比较三种逻辑运算符在AI合规分类中的表现，发现不同选择影响准确率与误报率。
T-Norm Operators for EU AI Act Compliance Classification: An Empirical Comparison of Lukasiewicz, Product, and Gödel Semantics in a Neuro-Symbolic Reasoning System
- 用三种模糊逻辑合取算子构建神经符号推理系统，评估合规分类效果。
- Gödel算子准确率达84.5%，但有0.8%误报；其他两者零误报但漏检边界案例。
- 研究结果对AI监管工具设计有参考价值，适合法律与AI交叉领域研究者。
我们首次对三种t-范数算子——Lukasiewicz（T_L）、Product（T_P）和Gödel（T_G）——在神经符号推理系统中作为逻辑合取机制的性能进行了对比研究，用于欧盟《人工智能法案》合规性分类。基于LGGT+（Logic-Guided Graph Transformers Plus）引擎和包含1035个标注样本的基准数据集（覆盖四类风险：禁止类、高风险、有限风险、低风险），我们评估了分类准确率、假阳性与假阴性率，以及算子在模糊案例中的行为表现。在n=1035的样本下，三者差异显著（McNemar p<0.001）。T_G达到最高准确率（84.5%）和最佳边界召回率（85%），但因最小语义导致8例假阳性（0.8%）。T_L与T_P保持零假阳性，其中T_P优于T_L（81.2% vs. 78.5%）。主要发现包括：(1) 算子选择次于规则库完整性；(2) T_L与T_P零假阳性但遗漏边界案例；(3) T_G的最小语义提升召回率，代价为0.8%假阳性；(4) 混合语义分类器是下一阶段关键方向。我们已将LGGT+核心引擎（201/201测试通过）和基准数据集（n=1035）以Apache 2.0许可开源。
原文摘要 · Abstract (English)
We present a first comparative pilot study of three t-norm operators -- Lukasiewicz (T_L), Product (T_P), and Gödel (T_G) - as logical conjunction mechanisms in a neuro-symbolic reasoning system for EU AI Act compliance classification. Using the LGGT+ (Logic-Guided Graph Transformers Plus) engine and a benchmark of 1035 annotated AI system descriptions spanning four risk categories (prohibited, high_risk, limited_risk, minimal_risk), we evaluate classification accuracy, false positive and false negative rates, and operator behaviour on ambiguous cases. At n=1035, all three operators differ significantly (McNemar p<0.001). T_G achieves highest accuracy (84.5%) and best borderline recall (85%), but introduces 8 false positives (0.8%) via min-semantics over-classification. T_L and T_P maintain zero false positives, with T_P outperforming T_L (81.2% vs. 78.5%). Our principal findings are: (1) operator choice is secondary to rule base completeness; (2) T_L and T_P maintain zero false positives but miss borderline cases; (3) T_G's min-semantics achieves higher recall at cost of 0.8% false positive rate; (4) a mixed-semantics classifier is the productive next step. We release the LGGT+ core engine (201/201 tests passing) and benchmark dataset (n=1035) under Apache 2.0.
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