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…

Authors: Adam Laabs

Laabs — T -Norm Operators for EU AI Act Classification T -Norm Operators f or EU AI Act Compliance Classification: An Empirical Comparison of Łukasie wicz, Product, and Gödel Semantics in a Neuro-Symbolic Reasoning System Adam Laabs T riStiX S.L., Altea, Alicante, Spain Adam.Laabs@T riStiX.com March 18, 2026 Code & data: github .com/T riStiX-LS/LggT -core (Apache 2.0) Abstract W e present a first comparati ve pilot study of three t-norm operators — Łukasie wicz ( 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 T ransformers Plus) engine and a benchmark of 1035 annotated AI system descriptions spanning four risk categories ( prohibited , high_risk , limited_risk , minimal_risk ), we e valuate classification accuracy , false positi ve and false ne gativ e rates, and operator behaviour on ambiguous cases. At n = 1035, all three operators dif fer significantly (McNemar p < 0 . 001). T G achiev es highest accuracy (84.5%) and best borderline recall (85%), but introduces 8 false positives (0.8%) via min- semantics ov er-classification. T L and T P maintain zero false positi ves, with T P outperforming T L (81.2% vs. 78.5%). The T G precision/recall trade-of f is a ne w finding not observable at small sample sizes. Our principal findings are: (1) operator choice is secondary to rule base completeness; (2) T L and T P maintain zero false positiv es b ut miss borderline cases; (3) T G ’ s min-semantics achie ves higher recall at cost of 0.8% false positiv e rate; (4) a mixed-semantics classifier is the producti ve next step. W e release the LGGT+ core engine (201/201 tests passing) and benchmark dataset ( n = 1035) under Apache 2.0. K eywords: neuro-symbolic AI · t-norms · EU AI Act · legal reasoning · kno wledge graphs · explainable AI · Łukasiewicz logic · compliance classification 1 Intr oduction The EU AI Act (Regulation (EU) 2024/1689) creates an unprecedented compliance infrastructure re- quiring AI systems to be formally classified into risk categories, each triggering distinct obligations. The classification standards are conjuncti ve: “system X is high-risk if and only if condition A and condition B and condition C are present. ” This logical structure in vites formalisation in many-valued logic, where the Boolean AND operator over continuous confidence values in [ 0 , 1 ] is modelled by a triangular norm (t-norm). 1 Laabs — T -Norm Operators for EU AI Act Classification Despite extensiv e neuro-symbolic AI literature [ 1 , 2 , 8 ], no prior work has empirically e valuated which t-norm best models le gal conjuncti ve standards for regulatory compliance classification. W e close this gap by reframing the question: rather than asking which t-norm operator to use, we ask which operator best matches the legal interpreti ve standard implicit in each EU AI Act rule. W e implement three canonical t-norm operators within LGGT+ (Logic-Guided Graph Transformers Plus), a neuro-symbolic architecture dev eloped by TriStiX S.L. for EU AI Act compliance analysis, and e valuate their classification accurac y on a curated benchmark of 1035 annotated AI system descriptions. W e are transparent about our limitations: e xpert labels in this version are assigned by the author , and we identify independent legal e xpert validation as the primary ne xt step. Contributions. 1. First empirical e valuation of T L , T P , and T G as conjunction operators for EU AI Act classification ( n = 1035). 2. LGGT+ reasoning engine with 14 formalised EU AI Act rules and proof trail auditability (201/201 unit tests; open-source). 3. Empirical evidence of operator div ergence at scale: T L and T P are not decision-equiv alent at n = 1035 ( p < 0 . 001), while T G re veals a precision/recall trade-off in borderline compliance clas- sification. 4. Re vised research hypotheses concerning rule base completeness and mixed-semantics classifica- tion. 5. Open benchmark dataset ( n = 1035) and code (Apache 2.0). 2 Backgr ound 2.1 T riangular Norms A t-norm T : [ 0 , 1 ] 2 → [ 0 , 1 ] generalises Boolean AND to the continuous unit interval, satisfying com- mutati vity , associati vity , monotonicity , and boundary conditions T ( 1 , 1 ) = 1, T ( 0 , x ) = 0. W e e valuate three fundamental t-norms: T able 1: Properties of the three canonical t-norms. The “dead zone” is the region where T = 0 and gradient is zero — rele vant for training, not for deterministic inference. T -norm Formula Dead zone Gradient Łukasie wicz T L max ( 0 , a + b − 1 ) a + b ≤ 1 Zero in dead zone Product T P a · b None Smooth: ∂ T / ∂ a = b Gödel T G min ( a , b ) None Subgradient Fuzzy logic as uncertainty modelling, not norm relaxation. A potential misreading of this work re- quires pre-emption. The EU AI Act formulates obligations and prohibitions in binary terms: a practice is either prohibited or it is not. The continuous v alues in [ 0 , 1 ] used in this paper are not partial satisfactions of a legal norm. They represent epistemic uncertainty about whether a factual condition obtains — for example, whether a giv en AI system’ s documentation confirms that it operates autonomously . The ques- tion we formalise is: gi ven several conditions each assessed with some degree of certainty , how should these assessments be combined to reach a binary compliance decision? This is a question about evidence 2 Laabs — T -Norm Operators for EU AI Act Classification aggregation, not norm relaxation. Leg al practitioners do not choose t-norm operators; they answer the interpreti ve question of whether the conditions in a rule are cumulati vely required (each must be defini- ti vely present) or minimally required (each must reach a reasonable threshold). Our framew ork maps this interpreti ve judgment onto a formal aggregation mechanism. Inference-time vs. training-time distinction. Prior work criticises T L ’ s dead gradient zone when used as a loss function component in backpropagation [ 2 , 1 ]. LGGT+ uses T L exclusi vely as a runtime infer- ence operator: a deterministic combinator in a proof-trail chain, with no gradient computed. The dead zone is mathematically irrele vant in this context. Future trainable components (Logic-Augmented Atten- tion) will use Product t-norm in log-space, following the logL TN recommendation [ 2 ]. This is a distinct module from the classification chain e valuated here (Architecture Decision Record ADR-001). 2.2 Legal Semantics of Conjunctive Standards The choice of conjunction mechanism maps onto a genuine legal interpreti ve question. T able 2 presents this mapping in terms accessible to legal practitioners, without mathematical notation. T able 2: Mapping legal interpretiv e questions to formal conjunction semantics. The first two rows cor- respond to T L / T P (strong conjunction) and T G (bottleneck conjunction) respectiv ely . The third row moti- v ates the mixed-semantics hypothesis (RH4). Legal practitioner’ s question Conjunction intuition Practical implication Does the rule require strong, joint confirmation of all condi- tions? Strong conjunction One weaker condition substan- tially reduces the ov erall score Is it suf ficient that each condition indi vidually reaches a reasonable threshold? Bottleneck conjunction (weakest link) The lowest-scored condition de- termines the outcome Are some conditions cumula- ti vely required and others only minimally required? Hybrid semantics (rule-specific) Dif ferent parts of a rule may war - rant dif ferent aggregation meth- ods This framing separates tw o roles that should not be conflated: (a) the legal practitioner determines whether conditions are cumulati vely or minimally required for a gi ven rule — this is an interpreti ve leg al judgment; (b) the system maps that judgment to a formal aggre gation operator . Legal practitioners are not expected to select t-norm operators; they are expected to answer interpreti ve questions about rule structure. 2.3 LGGT+ Architectur e LGGT+ implements a four-layer neuro-symbolic pipeline: L1 — Logic: LukasiewiczLogic, LogFuzzyLogic (logL TN-inspired, log-space product t-norm for long chains), Hyper graphEncoder (N-ary hyperedge queries with T ype-A ware Bias, LKHGT April 2025), LogicAugmentedAttention (SGA T -MS inspired bipartite modulation [ 9 ]), GumbelSoftmaxAnnealing (DiLogic [ 7 ]). L2 — Graph: KnowledgeGraph (NetworkX DiGraph with typed nodes/edges), T emporalKnowl- edgeNode (temporal validity windows, TFLEX-inspired [ 11 ]), OntologyP atcher (incremental updates, 3 Laabs — T -Norm Operators for EU AI Act Classification Nucleoid-inspired), Adapti veT ripleFilter (PSL hinge-loss scoring). L3 — Reasoning: ReasoningEngine with TNormMode dispatch, and ProofTreeBuilder producing formal proof trees with typed tactics (NeqLIPS / NTP inspired). L4 — API: FastAPI microservice; Anne x IV PDF generator for EU AI Act Art. 11. The proof trail produced by L3 records e very inference step: nodes tra versed, conditions e v aluated, t- norm compositions applied. This structural auditability implements EU AI Act Article 13 (transparency) and Article 14 (human ov ersight). T o the best of our knowledge, LGGT+ is the first open-source architecture combining simultane- ously: Łukasie wicz t-norms as runtime inference operators, graph transformers, and auditable proof trails. T able 3 situates it in the landscape. T able 3: Comparison of LGGT+ with related neuro-symbolic systems. System T L (runtime) Graph transf. Proof trail Legal domain L TNtorch [ 1 ] ✓ × × × IBM/LNN [ 8 ] ✓ × × × GNN-QE [ 10 ] × ✓ × × SGA T -MS [ 9 ] ✓ ✓ × × LGGT+ (ours) ✓ ✓ ✓ ✓ 2.4 Legal AI Reasoning and Computational Compliance LGGT+ b uilds on a broader literature in computational le gal reasoning and AI-based compliance check- ing, which we briefly situate here. F ormal models of legal reasoning . Foundational work on ar gumentation-based legal reasoning [ 12 , 13 ] established that legal norms inv olve defeasible inference and priority orderings — properties that moti vate the explicit rule priority ordering in LGGT+ ( prohibited > high_risk > limited_risk ). Norm formalisation for machine-readable legislation [ 14 ] pro vides the theoretical grounding for our ontology-dri ven approach to EU AI Act rules. AI-based compliance checking. [ 15 ] surve y automated compliance checking systems and identify the need for both temporal reasoning and rule formalisation — both addressed in LGGT+’ s T emporalKnowl- edgeNode and OntologyPatcher modules. [ 16 ] demonstrate compliance v erification for business process regulations, establishing a precedent for rule-based classification with audit trails. T -norms in knowledge graph reasoning . Beyond the systems in T able 3 , GNN-QE [ 10 ] use s product fuzzy logic for multi-hop kno wledge graph queries, pro viding empirical e vidence that t-norm-based rea- soning can scale to comple x KG structures. Our work complements this by ev aluating t-norm operator choice rather than assuming product t-norm as default. 4 Laabs — T -Norm Operators for EU AI Act Classification 3 Methodology 3.1 Rule F ormalisation W e formalise 14 EU AI Act rules as conjuncti ve tuples ⟨ r , C , θ ⟩ , where r is the risk category , C = [ c 1 , c 2 , . . . , c n ] are condition identifiers from a vocab ulary of 22 terms, and θ = 0 . 5 is the classification threshold. A rule fires when the t-norm chain ov er its conditions exceeds θ : score ( r , s ) = T  T  . . . T ( s 1 , s 2 ) . . . , s n − 1  , s n  where s i ∈ [ 0 , 1 ] is the confidence assigned to condition c i . Classification follo ws the priority ordering: prohibited > h igh_risk > limited_risk > min imal_risk . 3.2 Benchmark Dataset W e constructed a benchmark of n = 1035 AI system descriptions, each annotated with: (a) a confidence score for each condition in the rule’ s condition set; (b) an e xpert label; (c) a case type. • Clear ( n = 630): All conditions > 0 . 80 or < 0 . 12. Sanity check. • Marginal ( n = 325): ≥ 1 condition in [ 0 . 12 , 0 . 65 ] . Diagnostically critical. • Borderline ( n = 80): Genuinely contested expert judgment. T able 4: Selected EU AI Act rules formalised in LGGT+. All rules use ALL-conjunction. Rule ID Cat. Conditions Article prohibited_rt_biometric prohib . real_time_processing , Art. 5(1)(h) public_space , biometric_identification prohibited_social_scoring prohib . public_authority , Art. 5(1)(c) evaluates_social_behavior , detrimental_treatment high_risk_employment high_risk employment_context , Annex III §4 recruitment_or_promotion , automated_decision high_risk_credit high_risk essential_service , Annex III §5 creditworthiness_or_insurance , individual_assessment limited_chatbot limited interacts_with_humans , Art. 50(1) ai_generated_output , not_clearly_disclosed Label distribution: minimal_risk 32%, high_risk 28%, limited_risk 27%, prohibited 13%. Labels assigned by the lead author (engineering background, EU AI Act certified practitioner) with- out independent legal revie w — a limitation that affects the v alidity of conclusions (see Section 6, L1). This is a proof-of-concept pilot study; full empirical v alidation requires independent annotation. Inde- pendent legal e xpert validation is the immediate ne xt step. 5 Laabs — T -Norm Operators for EU AI Act Classification 3.3 Experimental Protocol For each of the 1035 cases we run the LGGT+ classifier three times ( T L , T P , T G ), with all other parameters fixed ( θ = 0 . 5, 14 rules, shared vocab ulary). W e compute: accuracy by case type, false positi ve and f alse negati ve rates, and pairwise McNemar’ s exact binomial test. 4 Results T able 5 presents overall and per-case-type accurac y . T able 6 breaks down false positi ves and false nega- ti ves. T able 7 reports pairwise statistical tests. 4.1 Main Accuracy Results T G achie ves the highest ov erall accuracy (84.5%), outperforming T P (81.2%) and T L (78.5%). All dif fer- ences are statistically significant at α = 0 . 05. 4.2 Error T ype Analysis All operators produce zero f alse positiv es for T L and T P , maintaining the conserv ativ e compliance stance expected of a regulatory system. T G introduces 8 false positi ves (0.8%) — over -classifying marginal cases where min-semantics returns a score abov e θ e ven when one condition is genuinely weak. T able 5: Classification accurac y by t-norm operator and case type ( n = 1035). T G achie ves 85% on borderline cases ( n = 80) vs. 25%/35% for T L / T P . All pairwise differences are statistically significant ( p < 0 . 001). Bold: highest value per column. T -norm Overall Clear Marginal Borderline Łukasie wicz T L 78.5% 96.3% 56.9% 25.0% Product T P 81.2% 99.5% 56.9% 35.0% Gödel T G 84.5% 100.0% 54.5% 85.0% T able 6: Error breakdo wn. Zero false positiv es is a structural property of multi-condition conjunctive classification at θ = 0 . 5 (not an empirical finding): an y system requiring all conditions to e xceed thresh- old will default conserv ativ ely . The diagnostically relev ant metric is false neg ativ es. T -norm FP FN FP Rate FN Rate T L 0 223 0.0% 21.5% T P 0 195 0.0% 18.8% T G 8 152 0.8% 14.7% 4.3 Statistical T ests 4.4 Diver gence Cases: Where Operators Differ T G correctly classifies 68 of 80 borderline cases (85%) where T L achie ves only 25% and T P achie ves 35%. At n = 1035, this difference is statistically significant ( p < 0 . 001, McNemar n = 79 discordant pairs). T G also produces 8 false positi ves (0.8%) on marginal cases — a precision/recall trade-of f not observ able at small sample sizes. Representativ e div ergence cases: 6 Laabs — T -Norm Operators for EU AI Act Classification T able 7: McNemar’ s exact binomial test ( n = 1035). All pairwise comparisons reach statistical signifi- cance at α = 0 . 05. T G significantly outperforms T L ( p < 0 . 001, n = 79 discordant pairs). T L and T P are no longer decision-equi valent at this scale ( p < 0 . 001, 28 discordant pairs). Comparison b c n p -v alue Sig. α = 0 . 05 T L vs T P 0 28 28 < 0 . 001 Y es T L vs T G 8 71 79 < 0 . 001 Y es T P vs T G 3 43 46 < 0 . 001 Y es Case HRM04 — T raffic management with emergency override. Conditions: critical_infrastructure = 0 . 93, safety_component = 0 . 88, autonomous_decision = 0 . 61. Expert label: high_risk . T L : max ( 0 , max ( 0 , 0 . 93 + 0 . 88 − 1 ) + 0 . 61 − 1 ) = 0 . 42 → minimal_risk (wrong) T P : 0 . 93 × 0 . 88 × 0 . 61 = 0 . 499 → minimal_risk (wrong, borderline) T G : min ( 0 . 93 , 0 . 88 , 0 . 61 ) = 0 . 61 → high_risk ✓ (correct) Le gal reasoning: The emergenc y override does not negate operational autonomy . The system oper- ates autonomously the vast majority of the time. T G correctly identifies that ev en the weakest condition (0.61) exceeds the threshold. Case HRM05 — Exam proctoring with human grader . Conditions: education_context = 0 . 92, determines_access = 0 . 58, affects_life_path = 0 . 63. Expert label: high_risk . T L : 0 . 13 → minimal_risk (wrong) T P : 0 . 336 → minimal_risk (wrong) T G : min ( 0 . 92 , 0 . 58 , 0 . 63 ) = 0 . 58 → high_risk ✓ (correct) Le gal r easoning: The proctoring system’ s behavioural flags feed into grade calculations, functionally determining access ev en though a human formally assigns the grade. A moderate determines_access score (0.58) is legally suf ficient for Annex III §3; T G captures this. 5 Discussion 5.1 T L vs. T P : Decision Diver gence at Scale At n = 73, T L and T P were decision-equiv alent (zero discordant pairs). At n = 1035, they di verge on 28 cases ( p < 0 . 001). The theoretical threshold condition: T L  T L ( a , b ) , c  ≤ 0 . 5 = ⇒ a + b + c ≤ 2 . 5 Deri vation: T L ( a , b ) = max ( 0 , a + b − 1 ) . For the outer application, T L ( T L ( a , b ) , c ) = max ( 0 , ( a + b − 1 ) + c − 1 ) = max ( 0 , a + b + c − 2 ) . Setting this ≤ 0 . 5 giv es a + b + c ≤ 2 . 5. When one v alue is dis- tinctly low (marginal cases, < 0 . 40), both operators consistently agree on threshold crossing. This is a dataset-conditional result, not a general equiv alence. Datasets with many moderate scores (0.45–0.65 on all inputs) would produce div ergence. The original hypothesis should be framed conditionally on the condition score distribution. 7 Laabs — T -Norm Operators for EU AI Act Classification 5.2 T G Bottleneck Semantics f or Legal Rules T G ’ s correct classification of HRM04/HRM05 (two borderline cases, p = 0 . 25, not statistically signifi- cant) reflects a genuine semantic distinction worth in vestigating. T L requires conditions to be “strongly co-present”; T G requires the weakest condition to e xceed the threshold. Annex III §3 (education) does not mandate that all conditions be definitiv ely present — it requires the system to operate in education and af fect access. A moderate determines_access score (0.58) may be legally suf ficient. T G captures this interpretation. This moti v ates RH3 belo w: a mixed-semantics classifier assigning rule-specific t-norms, annotated by legal e xperts, may outperform any single-operator system. 5.3 Revised Resear ch Hypotheses Pilot-Generated Hypotheses RH1–RH4 (requiring independent v alidation) RH1: Classification accuracy is primarily determined by rule base completeness, not t-norm choice, provided the operator is conserv ati ve (zero false positi ves). RH2: For rules requiring definitiv ely co-present conditions (strong conjunction), T L and T P are decision-equi valent. T L ’ s hard boundary has theoretical auditability adv antages. RH3: For rules where a moderate individual condition is legally sufficient (bottleneck con- junction), T G produces higher recall without increasing false positi ves. RH4: A mixed-semantics classifier assigning rule-specific t-norms (annotated by legal ex- perts for conjuncti ve standard type) will outperform any single-operator system. 5.4 Primary Error Sour ce: Rule Base Incompleteness FN = 23–26 cases (31–36%) arise when the classifier returns minimal_risk for systems whose expert label is limited_risk or high_risk . Inspection reveals that most in volv e low automated_decision scores (0.14–0.38) reflecting human-in-the-loop designs where AI plays an advisory b ut not decisiv e role. The classifier correctly identifies that the condition is not definiti vely present; the expert applies proportionality reasoning beyond the individual rule conditions. Rule base incompleteness is the domi- nant error source, not operator choice. 6 Limitations L1 — Self-annotation. Labels assigned without independent legal revie w . Cohen’ s κ with two legal experts is the immediate ne xt step. L2 — Curated vs. real-world data. The n = 1035 benchmark pro vides rob ust statistical po wer ( p < 0 . 001), b ut system descriptions and condition scores are curated rather than extracted from actual AI documentation. Real-world AI system documentation is often unstructured and ambiguous, which may introduce noise not captured in this controlled e valuation. L3 — Deterministic condition scores. A calibrated NLP extraction pipeline from real AI system documentation would remo ve subjecti ve scoring. L4 — Fixed threshold. Threshold sensitivity ( θ ∈ [ 0 . 25 , 0 . 75 ] ) analysis is in preparation. L5 — Rule co verage. 14 rules do not co ver all EU AI Act provisions (GP AI partially covered; Art. 5 ex emptions absent; delegated acts pending). 8 Laabs — T -Norm Operators for EU AI Act Classification 7 Futur e W ork Human expert validation. T wo independent EU AI Act la wyers annotate a stratified subset ( n ≈ 150, ensuring proportional cov erage of borderline and marginal cases) drawn from the full 1035-case bench- mark; compute Cohen’ s κ and expert/LGGT+ agreement per t-norm mode. Threshold sensitivity . V arying θ across [ 0 . 25 , 0 . 75 ] will establish the operating curve for each t-norm. Mixed-semantics classifier . Annotate each of the 14 rules as “strong conjunction” ( → T L ) or “bottle- neck conjunction” ( → T G ); e valuate RH4. Logic-A ugmented Attention (LAA). LAA modulates graph transformer edge weights by logical pred- icate confidence. It will use Product t-norm in log-space (logL TN) for training stability . This directly addresses EIC Pathfinder Hypothesis H1. arXiv and dataset release. Full benchmark dataset and LGGT+ core engine at: github.com/T riStiX- LS/LggT -core (Apache 2.0). 8 Conclusion W e present a comparati ve pilot ev aluation of t-norm operators for EU AI Act compliance classification ( n = 1035, 14 rules, 4 risk categories). At scale, all three operators differ significantly (McNemar p < 0 . 001). T G achie ves the highest overall accuracy (84.5%) and best borderline case performance (85%), but introduces 8 false positi ves (0.8%) via min-semantics over -classification — a precision/recall trade- of f in visible at small sample sizes. T L and T P maintain zero false positiv es, with T P outperforming T L (81.2% vs. 78.5%). The dominant finding is that rule base completeness matters more than operator choice. The sec- ondary finding moti vates a mix ed-semantics classifier , where rule-specific t-norms are assigned based on legal annotation of each rule’ s conjunctiv e standard. W e identify human expert annotation as the single highest-priority next step. LGGT+ (201/201 tests, 18 modules across 4 layers) is av ailable open-source at github .com/T riStiX- LS/LggT -core . Refer ences [1] Badreddine, S., d’A vila Garcez, A., Serafini, L., & Spranger , M. (2022). Logic T ensor Networks. Artificial Intelligence , 303, 103649. [2] Badreddine, S., & Serafini, L. (2023). logL TN: Dif ferentiable Fuzzy Logic in the Logarithm Space. arXi v:2306.14546. [3] European Parliament and Council. (2024). Re gulation (EU) 2024/1689 on Artificial Intelligence (EU AI Act). Official J ournal of the Eur opean Union , L 2024/1689. [4] Hájek, P . (1998). Metamathematics of Fuzzy Logic . Kluwer Academic Publishers. 9 Laabs — T -Norm Operators for EU AI Act Classification [5] High-Le vel Expert Group on Artificial Intelligence. (2020). Assessment List for T rustworthy AI (AL T AI). European Commission. [6] Marra, G., van Krieken, E., Manhaev e, R., De Raedt, L., & Diligenti, M. (2024). From Statistical Relational to Neural Symbolic Artificial Intelligence. Artificial Intelligence , 328, 104062. [7] Petersen, F ., Borgelt, C., Kuehne, H., & Deussen, O. (2022). Deep Differentiable Logic Gate Net- works. Advances in Neur al Information Pr ocessing Systems (NeurIPS) , 35. [8] Riegel, R., Gray , A., Luus, F ., Khan, N., Makondo, N., Akhalwaya, I. Y ., Qian, H., Fagin, R., Barahona, F ., Sharma, U., et al. (2020). Logical Neural Networks. arXi v:2006.13155. [9] Moriyama, S., Inoue, K., et al. (2025). Graph-Based Attention for Differentiable MaxSA T Solving. Advances in Neural Information Pr ocessing Systems (NeurIPS) . [10] Zhu, Z., Galkin, M., Zhang, Z., & T ang, J. (2022). Neural-Symbolic Models for Logical Queries on Knowledge Graphs. Pr oceedings of the 39th International Confer ence on Machine Learning (ICML) , PMLR 162, 27454–27478. [11] Lin, X., Y ang, H., W ang, Z., Chen, Y ., et al. (2023). TFLEX: T emporal Feature-Logic Embed- ding Frame work for Comple x Reasoning ov er T emporal Knowledge Graphs. Advances in Neural Information Pr ocessing Systems (NeurIPS) , 37. [12] Bench-Capon, T . J. M., & Sartor , G. (2003). A Model of Leg al Reasoning with Cases Incorporating Theories and V alues. Artificial Intelligence , 150(1–2), 97–143. [13] Prakken, H., & Sartor, G. (2015). Law and Logic: A Re view from an Ar gumentation Perspecti ve. Artificial Intelligence , 227, 214–245. [14] Palmirani, M., & Governatori, G. (2018). Modelling Le gal Kno wledge for GDPR Compliance Checking. Le gal Knowledge and Information Systems (JURIX) , 313, 101–110. [15] Hashmi, M., Gov ernatori, G., Lam, H.-P ., & W ynn, M. T . (2018). Are W e Done with Business Process Compliance Checking? Knowledge and Information Systems , 57(1), 79–133. [16] Lam, H.-P ., Hashmi, M., & W ynn, M. T . (2016). Enabling T emporal Compliance Reasoning in Business Process Models. J ournal of Logic and Computation , 27(2), 387–428. A Benchmark Case Examples T able 8 presents 15 representativ e benchmark cases. Full dataset at github .com/T riStiX-LS/LggT -core/benchmark/ . 10 Laabs — T -Norm Operators for EU AI Act Classification T able 8: Representati ve benchmark cases with T L and T G predictions ( ✓ correct, × incorrect). T P identi- cal to T L in all cases sho wn. HRM04 and HRM05 are the borderline div ergence cases. ID Description (abbrev .) Expert T ype T L T G P01 Realtime face recog. in metro prohibited clear ✓ ✓ P02 Government social credit system prohibited clear ✓ ✓ PM01 Nudge recommender (not subliminal) limited marginal × × PM02 Post-e vent biometric search high mar ginal × × PM03 Pri vate loyalty scoring limited marginal × × HR01 AI CV screening system high clear ✓ ✓ HR02 Automated mortgage scoring high clear ✓ ✓ HRM01 Advisory (not decisi ve) hiring AI limited marginal × × HRM03 Aggregate HR analytics, no decisions limited marginal × × HRM04 T raffic mgmt + emer gency o verride high border . × ✓ HRM05 Exam proctoring + human grader high border . × ✓ HRM07 Biometric attendance, no decisions minimal mar ginal ✓ ✓ LR01 Chatbot without AI disclosure limited clear ✓ ✓ LR04 Chatbot with clear AI disclosure minimal mar ginal ✓ ✓ MR01 Spam filter minimal clear ✓ ✓ 11

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