Bridging Neural Learning and Symbolic Reasoning: A Differentiable Fuzzy Description Logic Framework

Zihan Shao, Yizheng Zhao

Keywords: neural-symbolic AI, fuzzy semantics, description logics

Abstract:

Injecting logical reasoning as a structural prior into deep learning models is a central goal of Neural-Symbolic AI. A key challenge is
making expressive formalisms like the Description Logic (DL) $\mathcal{ALC}$ compatible with gradient-based optimization without sacrificing their rich semantics. While the theory of fuzzy $\mathcal{ALC}$ offers a path, a significant methodological gap has persisted: although operator-agnostic fuzzy reasoning has been explored in first-order logic-based frameworks, these methods face fundamental computational barriers when scaling to real-world ontologies, leaving the choice of fuzzy operators for DLs largely unexplored. This paper introduces NeSy$\mathcal{ALC}$, an end-to-end learning framework designed to bridge this gap by transforming fuzzy $\mathcal{ALC}$ from a theoretical construct into a practical tool for representation learning at scale. Our framework is operator-agnostic within the DL setting, allowing us to conduct the first systematic empirical analysis of how different t-norms and fuzzy implications impact learning on diverse knowledge bases. We find that no single operator is universally optimal, motivating our second contribution: a novel adaptive dual-loss optimization strategy that dynamically adjusts its objective based on the logical structure of the knowledge base, enhancing learning robustness. Through extensive experiments on ontology completion and semantic image interpretation tasks, we demonstrate that NeSy$\mathcal{ALC}$ consistently and statistically significantly outperforms established baselines. Our work operationalizes fuzzy $\mathcal{ALC}$ for modern machine learning, providing a practical and robust framework for injecting rich symbolic knowledge into neural models.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Submission Number: 10356