Neural-Symbolic Logic Query Answering in Non-Euclidean Space

2026-03-19 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Advanced, extended

Summary

HyQNet is a novel neural-symbolic model designed for answering complex First-Order Logic (FOL) queries on knowledge graphs, particularly addressing challenges with incomplete data and hierarchical query structures. It integrates the interpretability of symbolic methods with the generalization capabilities of neural networks by operating within hyperbolic space. The model decomposes FOL queries into relation projections and logical operations over fuzzy sets, enhancing transparency. For knowledge graph completion, HyQNet employs a hyperbolic Graph Neural Network (GNN) with learned curvature, which effectively embeds recursive query trees and preserves structural dependencies. This hyperbolic approach, unlike Euclidean-based methods, is better suited for capturing the inherent hierarchical nature of logical projection reasoning. Experiments on three benchmark datasets (FB15k, FB15k-237, NELL995) demonstrate that HyQNet achieves state-of-the-art performance across various query types, including those with negation, and also excels in answer set cardinality prediction.

Key takeaway

For AI Scientists and Research Scientists working on knowledge graph reasoning, HyQNet offers a superior approach to handling complex FOL queries, especially when dealing with hierarchical data and incomplete graphs. You should consider adopting hyperbolic GNNs with learned curvature to improve reasoning accuracy and interpretability over traditional Euclidean embedding methods. This can lead to more robust and generalizable models for real-world applications like question answering and recommendation systems.

Key insights

Hyperbolic GNNs with learned curvature effectively capture hierarchical logic query structures for knowledge graph reasoning.

Principles

• Hyperbolic space naturally represents hierarchical data.
• Decompose FOL queries into fuzzy set operations.
• Learned curvature enhances GNN adaptability.

Method

HyQNet decomposes FOL queries into fuzzy set operations, using a hyperbolic GNN with learned curvature for relation projection and product fuzzy logic for conjunction, disjunction, and negation. It minimizes binary cross-entropy loss.

In practice

• Use hyperbolic embeddings for hierarchical data.
• Apply fuzzy logic for robust logical operations.
• Train with binary cross-entropy loss.

Topics

• Neural-Symbolic AI
• Knowledge Graph Reasoning
• Hyperbolic Embeddings
• First-Order Logic Queries
• Graph Neural Networks

Best for: AI Scientist, Research Scientist, AI Researcher, Machine Learning Engineer, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.