Legal Reasoning

Reasoning with complex, context-specific rules remains challenging for large language models (LLMs). In legal and policy settings, this manifests as deontic reasoning: reasoning about obligations, permissions, and prohibitions under explicit rules. While many recent benchmarks emphasize short-context mathematical reasoning, fewer focus on long-context, high-stakes deontic reasoning. To address this gap, we introduce DEONTICBENCH, a benchmark of 6,232 tasks across U.S. federal taxes, airline baggage policies, U.S. immigration administration, and U.S. state housing law. These tasks can be approached in multiple ways, including direct reasoning in language or with the aid of symbolic computation. Besides free-form chain-of-thought reasoning, DEONTICBENCH enables an optional solver-based workflow in which models translate statutes and case facts into executable Prolog, leading to formal problem interpretations and an explicit program trace. We release reference Prolog programs for all instances. Across frontier LLMs and coding models, best hard-subset performance reaches only 44.4% on SARA Numeric and 46.6 macro-F1 on Housing. We further study training with supervised fine-tuning and reinforcement learning for symbolic program generation. Although training improves Prolog generation quality, current RL methods still fail to solve these tasks reliably. Overall, DEONTICBENCH provides a benchmark for studying context-grounded rule reasoning in real-world domains under both symbolic and non-symbolic settings.

Islamic inheritance law (ilm al-mawarıth) presents a challenging domain for evaluating large language models' structured reasoning capabilities, requiring multi-step legal analysis, rule-based blocking decisions, and precise fractional calculations. We present QU-NLP's submission to the QIAS 2026 shared task on Arabic Islamic inheritance reasoning. Our approach employs a multi-stage Quantized Low-Rank Adaptation (QLoRA) fine-tuning strategy on Qwen3-4B: (1) domain adaptation on 3,166 Islamic fatwa records to acquire inheritance terminology and jurisprudential reasoning patterns, followed by (2) task-specific training on 12,000 structured inheritance cases to optimize JSON-formatted output generation. Using 4-bit NF4 quantization with rank-128 LoRA adapters, our model achieves 90% MIR-E (Mawarith Inheritance Reasoning Evaluation) score on the test set, demonstrating competitive performance while requiring minimal computational resources. Our results show that domain-specific pre-adaptation combined with structured output training enables small language models to perform complex legal reasoning tasks effectively comparing to commercial systems such as Gemini-2.5-flash.

Legal reasoning requires not only the application of legal rules but also an understanding of the context in which those rules operate. However, existing legal benchmarks primarily evaluate rule application under the assumption of fixed norms, and thus fail to capture situations where legal judgments shift or where multiple norms interact. In this work, we propose CALRK-Bench, a context-aware legal reasoning benchmark based on the legal system in Korean. CALRK-Bench evaluates whether models can identify the temporal validity of legal norms, determine whether sufficient legal information is available for a given case, and understand the reasons behind shifts in legal judgments. The dataset is constructed from legal precedents and legal consultation records, and is validated by legal experts. Experimental results show that even recent large language models consistently exhibit low performance on these three tasks. CALRK-Bench provides a new stress test for evaluating context-aware legal reasoning rather than simple memorization of legal knowledge. Our code is available at https://github.com/jhCOR/CALRKBench.

Large language models show promise for legal applications, but deploying frontier models raises concerns about cost, latency, and data privacy. We evaluate whether sub-10B parameter models can serve as practical alternatives by testing nine models across three legal benchmarks (ContractNLI, CaseHOLD, and ECtHR) using five prompting strategies (direct, chain-of-thought, few-shot, BM25 RAG, and dense RAG). Across 405 experiments with three random seeds per configuration, we find that a Mixture-of-Experts model activating only 3B parameters matches GPT-4o-mini in mean accuracy while surpassing it on legal holding identification, and that architecture and training quality matter more than raw parameter count. Our largest model (9B parameters) performs worst overall. Chain-of-thought prompting proves sharply task-dependent, improving contract entailment but degrading multiple-choice legal reasoning, while few-shot prompting emerges as the most consistently effective strategy. Comparing BM25 and dense retrieval for RAG, we find near-identical results, suggesting the bottleneck lies in the language model's utilization of retrieved context rather than retrieval quality. All experiments were conducted via cloud inference APIs at a total cost of $62, demonstrating that rigorous LLM evaluation is accessible without dedicated GPU infrastructure.

Islamic inheritance (Ilm al-Mawarith) is a multi-stage legal reasoning task requiring the identification of eligible heirs, resolution of blocking rules (hajb), assignment of fixed and residual shares, handling of adjustments such as awl and radd, and generation of a consistent final distribution. The task is further complicated by variations across legal schools and civil-law codifications, requiring models to operate under explicit legal configurations. We present a retrieval-augmented generation (RAG) pipeline for this setting, combining rule-grounded synthetic data generation, hybrid retrieval (dense and BM25) with cross-encoder reranking, and schema-constrained output validation. A symbolic inheritance calculator is used to generate a large high-quality synthetic corpus with full intermediate reasoning traces, ensuring legal and numerical consistency. The proposed system achieves a MIR-E score of 0.935 and ranks first on the official QIAS 2026 blind-test leaderboard. Results demonstrate that retrieval-grounded, schema-aware generation significantly improves reliability in high-precision Arabic legal reasoning tasks.

This paper introduces PYTHEN, a novel Python-based framework for defeasible legal reasoning. PYTHEN is designed to model the inherently defeasible nature of legal argumentation, providing a flexible and intuitive syntax for representing legal rules, conditions, and exceptions. Inspired by PROLEG (PROlog-based LEGal reasoning support system) and guided by the philosophy of The Zen of Python, PYTHEN leverages Python's built-in any() and all() functions to offer enhanced flexibility by natively supporting both conjunctive (ALL) and disjunctive (ANY) conditions within a single rule, as well as a more expressive exception-handling mechanism. This paper details the architecture of PYTHEN, provides a comparative analysis with PROLEG, and discusses its potential applications in autoformalization and the development of next-generation legal AI systems. By bridging the gap between symbolic reasoning and the accessibility of Python, PYTHEN aims to democratize formal legal reasoning for young researchers, legal tech developers, and professionals without extensive logic programming expertise. We position PYTHEN as a practical bridge between the powerful symbolic reasoning capabilities of logic programming and the rich, ubiquitous ecosystem of Python, making formal legal reasoning accessible to a broader range of developers and legal professionals.

Legal Judgment Prediction (LJP) predicts applicable law articles, charges, and penalty terms from case facts. Beyond accuracy, LJP calls for intrinsically interpretable and legally grounded reasoning that can reconcile statutory rules with precedent-informed standards. However, existing methods often behave as static, one-shot predictors, providing limited procedural support for verifiable reasoning and little capability to adapt as jurisprudential practice evolves. We propose VERDICT, a self-refining collaborative multi-agent framework that simulates a virtual collegial panel. VERDICT assigns specialized agents to complementary roles (e.g., fact structuring, legal retrieval, opinion drafting, and supervisory verification) and coordinates them in a traceable draft--verify--revise workflow with explicit Pass/Reject feedback, producing verifiable reasoning traces and revision rationales. To capture evolving case experience, we further introduce a Hybrid Jurisprudential Memory (HJM) grounded in the Micro-Directive Paradigm, which stores precedent standards and continually distills validated multi-agent verification trajectories into updated Micro-Directives for continual learning across cases. We evaluate VERDICT on CAIL2018 and a newly constructed CJO2025 dataset with a strict future time-split for temporal generalization. VERDICT achieves state-of-the-art performance on CAIL2018 and demonstrates strong generalization on CJO2025. To facilitate reproducibility and further research, we release our code and the dataset at https://anonymous.4open.science/r/ARR-4437.

Islamic inheritance law is challenging for large language models because solving inheritance cases requires complex, structured, multi-step reasoning and the correct application of juristic rules to compute heirs' shares. We introduce MAWARITH, a large-scale annotated dataset of 12,500 Arabic inheritance cases for training and evaluating models on the full reasoning chain: (i) identifying eligible heirs, (ii) applying blocking (\d{h}ajb) and allocation rules, and (iii) computing exact inheritance shares. To the best of our knowledge, MAWARITH is the first Arabic corpus and benchmark designed for end-to-end Islamic inheritance reasoning. Unlike prior datasets that restrict inheritance case solving to multiple-choice questions, MAWARITH supports the full reasoning chain and provides step-by-step solutions with justifications grounded in classical juristic sources and established inheritance rules, as well as exact share calculations. This enables models to learn how to generate detailed, step-by-step responses to user queries that reflect real-world Islamic inheritance cases. To evaluate models beyond final-answer accuracy, we propose MIR-E (Mawarith Inheritance Reasoning Evaluation), a weighted multi-stage metric that scores key reasoning stages and captures error propagation across the pipeline. We evaluate six large language models in a zero-shot setting. A commercial model achieves about 90%, whereas all evaluated open-source models remain below 50%. Our error analysis identifies recurring failure patterns, including scenario misinterpretation, errors in heir identification, errors in share allocation, and missing or incorrect application of key inheritance rules such as \textquotesingle awl and radd. The MAWARITH dataset is publicly available at https://gitlab.com/nlpresearcher/mawarith.

AI and Law research has encountered legal interpretation in different ways, in the context of its evolving approaches and methodologies. Research on expert system has focused on legal knowledge engineering, with the goal of ensuring that human-generated interpretations can be precisely transferred into knowledge-bases, to be consistently applied. Research on argumentation has aimed at representing the structure of interpretive arguments, as well as their dialectical interactions, to assess of the acceptability of interpretive claims within argumentation frameworks. Research on machine learning has focused on the automated generation of interpretive suggestions and arguments, through general and specialised language models, now being increasingly deployed in legal practice.

This Guideline presents a systematic and operationalizable annotation framework for representing legal argumentation structures in judicial decisions. Grounded in theories of legal reasoning and argumentation, the framework aims to reveal the logical organization of judicial reasoning and provide a reliable foundation for computational analysis. At the element level, the Guideline distinguishes between the non-propositional layer and the propositional layer. The non-propositional layer consists of two elements: Issue and Non-argumentative Component. At the propositional level, the Guideline defines four proposition types: General Normative Judgment, Particular Normative Judgment, General Factual Judgment, and Particular Factual Judgment. At the relational level, five relation types are defined to represent argumentative structures: Support, Attack, Joint, Match, and Identity. These relations capture positive and negative argumentative connections, conjunctive reasoning structures, correspondences between legal norms and case facts, and identity or semantic equivalence between propositions. The Guideline further specifies formal representation rules and visualization conventions for both basic and nested structures, enabling consistent visualization of complex argumentation patterns. In addition, it establishes a standardized annotation workflow and consistency control mechanisms to ensure the reproducibility and reliability of annotated data. By providing a clear conceptual model, formal representation rules, and practical annotation procedures, this Guideline supports large-scale analysis of judicial reasoning and future research in legal argument mining, computational modeling of legal reasoning, and AI-assisted legal analysis.

Legal reasoning requires not only high accuracy but also the ability to justify decisions through verifiable and contestable arguments. However, existing Large Language Model (LLM) approaches, such as Chain-of-Thought (CoT) and Retrieval-Augmented Generation (RAG), often produce unstructured explanations that lack a formal mechanism for verification or user intervention. To address this limitation, we propose Adaptive Collaboration of Argumentative LLMs (ACAL), a neuro-symbolic framework that integrates adaptive multi-agent collaboration with an Arena-based Quantitative Bipolar Argumentation Framework (A-QBAF). ACAL dynamically deploys expert agent teams to construct arguments, employs a clash resolution mechanism to adjudicate conflicting claims, and utilizes uncertainty-aware escalation for borderline cases. Crucially, our framework supports a Human-in-the-Loop (HITL) contestability workflow, enabling users to directly audit and modify the underlying reasoning graph to influence the final judgment. Empirical evaluations on the LegalBench benchmark demonstrate that ACAL outperforms strong baselines across Gemini-2.5-Flash-Lite and Gemini-2.5-Flash architectures, effectively balancing efficient predictive performance with structured transparency and contestability. Our implementation is available at: https://github.com/loc110504/ACAL.

The use of profiling evidence in criminal trials is a longstanding controversy in legal epistemology and evidence law theory. Many scholars, even when they oppose its use at trial, still assume that profiling evidence can be probative of guilt. We reject that assumption. Profiling evidence may support a generic hypothesis, but is not evidence that the defendant is guilty of the specific crime of which they are accused. We contrast profiling evidence with case-specific evidence, which speaks more directly to the facts of the case. Our critique departs from others by grounding the argument in a probabilistic analysis of evidentiary value. We also explore the implications of our account for debates about stereotyping.

This paper provides an experimental evaluation of the capability of large language models (LLMs) to assist in legal decision-making within the framework of Austrian and European Union value-added tax (VAT) law. In tax consulting practice, clients often describe cases in natural language, making LLMs a prime candidate for supporting automated decision-making and reducing the workload of tax professionals. Given the requirement for legally grounded and well-justified analyses, the propensity of LLMs to hallucinate presents a considerable challenge. The experiments focus on two common methods for enhancing LLM performance: fine-tuning and retrieval-augmented generation (RAG). In this study, these methods are applied on both textbook cases and real-world cases from a tax consulting firm to systematically determine the best configurations of LLM-based systems and assess the legal-reasoning capabilities of LLMs. The findings highlight the potential of using LLMs to support tax consultants by automating routine tasks and providing initial analyses, although current prototypes are not ready for full automation due to the sensitivity of the legal domain. The findings indicate that LLMs, when properly configured, can effectively support tax professionals in VAT tasks and provide legally grounded justifications for decisions. However, limitations remain regarding the handling of implicit client knowledge and context-specific documentation, underscoring the need for future integration of structured background information.