CVPD at QIAS 2026: RAG-Guided LLM Reasoning for Al-Mawarith Share Computation and Heir Allocation

2026-03-25

AI Summary

This work addresses the complexity of multi-stage legal reasoning in Islamic inheritance law (Ilm al-Mawarith)—encompassing heir identification, exclusion rules, allocation of fixed and residual shares, and awl/radd adjustment mechanisms—while accounting for doctrinal variations across jurisprudential schools and civil codes. To tackle this challenge, we propose a novel reasoning framework that integrates retrieval-augmented generation (RAG) with symbolic computation. The system ensures legal and numerical consistency through rule-driven synthetic data generation, hybrid dense and BM25 retrieval, cross-encoder reranking, and schema-constrained decoding. Evaluated in the QIAS 2026 blind test, our approach achieved a state-of-the-art MIR-E score of 0.935, ranking first and demonstrating, for the first time, high-precision, configurable Arabic legal reasoning. This result validates the efficacy of structured output generation guided by retrieval in complex legal domains.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Multiagent Systems: Mechanism Design

Application Category

• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

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.

Problem

• Islamic inheritance
• Ilm al-Mawarith
• heir allocation
• share computation
• legal reasoning

Innovation

• Retrieval-Augmented Generation (RAG)
• Symbolic Inheritance Calculator
• Synthetic Data with Reasoning Traces
• Schema-Constrained Generation
• Hybrid Retrieval