Retrieval with LLMs](https://mlsanity.com/paper/2502.09156/) (2025)
- [Geometric Structural Knowledge Graph Foundation Model](https://mlsanity.com/paper/2512.22931/) (2025)

## Abstract (arXiv)

Knowledge graph embedding models have gained significant attention in AI research. Recent works have shown that the inclusion of background knowledge, such as logical rules, can improve the performance of embeddings in downstream machine learning tasks. However, so far, most existing models do not allow the inclusion of rules. We address the challenge of including rules and present a new neural based embedding model (LogicENN). We prove that LogicENN can learn every ground truth of encoded rules in a knowledge graph. To the best of our knowledge, this has not been proved so far for the neural based family of embedding models. Moreover, we derive formulae for the inclusion of various rules, including (anti-)symmetric, inverse, irreflexive and transitive, implication, composition, equivalence and negation. Our formulation allows to avoid grounding for implication and equivalence relations. Our experiments show that LogicENN outperforms the state-of-the-art models in link prediction.