T-Norm Operators for EU AI Act Compliance Classification: An Empirical Comparison of Lukasiewicz, Product, and Gödel Semantics in a Neuro-Symbolic Reasoning System
This work addresses the problem of accurate compliance classification for AI systems under the EU AI Act, providing empirical insights for developers and regulators, though it is incremental as it compares existing operators in a specific application.
The study compared three t-norm operators (Lukasiewicz, Product, and Gödel) in a neuro-symbolic system for classifying AI systems under the EU AI Act, finding that Gödel semantics achieved the highest accuracy at 84.5% and best borderline recall at 85%, but introduced a 0.8% false positive rate, while Lukasiewicz and Product maintained zero false positives with accuracies of 78.5% and 81.2%, respectively.
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.