# Neural-Symbolic Entangled Framework for Complex Query Answering

arXiv: https://arxiv.org/abs/2209.08779 · HTML: https://mlsanity.com/paper/2209.08779/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 19 Sep 2022.

## Builds on (most cited first, 16 of 16)

- [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)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [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)
- [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)
- [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)
- [Iteratively Learning Embeddings and Rules for Knowledge Graph Reasoning](https://mlsanity.com/paper/1903.08948/) (2019)
- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [Modeling Relation Paths for Representation Learning of Knowledge Bases](https://mlsanity.com/paper/1506.00379/) (2015)
- [Query2Particles: Knowledge Graph Reasoning with Particle Embeddings](https://mlsanity.com/paper/2204.12847/) (2022)
- [Fuzzy Logic Based Logical Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2108.02390/) (2021)

## Built on by (most cited first, 18 of 18)

- [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)
- [Learning to Plan for Retrieval-Augmented Large Language Models from Knowledge Graphs](https://mlsanity.com/paper/2406.14282/) (2024)
- [Complex Query Answering on Eventuality Knowledge Graph with Implicit Logical Constraints](https://mlsanity.com/paper/2305.19068/) (2023)
- [Structure Pretraining and Prompt Tuning for Knowledge Graph Transfer](https://mlsanity.com/paper/2303.03922/) (2023)
- [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023)
- [Sequential Query Encoding For Complex Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2302.13114/) (2023)
- [Rethinking Complex Queries on Knowledge Graphs with Neural Link Predictors](https://mlsanity.com/paper/2304.07063/) (2023)
- [EFOk-CQA: Towards Knowledge Graph Complex Query Answering beyond Set Operation](https://mlsanity.com/paper/2307.13701/) (2023)
- [Large Knowledge Model: Perspectives and Challenges](https://mlsanity.com/paper/2312.02706/) (2023)
- [Knowledge Graph Reasoning over Entities and Numerical Values](https://mlsanity.com/paper/2306.01399/) (2023)
- [Entity-Agnostic Representation Learning for Parameter-Efficient Knowledge Graph Embedding](https://mlsanity.com/paper/2302.01849/) (2023)
- [Conditional Logical Message Passing Transformer for Complex Query Answering](https://mlsanity.com/paper/2402.12954/) (2024)
- [Transformers for Complex Query Answering over Knowledge Hypergraphs](https://mlsanity.com/paper/2504.16537/) (2025)
- [FUSE: Measure-Theoretic Compact Fuzzy Set Representation for Taxonomy Expansion](https://mlsanity.com/paper/2506.08409/) (2025)
- [Pathformer: Recursive Path Query Encoding for Complex Logical Query Answering](https://mlsanity.com/paper/2406.14880/) (2024)
- [Prompt-fused framework for Inductive Logical Query Answering](https://mlsanity.com/paper/2403.12646/) (2024)
- [Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables](https://mlsanity.com/paper/2605.25985/) (2026)

## Abstract (arXiv)

Answering complex queries over knowledge graphs (KG) is an important yet challenging task because of the KG incompleteness issue and cascading errors during reasoning. Recent query embedding (QE) approaches to embed the entities and relations in a KG and the first-order logic (FOL) queries into a low dimensional space, answering queries by dense similarity search. However, previous works mainly concentrate on the target answers, ignoring intermediate entities' usefulness, which is essential for relieving the cascading error problem in logical query answering. In addition, these methods are usually designed with their own geometric or distributional embeddings to handle logical operators like union, intersection, and negation, with the sacrifice of the accuracy of the basic operator - projection, and they could not absorb other embedding methods to their models. In this work, we propose a Neural and Symbolic Entangled framework (ENeSy) for complex query answering, which enables the neural and symbolic reasoning to enhance each other to alleviate the cascading error and KG incompleteness. The projection operator in ENeSy could be any embedding method with the capability of link prediction, and the other FOL operators are handled without parameters. With both neural and symbolic reasoning results contained, ENeSy answers queries in ensembles. ENeSy achieves the SOTA performance on several benchmarks, especially in the setting of the training model only with the link prediction task.