# 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

arXiv: https://arxiv.org/abs/2603.28558 · HTML: https://mlsanity.com/paper/2603.28558/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 7 of 7)

- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [From Statistical Relational to Neuro-Symbolic Artificial Intelligence](https://mlsanity.com/paper/2003.08316/) (2020)
- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [TFLEX: Temporal Feature-Logic Embedding Framework for Complex Reasoning over Temporal Knowledge Graph](https://mlsanity.com/paper/2205.14307/) (2022)
- [logLTN: Differentiable Fuzzy Logic in the Logarithm Space](https://mlsanity.com/paper/2306.14546/) (2023)

## Abstract (arXiv)

We present a first comparative pilot study of three t-norm operators -- Lukasiewicz (TL), Product (TP), and G"odel (TG) - 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, highrisk, limitedrisk, minimalrisk), 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). TG achieves highest accuracy (84.5%) and best borderline recall (85%), but introduces 8 false positives (0.8%) via min-semantics over-classification. TL and TP maintain zero false positives, with TP outperforming TL (81.2% vs. 78.5%). Our principal findings are: (1) operator choice is secondary to rule base completeness; (2) TL and TP maintain zero false positives but miss borderline cases; (3) TG'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.