# Neural-Symbolic Models for Logical Queries on Knowledge Graphs

arXiv: https://arxiv.org/abs/2205.10128 · HTML: https://mlsanity.com/paper/2205.10128/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 44 references that are in the map.
- First posted on arXiv 16 May 2022.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Go for a Walk and Arrive at the Answer: Reasoning Over Paths in Knowledge Bases using Reinforcement Learning](https://mlsanity.com/paper/1711.05851/) (2017)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [Complex Query Answering with Neural Link Predictors](https://mlsanity.com/paper/2011.03459/) (2020)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [Traversing Knowledge Graphs in Vector Space](https://mlsanity.com/paper/1506.01094/) (2015)
- [Self-Supervised Hyperboloid Representations from Logical Queries over Knowledge Graphs](https://mlsanity.com/paper/2012.13023/) (2020)
- [LowFER: Low-rank Bilinear Pooling for Link Prediction](https://mlsanity.com/paper/2008.10858/) (2020)
- [Reasoning on Knowledge Graphs with Debate Dynamics](https://mlsanity.com/paper/2001.00461/) (2020)
- [Learning to Walk with Dual Agents for Knowledge Graph Reasoning](https://mlsanity.com/paper/2112.12876/) (2021)
- [Fuzzy Logic Based Logical Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2108.02390/) (2021)

## Built on by (most cited first, 30 of 61)

- [Binding Language Models in Symbolic Languages](https://mlsanity.com/paper/2210.02875/) (2022)
- [Towards Foundation Models for Knowledge Graph Reasoning](https://mlsanity.com/paper/2310.04562/) (2023)
- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [Answering Complex Logical Queries on Knowledge Graphs via Query Computation Tree Optimization](https://mlsanity.com/paper/2212.09567/) (2022)
- [Weisfeiler and Leman Go Relational](https://mlsanity.com/paper/2211.17113/) (2022)
- [Logical Message Passing Networks with One-hop Inference on Atomic Formulas](https://mlsanity.com/paper/2301.08859/) (2023)
- [Inductive Logical Query Answering in Knowledge Graphs](https://mlsanity.com/paper/2210.08008/) (2022)
- [Double Equivariance for Inductive Link Prediction for Both New Nodes and New Relation Types](https://mlsanity.com/paper/2302.01313/) (2023)
- [Complex Query Answering on Eventuality Knowledge Graph with Implicit Logical Constraints](https://mlsanity.com/paper/2305.19068/) (2023)
- [Neural-Symbolic Entangled Framework for Complex Query Answering](https://mlsanity.com/paper/2209.08779/) (2022)
- [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023)
- [A Foundation Model for Zero-shot Logical Query Reasoning](https://mlsanity.com/paper/2404.07198/) (2024)
- [Adapting Neural Link Predictors for Data-Efficient Complex Query Answering](https://mlsanity.com/paper/2301.12313/) (2023)
- [Sequential Query Encoding For Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2302.13114/) (2023)
- [A Review on Knowledge Graphs for Healthcare: Resources, Applications, and Promises](https://mlsanity.com/paper/2306.04802/) (2023)
- [Rethinking Language Models as Symbolic Knowledge Graphs](https://mlsanity.com/paper/2308.13676/) (2023)
- [Knowledge Graph Reasoning over Entities and Numerical Values](https://mlsanity.com/paper/2306.01399/) (2023)
- [Artificial Intelligence for Drug Discovery: Are We There Yet?](https://mlsanity.com/paper/2307.06521/) (2023)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [NQE: N-ary Query Embedding for Complex Query Answering over Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2211.13469/) (2022)
- [Adaptive Path-Memory Network for Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2304.12604/) (2023)
- [Temporal Inductive Path Neural Network for Temporal Knowledge Graph Reasoning](https://mlsanity.com/paper/2309.03251/) (2023)
- [Is Complex Query Answering Really Complex?](https://mlsanity.com/paper/2410.12537/) (2024)
- [Knowledge-augmented Graph Machine Learning for Drug Discovery: A Survey](https://mlsanity.com/paper/2302.08261/) (2023)
- [LitCQD: Multi-Hop Reasoning in Incomplete Knowledge Graphs with Numeric Literals](https://mlsanity.com/paper/2304.14742/) (2023)
- [Enhancing Transformers for Generalizable First-Order Logical Entailment](https://mlsanity.com/paper/2501.00759/) (2025)
- [Knowledge Graphs Querying](https://mlsanity.com/paper/2305.14485/) (2023)
- [Privacy-Preserved Neural Graph Databases](https://mlsanity.com/paper/2312.15591/) (2023)
- [Conditional Logical Message Passing Transformer for Complex Query Answering](https://mlsanity.com/paper/2402.12954/) (2024)
- [Generating SROI^- Ontologies via Knowledge Graph Query Embedding Learning](https://mlsanity.com/paper/2407.09212/) (2024)

## Abstract (arXiv)

Answering complex first-order logic (FOL) queries on knowledge graphs is a fundamental task for multi-hop reasoning. Traditional symbolic methods traverse a complete knowledge graph to extract the answers, which provides good interpretation for each step. Recent neural methods learn geometric embeddings for complex queries. These methods can generalize to incomplete knowledge graphs, but their reasoning process is hard to interpret. In this paper, we propose Graph Neural Network Query Executor (GNN-QE), a neural-symbolic model that enjoys the advantages of both worlds. GNN-QE decomposes a complex FOL query into relation projections and logical operations over fuzzy sets, which provides interpretability for intermediate variables. To reason about the missing links, GNN-QE adapts a graph neural network from knowledge graph completion to execute the relation projections, and models the logical operations with product fuzzy logic. Experiments on 3 datasets show that GNN-QE significantly improves over previous state-of-the-art models in answering FOL queries. Meanwhile, GNN-QE can predict the number of answers without explicit supervision, and provide visualizations for intermediate variables.