# Embedding Logical Queries on Knowledge Graphs

arXiv: https://arxiv.org/abs/1806.01445 · HTML: https://mlsanity.com/paper/1806.01445/

## Key facts

- Cited by 120 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2018.

## Built on by (most cited first, 30 of 120)

- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [DistGNN: Scalable Distributed Training for Large-Scale Graph Neural Networks](https://mlsanity.com/paper/2104.06700/) (2021)
- [Incorporating Domain Knowledge into Deep Neural Networks](https://mlsanity.com/paper/2103.00180/) (2021)
- [Mask and Reason: Pre-Training Knowledge Graph Transformers for Complex Logical Queries](https://mlsanity.com/paper/2208.07638/) (2022)
- [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)
- [Probabilistic Entity Representation Model for Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13522/) (2021)
- [Complex Logical Reasoning over Knowledge Graphs using Large Language Models](https://mlsanity.com/paper/2305.01157/) (2023)
- [Inductive Logical Query Answering in Knowledge Graphs](https://mlsanity.com/paper/2210.08008/) (2022)
- [RuleBert: Teaching Soft Rules to Pre-trained Language Models](https://mlsanity.com/paper/2109.13006/) (2021)
- [Query2Particles: Knowledge Graph Reasoning with Particle Embeddings](https://mlsanity.com/paper/2204.12847/) (2022)
- [Learning to Plan for Retrieval-Augmented Large Language Models from Knowledge Graphs](https://mlsanity.com/paper/2406.14282/) (2024)
- [Query Embedding on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2106.08166/) (2021)
- [Benchmarking the Combinatorial Generalizability of Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2109.08925/) (2021)
- [GammaE: Gamma Embeddings for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2210.15578/) (2022)
- [Neurosymbolic AI for Reasoning over Knowledge Graphs: A Survey](https://mlsanity.com/paper/2302.07200/) (2023)
- [Complex Query Answering on Eventuality Knowledge Graph with Implicit Logical Constraints](https://mlsanity.com/paper/2305.19068/) (2023)
- [Knowledge Graph Reasoning with Logics and Embeddings: Survey and Perspective](https://mlsanity.com/paper/2202.07412/) (2022)
- [Neural-Symbolic Entangled Framework for Complex Query Answering](https://mlsanity.com/paper/2209.08779/) (2022)
- [Logic Embeddings for Complex Query Answering](https://mlsanity.com/paper/2103.00418/) (2021)
- [SMORE: Knowledge Graph Completion and Multi-hop Reasoning in Massive Knowledge Graphs](https://mlsanity.com/paper/2110.14890/) (2021)
- [Neural Methods for Logical Reasoning Over Knowledge Graphs](https://mlsanity.com/paper/2209.14464/) (2022)
- [Learning to Walk with Dual Agents for Knowledge Graph Reasoning](https://mlsanity.com/paper/2112.12876/) (2021)
- [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023)
- [Logic Jailbreak: Efficiently Unlocking LLM Safety Restrictions Through Formal Logical Expression](https://mlsanity.com/paper/2505.13527/) (2025)
- [A Unified Framework for Rank-based Evaluation Metrics for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/2203.07544/) (2022)

## Abstract (arXiv)

Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple unobserved edges, entities, and variables. For instance, given an incomplete biological knowledge graph, we might want to predict "em what drugs are likely to target proteins involved with both diseases X and Y?" -- a query that requires reasoning about all possible proteins that em might interact with diseases X and Y. Here we introduce a framework to efficiently make predictions about conjunctive logical queries -- a flexible but tractable subset of first-order logic -- on incomplete knowledge graphs. In our approach, we embed graph nodes in a low-dimensional space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space. By performing logical operations within a low-dimensional embedding space, our approach achieves a time complexity that is linear in the number of query variables, compared to the exponential complexity required by a naive enumeration-based approach. We demonstrate the utility of this framework in two application studies on real-world datasets with millions of relations: predicting logical relationships in a network of drug-gene-disease interactions and in a graph-based representation of social interactions derived from a popular web forum.