Neural-Symbolic Logic Query Answering in Non-Euclidean Space

Computer Science > Artificial Intelligence [Submitted on 25 Feb 2026] Neural-Symbolic Logic Query Answering in Non-Euclidean Space Lihui Liu Answering complex first-order logic (FOL) queries on knowledge graphs is essential for reasoning. Symbolic methods offer interpretability but struggle with incomplete graphs, while neural approaches generalize better but lack trans- parency. Neural-symbolic models aim to integrate both strengths but often fail to capture the hierarchical structure of logical queries, limiting their effectiveness. We propose HYQNET, a neural-symbolic model for logic query reasoning that fully leverages hyperbolic space. HYQNET decomposes FOL queries into relation projections and logical operations over fuzzy sets, enhancing interpretability. To address missing links, it employs a hyperbolic GNN-based approach for knowledge graph completion in hyperbolic space, effectively embedding the re- cursive query tree while preserving structural dependencies. By utilizing hyperbolic representations, HYQNET captures the hierarchical nature of logical projection reasoning more effectively than Euclidean-based approaches. Experiments on three benchmark datasets demonstrate that HYQNET achieves strong performance, highlighting the advantages of reasoning in hyperbolic space. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2603.15633 [cs.AI]   (or arXiv:2603.15633v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2603.15633 Focus to learn more Submission history From: Lihui Liu [view email] [v1] Wed, 25 Feb 2026 23:46:04 UTC (2,746 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)