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Abstract - T-Norm Operators for EU AI Act Compliance Classification: An Empirical Comparison of Lukasiewicz, Product, and Gödel Semantics in a Neuro-Symbolic Reasoning System
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.
用于欧盟《人工智能法案》合规性分类的T-范数算子实证比较:卢卡西维茨、乘积与哥德尔语义在神经符号推理系统中的表现 /
T-Norm Operators for EU AI Act Compliance Classification: An Empirical Comparison of Lukasiewicz, Product, and Gödel Semantics in a Neuro-Symbolic Reasoning System
1️⃣ 一句话总结
本研究首次比较了三种逻辑算子(卢卡西维茨、乘积和哥德尔)在判断AI系统是否符合欧盟法规时的表现,发现哥德尔算子准确率最高但会误判少量安全系统,而另两种算子虽无误判却可能漏掉风险,最终建议结合使用不同算子来构建更优的分类器。