# Fuzzy Logic Based Logical Query Answering on Knowledge Graphs

arXiv: https://arxiv.org/abs/2108.02390 · HTML: https://mlsanity.com/paper/2108.02390/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 5 Aug 2021.

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

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (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)
- [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)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS)](https://mlsanity.com/paper/1405.5869/) (2014)
- [Complex Query Answering with Neural Link Predictors](https://mlsanity.com/paper/2011.03459/) (2020)
- [Traversing Knowledge Graphs in Vector Space](https://mlsanity.com/paper/1506.01094/) (2015)
- [Symbolic Querying of Vector Spaces: Probabilistic Databases Meets Relational Embeddings](https://mlsanity.com/paper/2002.10029/) (2020)

## Built on by (most cited first, 11 of 11)

- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [Inductive Logical Query Answering in Knowledge Graphs](https://mlsanity.com/paper/2210.08008/) (2022)
- [Neural-Symbolic Entangled Framework for Complex Query Answering](https://mlsanity.com/paper/2209.08779/) (2022)
- [SMORE: Knowledge Graph Completion and Multi-hop Reasoning in Massive Knowledge Graphs](https://mlsanity.com/paper/2110.14890/) (2021)
- [logLTN: Differentiable Fuzzy Logic in the Logarithm Space](https://mlsanity.com/paper/2306.14546/) (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)
- [TAR: Neural Logical Reasoning across TBox and ABox](https://mlsanity.com/paper/2205.14591/) (2022)
- [LogicRec: Recommendation with Users' Logical Requirements](https://mlsanity.com/paper/2304.11722/) (2023)
- [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 First-Order Logical (FOL) queries on large-scale incomplete knowledge graphs (KGs) is an important yet challenging task. Recent advances embed logical queries and KG entities in the same space and conduct query answering via dense similarity search. However, most logical operators designed in previous studies do not satisfy the axiomatic system of classical logic, limiting their performance. Moreover, these logical operators are parameterized and thus require many complex FOL queries as training data, which are often arduous to collect or even inaccessible in most real-world KGs. We thus present FuzzQE, a fuzzy logic based logical query embedding framework for answering FOL queries over KGs. FuzzQE follows fuzzy logic to define logical operators in a principled and learning-free manner, where only entity and relation embeddings require learning. FuzzQE can further benefit from labeled complex logical queries for training. Extensive experiments on two benchmark datasets demonstrate that FuzzQE provides significantly better performance in answering FOL queries compared to state-of-the-art methods. In addition, FuzzQE trained with only KG link prediction can achieve comparable performance to those trained with extra complex query data.