Computational Extraction of Legal Causes via al-Sabr wa al-Taqsim: A Set-Theoretic Formalization for Closed Fiqh Chapters

This paper presents a set-theoretic formalization of the classical usuli method of al-Sabr wa al-Taqsim (Examination and Division) for extracting legal causes ('ilal) within closed chapters of jurisprudence. A computational algorithm is introduced that extracts minimal operational rules from a truth table of juristic verdicts. The principal result is that, given a complete truth table for a closed chapter, the algorithm computes the minimal structural generators of the ruling and eliminates all logically redundant attributes. The resulting structures constitute admissible candidate causes for subsequent juristic evaluation. The framework is conditional upon the availability of a finite school-relative concept vocabulary and a complete ruling table for the chapter under investigation.