# Extending Complex Logical Queries on Uncertain Knowledge Graphs

arXiv: https://arxiv.org/abs/2403.01508 · HTML: https://mlsanity.com/paper/2403.01508/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 47 references that are in the map.
- First posted on arXiv 3 Mar 2024.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [ConceptNet 5.5: An Open Multilingual Graph of General Knowledge](https://mlsanity.com/paper/1612.03975/) (2016)
- [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)
- [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)
- [ASER: A Large-scale Eventuality Knowledge Graph](https://mlsanity.com/paper/1905.00270/) (2019)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (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)
- [Logical Message Passing Networks with One-hop Inference on Atomic Formulas](https://mlsanity.com/paper/2301.08859/) (2023)
- [Embedding Uncertain Knowledge Graphs](https://mlsanity.com/paper/1811.10667/) (2018)
- [Query2Particles: Knowledge Graph Reasoning with Particle Embeddings](https://mlsanity.com/paper/2204.12847/) (2022)
- [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (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)
- [Advancing Abductive Reasoning in Knowledge Graphs through Complex Logical Hypothesis Generation](https://mlsanity.com/paper/2312.15643/) (2023)
- [Logic Embeddings for Complex Query Answering](https://mlsanity.com/paper/2103.00418/) (2021)
- [Rethinking Knowledge Graph Evaluation Under the Open-World Assumption](https://mlsanity.com/paper/2209.08858/) (2022)
- [Neural Methods for Logical Reasoning Over Knowledge Graphs](https://mlsanity.com/paper/2209.14464/) (2022)
- [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023)
- [Learning Embeddings from Knowledge Graphs With Numeric Edge Attributes](https://mlsanity.com/paper/2105.08683/) (2021)
- [Understanding Inter-Session Intentions via Complex Logical Reasoning](https://mlsanity.com/paper/2312.13866/) (2023)
- [Learning Language Representations with Logical Inductive Bias](https://mlsanity.com/paper/2302.09458/) (2023)
- [Possibilistic Constraint Satisfaction Problems or "How to handle soft constraints?"](https://mlsanity.com/paper/1303.5427/) (2013)

## Built on by (most cited first, 2 of 2)

- [Efficient Prompt Compression with Evaluator Heads for Long-Context Transformer Inference](https://mlsanity.com/paper/2501.12959/) (2025)
- [Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables](https://mlsanity.com/paper/2605.25985/) (2026)

## Abstract (arXiv)

The study of machine learning-based logical query answering enables reasoning with large-scale and incomplete knowledge graphs. This paper advances this area of research by addressing the uncertainty inherent in knowledge. While the uncertain nature of knowledge is widely recognized in the real world, it does not align seamlessly with the first-order logic that underpins existing studies. To bridge this gap, we explore the soft queries on uncertain knowledge, inspired by the framework of soft constraint programming. We propose a neural symbolic approach that incorporates both forward inference and backward calibration to answer soft queries on large-scale, incomplete, and uncertain knowledge graphs. Theoretical discussions demonstrate that our method avoids catastrophic cascading errors in the forward inference while maintaining the same complexity as state-of-the-art symbolic methods for complex logical queries. Empirical results validate the superior performance of our backward calibration compared to extended query embedding methods and neural symbolic approaches.