Inductive Logic Programming (ILP) aims to learn interpretable first-order rules from data, but existing symbolic and neuro-symbolic approaches struggle to scale to noisy and probabilistic settings. Classical ILP relies on discrete combinatorial rule search and is brittle under uncertainty, while differentiable ILP methods typically depend on predefined rule templates or inaccurate fuzzy operators that suffer from vanishing gradients or poor approximation of logical structure when reasoning over probabilistic predicate valuations. This paper proposes an Attention-based Neuro-symbolic Differentiable Rule Extractor (ANDRE), a novel ILP framework that learns first-order logic programs by optimizing over a continuous rule space with attention-based logical operators. ANDRE replaces both rule templates and logical operators with fully differentiable, attention-driven conjunction and disjunction operators that approximate logical min-max semantics, enabling accurate, stable, and interpretable reasoning over probabilistic data. By softly selecting, negating, or excluding predicates within each rule, ANDRE supports flexible rule induction while preserving symbolic structure. Extensive experiments on classical ILP benchmarks, large-scale knowledge bases, and synthetic datasets with probabilistic predicates and noisy supervision demonstrate that ANDRE achieves competitive or superior predictive performance while reliably recovering correct symbolic rules under uncertainty. In particular, ANDRE remains robust to moderate label noise, substantially outperforming existing differentiable ILP methods in both rule extraction quality and stability.

翻译：归纳逻辑编程（ILP）旨在从数据中学习可解释的一阶规则，但现有的符号主义和神经符号方法难以扩展到含噪声和概率设置中的场景。经典ILP依赖离散的组合规则搜索，在不确定性下表现脆弱；而可微ILP方法通常依赖于预定义规则模板或不精确的模糊算子，在推理概率谓词赋值时存在梯度消失或逻辑结构近似不佳的问题。本文提出了一种基于注意力的神经符号可微规则提取器（ANDRE），这是一种新型ILP框架，通过基于注意力的逻辑算子在连续规则空间中进行优化来学习一阶逻辑程序。ANDRE用完全可微、注意力驱动的合取与析取算子替代规则模板和逻辑算子，这些算子近似逻辑极小-极大语义，从而实现对概率数据的准确、稳定且可解释的推理。通过在每个规则中软选择、否定或排除谓词，ANDRE在保持符号结构的同时支持灵活的规则归纳。在经典ILP基准测试、大规模知识库以及包含概率谓词和噪声监督的合成数据集上的大量实验表明，ANDRE在实现竞争性或更优预测性能的同时，能在不确定性下可靠地恢复正确的符号规则。特别地，ANDRE对中等程度的标签噪声具有鲁棒性，在规则提取质量和稳定性方面显著优于现有可微ILP方法。