# Relational Graph Convolutional Networks Do Not Learn Sound Rules

arXiv: https://arxiv.org/abs/2408.10261 · HTML: https://mlsanity.com/paper/2408.10261/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 18 of 18)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [KG-BERT: BERT for Knowledge Graph Completion](https://mlsanity.com/paper/1909.03193/) (2019)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [End-to-end Structure-Aware Convolutional Networks for Knowledge Base Completion](https://mlsanity.com/paper/1811.04441/) (2018)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [DRew: Dynamically Rewired Message Passing with Delay](https://mlsanity.com/paper/2305.08018/) (2023)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [TransGCN:Coupling Transformation Assumptions with Graph Convolutional Networks for Link Prediction](https://mlsanity.com/paper/1910.00702/) (2019)
- [A Recurrent Graph Neural Network for Multi-Relational Data](https://mlsanity.com/paper/1811.02061/) (2018)
- [On the Correspondence Between Monotonic Max-Sum GNNs and Datalog](https://mlsanity.com/paper/2305.18015/) (2023)

## Built on by (most cited first, 2 of 2)

- [Sound Logical Explanations for Mean Aggregation Graph Neural Networks](https://mlsanity.com/paper/2511.11593/) (2025)
- [Structural Preservation and the Logical Expressiveness of Graph Neural Networks](https://mlsanity.com/paper/2606.17882/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) are frequently used to predict missing facts in knowledge graphs (KGs). Motivated by the lack of explainability for the outputs of these models, recent work has aimed to explain their predictions using Datalog, a widely used logic-based formalism. However, such work has been restricted to certain subclasses of GNNs. In this paper, we consider one of the most popular GNN architectures for KGs, R-GCN, and we provide two methods to extract rules that explain its predictions and are sound, in the sense that each fact derived by the rules is also predicted by the GNN, for any input dataset. Furthermore, we provide a method that can verify that certain classes of Datalog rules are not sound for the R-GCN. In our experiments, we train R-GCNs on KG completion benchmarks, and we are able to verify that no Datalog rule is sound for these models, even though the models often obtain high to near-perfect accuracy. This raises some concerns about the ability of R-GCN models to generalise and about the explainability of their predictions. We further provide two variations to the training paradigm of R-GCN that encourage it to learn sound rules and find a trade-off between model accuracy and the number of learned sound rules.