# Neural Methods for Logical Reasoning Over Knowledge Graphs

arXiv: https://arxiv.org/abs/2209.14464 · HTML: https://mlsanity.com/paper/2209.14464/

## Key facts

- Cited by 17 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 15 of its 27 references that are in the map.
- First posted on arXiv 28 Sep 2022.

## Placed in

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

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [QA-GNN: Reasoning with Language Models and Knowledge Graphs for Question Answering](https://mlsanity.com/paper/2104.06378/) (2021)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Scalable Multi-Hop Relational Reasoning for Knowledge-Aware Question Answering](https://mlsanity.com/paper/2005.00646/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Probabilistic Logic Neural Networks for Reasoning](https://mlsanity.com/paper/1906.08495/) (2019)
- [Heterogeneous Hypergraph Embedding for Graph Classification](https://mlsanity.com/paper/2010.10728/) (2020)
- [Traversing Knowledge Graphs in Vector Space](https://mlsanity.com/paper/1506.01094/) (2015)
- [Neural Logic Reasoning](https://mlsanity.com/paper/2008.09514/) (2020)
- [Chains of Reasoning over Entities, Relations, and Text using Recurrent Neural Networks](https://mlsanity.com/paper/1607.01426/) (2016)
- [Variational Knowledge Graph Reasoning](https://mlsanity.com/paper/1803.06581/) (2018)
- [Neural Logic Networks](https://mlsanity.com/paper/1910.08629/) (2019)

## Built on by (most cited first, 17 of 17)

- [FactKB: Generalizable Factuality Evaluation using Language Models Enhanced with Factual Knowledge](https://mlsanity.com/paper/2305.08281/) (2023)
- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [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)
- [Complex Query Answering on Eventuality Knowledge Graph with Implicit Logical Constraints](https://mlsanity.com/paper/2305.19068/) (2023)
- [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)
- [Sequential Query Encoding For Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2302.13114/) (2023)
- [Knowledge Graph Reasoning over Entities and Numerical Values](https://mlsanity.com/paper/2306.01399/) (2023)
- [KALM: Knowledge-Aware Integration of Local, Document, and Global Contexts for Long Document Understanding](https://mlsanity.com/paper/2210.04105/) (2022)
- [Applications of Generative AI (GAI) for Mobile and Wireless Networking: A Survey](https://mlsanity.com/paper/2405.20024/) (2024)
- [A Smooth Transition Between Induction and Deduction: Fast Abductive Learning Based on Probabilistic Symbol Perception](https://mlsanity.com/paper/2502.12919/) (2025)
- [Neuro-Symbolic Recommendation Model based on Logic Query](https://mlsanity.com/paper/2309.07594/) (2023)
- [Extending Complex Logical Queries on Uncertain Knowledge Graphs](https://mlsanity.com/paper/2403.01508/) (2024)
- [Meta Operator for Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2403.10110/) (2024)
- [Pathformer: Recursive Path Query Encoding for Complex Logical Query Answering](https://mlsanity.com/paper/2406.14880/) (2024)
- [Efficient and Scalable Neural Symbolic Search for Knowledge Graph Complex Query Answering](https://mlsanity.com/paper/2505.08155/) (2025)

## Abstract (arXiv)

Reasoning is a fundamental problem for computers and deeply studied in Artificial Intelligence. In this paper, we specifically focus on answering multi-hop logical queries on Knowledge Graphs (KGs). This is a complicated task because, in real-world scenarios, the graphs tend to be large and incomplete. Most previous works have been unable to create models that accept full First-Order Logical (FOL) queries, which include negative queries, and have only been able to process a limited set of query structures. Additionally, most methods present logic operators that can only perform the logical operation they are made for. We introduce a set of models that use Neural Networks to create one-point vector embeddings to answer the queries. The versatility of neural networks allows the framework to handle FOL queries with Conjunction (wedge), Disjunction (vee) and Negation (neg) operators. We demonstrate experimentally the performance of our model through extensive experimentation on well-known benchmarking datasets. Besides having more versatile operators, the models achieve a 10% relative increase over the best performing state of the art and more than 30% over the original method based on single-point vector embeddings.