Title: Bridging Neural Learning and Symbolic Reasoning: A Differentiable Fuzzy Description Logic Framework
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
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 Neuro-Symbolic AI. A key challenge is making expressive formalisms like Description Logic ($\mathcal{ALC}$) 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, leaving the choice of fuzzy operators---a critical decision that defines the optimization landscape---largely unexplored and ad-hoc. This paper introduces NeSy$\mathcal{ALC}$, the first 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. Our framework is uniquely operator-agnostic, 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 key 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 query answering under uncertainty, we demonstrate that NeSy$\mathcal{ALC}$ consistently and 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.