# Probabilistic Logic Neural Networks for Reasoning

arXiv: https://arxiv.org/abs/1906.08495 · HTML: https://mlsanity.com/paper/1906.08495/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2019.

## Built on by (most cited first, 30 of 69)

- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [Knowledge Graph Reasoning with Relational Digraph](https://mlsanity.com/paper/2108.06040/) (2021)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Towards Better Chain-of-Thought Prompting Strategies: A Survey](https://mlsanity.com/paper/2310.04959/) (2023)
- [LinearRAG: Linear Graph Retrieval Augmented Generation on Large-scale Corpora](https://mlsanity.com/paper/2510.10114/) (2025)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Prototypical Representation Learning for Relation Extraction](https://mlsanity.com/paper/2103.11647/) (2021)
- [ChatRule: Mining Logical Rules with Large Language Models for Knowledge Graph Reasoning](https://mlsanity.com/paper/2309.01538/) (2023)
- [Neural Multi-Hop Reasoning With Logical Rules on Biomedical Knowledge Graphs](https://mlsanity.com/paper/2103.10367/) (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)
- [Neural Methods for Logical Reasoning Over Knowledge Graphs](https://mlsanity.com/paper/2209.14464/) (2022)
- [SymbolicAI: A framework for logic-based approaches combining generative models and solvers](https://mlsanity.com/paper/2402.00854/) (2024)
- [Learning Logic Rules for Document-level Relation Extraction](https://mlsanity.com/paper/2111.05407/) (2021)
- [VigDet: Knowledge Informed Neural Temporal Point Process for Coordination Detection on Social Media](https://mlsanity.com/paper/2110.15454/) (2021)
- [Graph Collaborative Reasoning](https://mlsanity.com/paper/2112.13705/) (2021)
- [Evaluating Deep Unlearning in Large Language Models](https://mlsanity.com/paper/2410.15153/) (2024)
- [CARE: Certifiably Robust Learning with Reasoning via Variational Inference](https://mlsanity.com/paper/2209.05055/) (2022)
- [Knowledge-augmented Deep Learning and Its Applications: A Survey](https://mlsanity.com/paper/2212.00017/) (2022)
- [DMWM: Dual-Mind World Model with Long-Term Imagination](https://mlsanity.com/paper/2502.07591/) (2025)
- [A Unified Temporal Knowledge Graph Reasoning Model Towards Interpolation and Extrapolation](https://mlsanity.com/paper/2405.18106/) (2024)
- [Predictive Multiplicity of Knowledge Graph Embeddings in Link Prediction](https://mlsanity.com/paper/2408.08226/) (2024)
- [Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learning](https://mlsanity.com/paper/2305.12738/) (2023)
- [Comprehensible Artificial Intelligence on Knowledge Graphs: A survey](https://mlsanity.com/paper/2404.03499/) (2024)
- [Neuro-Symbolic Entity Alignment via Variational Inference](https://mlsanity.com/paper/2410.04153/) (2024)
- [Explainable Biomedical Recommendations via Reinforcement Learning Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2111.10625/) (2021)
- [Quant 4.0: Engineering Quantitative Investment with Automated, Explainable and Knowledge-driven Artificial Intelligence](https://mlsanity.com/paper/2301.04020/) (2022)
- [GIDN: A Lightweight Graph Inception Diffusion Network for High-efficient Link Prediction](https://mlsanity.com/paper/2210.01301/) (2022)
- [Learning by Applying: A General Framework for Mathematical Reasoning via Enhancing Explicit Knowledge Learning](https://mlsanity.com/paper/2302.05717/) (2023)

## Abstract (arXiv)

Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent knowledge graph embedding methods. A principled logic rule-based approach is the Markov Logic Network (MLN), which is able to leverage domain knowledge with first-order logic and meanwhile handle their uncertainty. However, the inference of MLNs is usually very difficult due to the complicated graph structures. Different from MLNs, knowledge graph embedding methods (e.g. TransE, DistMult) learn effective entity and relation embeddings for reasoning, which are much more effective and efficient. However, they are unable to leverage domain knowledge. In this paper, we propose the probabilistic Logic Neural Network (pLogicNet), which combines the advantages of both methods. A pLogicNet defines the joint distribution of all possible triplets by using a Markov logic network with first-order logic, which can be efficiently optimized with the variational EM algorithm. In the E-step, a knowledge graph embedding model is used for inferring the missing triplets, while in the M-step, the weights of logic rules are updated based on both the observed and predicted triplets. Experiments on multiple knowledge graphs prove the effectiveness of pLogicNet over many competitive baselines.