Applying a legal provision frequently requires both structured rule-based reasoning and sensitivity to open-textured terms developed in case law. The actio pauliana of Article 42 of the Dutch Bankruptcy Act (Faillissementswet, Fw), which allows an insolvency practitioner to avoid transactions that prejudice creditors, requires both. We present a neuro-symbolic model of Article 42 Fw. Its symbolic core is written in Catala in a literate style that keeps statute and formalisation aligned and was developed through pair programming, with open-textured terms represented as boolean inputs where neural components couple to the symbolic solver. A neural routine structures a case's natural-language facts into boolean and date inputs. Neural subroutines resolve the open-textured terms through case-based reasoning over Dutch civil judgments, retrieved through a pipeline that filters on the requirement being resolved and expands along the procedural chain of a case. Segmenting and labelling those judgments attains high precision and recall against a manually annotated gold standard of 100 judgments. On ten hand-annotated cases the neuro-symbolic model handles most criteria reasonably but struggles with the knowledge requirement. Retrieval depth shows no clear quantitative effect, although retrieved judgments provide explicit grounding in prior case law.
Figures & tables
Figure 1: Actio pauliana model based on Pannevis para. 7.2.1 [ 23 ] , translation based on Warendorf [ 32 ] .
Score
Score
Section
P
R
F1
n
Section
P
R
F1
n
Course of proceedings
1.00
0.99
0.99
100
Established facts
1.00
0.97
0.99
76
Dispute
0.98
0.94
0.96
63
Grounds of decision
0.95
0.92
0.94
114
Decision
0.99
0.99
0.99
101
Other
0.98
1.00
0.99
128
Micro average (all)
0.98
0.97
0.98
582
Table 1: Section segmentation performance on the Rechtspraak corpus, reporting precision, recall, and F1 per section against 100 manually segmented judgments.
mistral-medium-3.5-128b:fp8
gpt-5.4
Element
P
R
F1
n
P
R
F1
n
Voluntary performance
0.69
0.97
0.81
39
0.85
0.90
0.88
39
Prejudice to creditors
0.89
0.91
0.90
34
1.00
0.82
0.90
34
Knowledge
0.86
0.92
0.89
39
0.97
0.92
0.95
39
Micro average
0.80
0.94
0.86
112
0.93
0.88
0.91
112
Table 2: Pre-retrieval annotation performance per element against 100 manually annotated judgments.
k=0
k=5
k=10
Model
P
R
F1
P
R
F1
P
R
F1
gemini-3.5-flash
0.64
0.88
0.74
0.67
0.90
0.77
0.63
0.88
0.74
gpt-5.5
0.68
0.90
0.77
0.67
0.90
0.77
0.67
0.90
0.77
mistral-medium-3.5-128b:fp8
0.66
0.82
0.73
0.65
0.82
0.72
0.66
0.82
0.73
Table 3: Neuro-symbolic model performance, reporting micro-averaged precision, recall, and F1 of the boolean criteria and the final verdict over ten judgments against the gold standard, at retrieval depths k=0 , k=5 , and k=10 .
k=0
k=5
k=10
Model
Subroutine
P
R
F1
P
R
F1
P
R
F1
gemini-3.5-flash
Voluntary
0.78
0.88
0.82
0.88
0.88
0.88
0.78
0.88
0.82
Prejudice
0.67
1.00
0.80
0.60
1.00
0.75
0.67
1.00
0.80
Knowledge
0.10
0.40
0.16
0.16
0.60
0.25
0.10
0.40
0.16
gpt-5.5
Voluntary
0.88
0.88
0.88
0.88
0.88
0.88
0.88
0.88
0.88
Prejudice
0.67
1.00
0.80
0.75
1.00
0.86
0.75
1.00
0.86
Table 4: Per-subroutine micro-averaged precision, recall, and F1 at retrieval depths k=0 , k=5 , and k=10 .
Model
k=0
k=5
k=10
gemini-3.5-flash
7
7
6
gpt-5.5
7
7
7
mistral-medium-3.5-128b:fp8
6
6
6
Table 5: Correct final verdicts (avoidable under Article 42 Fw) out of ten gold-standard cases, by model and retrieval depth.
Legal texts often contain computational legal clauses--provisions whose understanding requires complex logic. While frontier Large Reasoning Models (LRMs) can describe such clauses, building production-ready systems is limited by reasoning errors and the high cost of inference. We propose Amortized Intelligence, a neuro-symbolic approach where we use an LLM once to translate a legal text into Deterministic Autonomous Contract Language (DACL): a typed graph intermediate representation. Adjudication then relies on deterministic graph executions with a visually auditable trace. In comparison against runtime LRM baselines (including GPT-5.2 and Gemini 3 Pro), our DACL-based Agent achieves near-perfect consistency and mitigates the "reasoning cliff" observed in probabilistic models. The system reduces compute costs by over 90% in high-volume workflows while satisfying the strict auditability requirements of legal adjudication.
Applying computational methods to law at scale requires separating genuine legal reasoning from surface similarity. We study this through a concrete task: detecting implicit citations of the French Civil Code, where a court applies a statutory rule without naming it (a post-hoc question about the reasoning a court actually used). We release a benchmark of 1,015 passage-article pairs annotated by three legal experts. Our central finding is that their disagreement is itself informative: the third of cases the experts dispute are where models fail. Our best ensemble reaches an F1 score of 0.70 overall. Yet, two-thirds of its false positives fall on those disputed cases, a concentration that holds across all ten models we evaluate. Expert disagreement thus signals uncertainty in the task and in its gold label, which aggregate metrics hide. This should not block useful tools, however: reframed as top-k ranking with multi-model consensus, the same signals reach 76% precision for the top-200 candidates of the benchmark without supervision.
Avrile Floro, Tamara Dhorasoo, Soline Pellez +1
UPHF · Télécom Paris, Institut Polytechnique de Paris · Université Polytechnique Hauts-de-France
Automating legal reasoning forces a choice between imperfect alternatives: symbolic systems offer transparency but struggle with ambiguity, whereas neural systems handle natural language flexibly but lack verifiability. This paper investigates whether a hybrid, neuro-symbolic approach can reconcile this trade-off. We evaluate this architecture in the domain of online content moderation, which serves as a proxy for high-volume legal decision-making such as mass administrative proceedings. In these settings, operators must assess thousands of cases daily under strict legal standards. Specifically, we examine whether constraining large language models (LLMs) within deterministic symbolic scaffolds improves statute-grounded illegality assessment while preventing "scope drift" (where LLMs conflate moral offensiveness with legal illegality). We evaluate the neuro-symbolic variant of Rulemapping - a visual logic-tree method that operationalises the classic legal syllogism - on online hate-speech classification under §130(1) of the German Criminal Code. Across diverse LLMs, Rulemapping maintains high recall (0.82-0.89) while achieving precision of 0.80-0.86, compared to 0.34-0.49 for unconstrained prompting. Expert-authored symbolic scaffolds thus enable robust legal automation aligned with regulatory requirements for auditability and verifiable decision-making.
Oskar von Cossel
Max Planck Institute for Comparative and International Private Law Hamburg, Germany · Rulemapping Group Berlin, Germany