A Model-Theoretic Formalization of AlKhwaremis ilm alfaraid

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.

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.

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.