T-Norm Operators for EU AI Act Compliance Classification: An Empirical Comparison of Lukasiewicz, Product, and G\"odel Semantics in a Neuro-Symbolic Reasoning System

TL;DR

This study compares three t-norm operators in a neuro-symbolic system for classifying EU AI Act compliance, evaluating their accuracy, false positive/negative rates, and behavior on ambiguous cases.

Contribution

It provides the first comparative analysis of Lukasiewicz, Product, and G"odel t-norms in this context, highlighting their strengths and limitations.

Findings

G"odel t-norm achieves highest accuracy and recall.

Product t-norm outperforms Lukasiewicz in accuracy.

T_L and T_P maintain zero false positives, T_G has higher recall.

Abstract

We present a first comparative pilot study of three t-norm operators -- Lukasiewicz (T_L), Product (T_P), and G\"odel (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.