Neural-Symbolic Logic Query Answering in Non-Euclidean Space

TL;DR

HYQNET is a novel neural-symbolic model that leverages hyperbolic space to improve logical query reasoning and knowledge graph completion, combining interpretability with better hierarchical structure modeling.

Contribution

It introduces HYQNET, a hyperbolic space-based neural-symbolic approach that enhances logical query reasoning and knowledge graph completion by capturing hierarchical structures more effectively.

Findings

HYQNET outperforms Euclidean models on benchmark datasets.

Hyperbolic embeddings better capture hierarchical query structures.

The model improves reasoning accuracy in incomplete knowledge graphs.

Abstract

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 transparency. 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 recursive 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.