# Efficient Probabilistic Logic Reasoning with Graph Neural Networks

arXiv: https://arxiv.org/abs/2001.11850 · HTML: https://mlsanity.com/paper/2001.11850/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2020.

## Built on by (most cited first, 30 of 50)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [Decoupling the Depth and Scope of Graph Neural Networks](https://mlsanity.com/paper/2201.07858/) (2022)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Explaining the Explainers in Graph Neural Networks: a Comparative Study](https://mlsanity.com/paper/2210.15304/) (2022)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Guiding the Growth: Difficulty-Controllable Question Generation through Step-by-Step Rewriting](https://mlsanity.com/paper/2105.11698/) (2021)
- [Entity Alignment with Noisy Annotations from Large Language Models](https://mlsanity.com/paper/2405.16806/) (2024)
- [Neurosymbolic AI for Reasoning over Knowledge Graphs: A Survey](https://mlsanity.com/paper/2302.07200/) (2023)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Improved Logical Reasoning of Language Models via Differentiable Symbolic Programming](https://mlsanity.com/paper/2305.03742/) (2023)
- [Data Scarcity in Recommendation Systems: A Survey](https://mlsanity.com/paper/2312.10073/) (2023)
- [Learning Logic Rules for Document-level Relation Extraction](https://mlsanity.com/paper/2111.05407/) (2021)
- [Relational Concept Bottleneck Models](https://mlsanity.com/paper/2308.11991/) (2023)
- [Graph Collaborative Reasoning](https://mlsanity.com/paper/2112.13705/) (2021)
- [Neural Structured Prediction for Inductive Node Classification](https://mlsanity.com/paper/2204.07524/) (2022)
- [Bottom-up Domain-specific Superintelligence: A Reliable Knowledge Graph is What We Need](https://mlsanity.com/paper/2507.13966/) (2025)
- [CARE: Certifiably Robust Learning with Reasoning via Variational Inference](https://mlsanity.com/paper/2209.05055/) (2022)
- [Topological Regularization for Graph Neural Networks Augmentation](https://mlsanity.com/paper/2104.02478/) (2021)
- [Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learning](https://mlsanity.com/paper/2305.12738/) (2023)
- [Neuro-Symbolic Entity Alignment via Variational Inference](https://mlsanity.com/paper/2410.04153/) (2024)
- [Calibrating Agent-based Models to Microdata with Graph Neural Networks](https://mlsanity.com/paper/2206.07570/) (2022)
- [RulE: Knowledge Graph Reasoning with Rule Embedding](https://mlsanity.com/paper/2210.14905/) (2022)
- [Adaptive Dependency Learning Graph Neural Networks](https://mlsanity.com/paper/2312.03903/) (2023)
- [RuAG: Learned-rule-augmented Generation for Large Language Models](https://mlsanity.com/paper/2411.03349/) (2024)
- [Relational Reasoning Networks](https://mlsanity.com/paper/2106.00393/) (2021)
- [Exploring & Exploiting High-Order Graph Structure for Sparse Knowledge Graph Completion](https://mlsanity.com/paper/2306.17034/) (2023)
- [Systematic Relational Reasoning With Epistemic Graph Neural Networks](https://mlsanity.com/paper/2407.17396/) (2024)
- [LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints](https://mlsanity.com/paper/2309.15458/) (2023)
- [A Smooth Transition Between Induction and Deduction: Fast Abductive Learning Based on Probabilistic Symbol Perception](https://mlsanity.com/paper/2502.12919/) (2025)

## Abstract (arXiv)

Markov Logic Networks (MLNs), which elegantly combine logic rules and probabilistic graphical models, can be used to address many knowledge graph problems. However, inference in MLN is computationally intensive, making the industrial-scale application of MLN very difficult. In recent years, graph neural networks (GNNs) have emerged as efficient and effective tools for large-scale graph problems. Nevertheless, GNNs do not explicitly incorporate prior logic rules into the models, and may require many labeled examples for a target task. In this paper, we explore the combination of MLNs and GNNs, and use graph neural networks for variational inference in MLN. We propose a GNN variant, named ExpressGNN, which strikes a nice balance between the representation power and the simplicity of the model. Our extensive experiments on several benchmark datasets demonstrate that ExpressGNN leads to effective and efficient probabilistic logic reasoning.