J.Acad.(N.Y.)4,2:52-87 2014 (36 pages) Abdelwahab et al. 1 Copyright © 2016 Journal Academica Foundation. All rights reserved. With perpetual, non-exclusive license to distribute for arxiv.org Originally received December 12 2013 - accepted May 7 2014 - published May 16 2014 J.Acad.(N.Y.)4,2:52-87 (36 pages) - Theoretical Computer Science - permalink: http://journalacademica.org/?smd_process_download=1&download_id=753 The Algorithm of Islamic Jurisprudence (Fiqh) with Validation of an Entscheidungsproblem Elnaserledinellah Mahmood Abdelwahab a*, Karim Daghbouche a, b Nadra Ahmad Shannan a makmad.org e.V., Hanover (Germany) b Faculty of Shariah, Umm Al-Qura University, Makkah (Kingdom of Saudi Arabia) Corresponding author: [email protected] ABSTRACT The historic background of algorithmic processing with regard to etymology and methodology is translated into terms of mathematical logic and Computer Science. A formal logic structure is introduced by exemplary questions posed to Fiqh-chapters to define a logic query language. As a foundation, a generic algorithm for deciding Fiqh- rulings is designed to enable and further leverage rule of law (vs. rule by law) with full transparency and complete algorithmic coverage of Islamic law eventually providing legal security, legal equality, and full legal accountability. This is implemented by disentangling and reinstating classic Fiqh-methodology (usul al-Fiqh) with the expressive power of subsets of First Order Logic (FOL) sustainably substituting ad hoc reasoning with falsifiable rational argumentation. The results are discussed in formal terms of completeness, decidability and complexity of formal Fiqh-systems. An Entscheidungsproblem for formal Fiqh-Systems is formulated and validated. Keywords: algorithm, Khwarizmi, Islam, balance, algebra, Shariah, Islamic law, jurisprudence, logic, syntax, semantics, Entscheidungsproblem, complexity, decidability, SAT-problem, transparency, security, accountability, rule of law, rule by law, Fiqh, usul al-Fiqh 1. INTRODUCTION The here presented Algorithm of Islamic Science and its underlying mathematics, Jurisprudence connects back some and a discussion (C) of the practical 1,200 years to the origin of the modern algorithmic results in computer term Algorithm which is the most programming while this introduction fundamental methodological driver of shall serve as a brief historic review: the current information technology pace It is commonly known that the term at internet speed. Algorithm is a Latin short-version of the It will be discussed in three major parts name Muhammad ibn Musa Al- which consist of (A) methodological Khwarizmi (163-235AH / 780-850AD), considerations in Islamic Jurisprudence who is the author of the Arabic book (Fiqh) with regard to (B) Computer Kitab Al-Jabr wa-l-Muqabala (215AH / 1 J.Acad.(N.Y.)4,2:52-87 2014 (36 pages) Abdelwahab et al. 2 830AD) [Al-Khwarizmi], i.e., The various sorts and kinds are concerned." Compendious Book on Calculation by [Al-Khwarizmi] Completion and Balancing. This book It is evident that the introduction of a was translated into Latin in the 12th new Fiqh-method back then as well as century A.D. entitled Liber Algebrae et today requires a standard set of Almucabola [Chester] with algebrae persuasive arguments in terms of and Almucabola being transliterated reproducible propositions and proofs. into Latin from the Arabic title where Therefore, every Fiqh-problem in Kitab the term Algebra is derived from Al-Jabr wa-l-Muqabala is reducible to a Al-Jabr in the title of Al-Khwarizmi's linear equation while the more book. fundamental method of quadratic While there is widespread belief that polynomials is never used but proven. Kitab Al-Jabr wa-l-Muqabala is a But before discussing the theory of textbook for mathematics which, among quadratic polynomials (cf. [Al- others, introduced general rules to solve Khwarizmi]), it was necessary to algebraic problems with one variable conclude some preliminary research reducible to quadratic equations, it is such as introducing the calculation with first and foremost a textbook for Islamic Hindu numerals including the number Jurisprudence: zero with Kitab Al-Jam wa-l-tafriq bi- As traditionally and practically done in hisab Al-Hind (The Book of Bringing Islamic Jurisprudence (Fiqh), the first together and Separating According to half of Kitab Al-Jabr wa-l-Muqabala the Hindu Calculation - lat.: Algoritmi introduced the applied methodology and de numero Indorum) written about term definitions, i.e., then as now the (210AH / 825AD), i.e.: Al-Khwarizmi domain of Algebra. developed and published the Hindu The remaining half of his book solves Calculation half a decade before legal questions on trade (commercial introducing the new Fiqh-method of transactions), geometry (plane surface reducing variables to quadratic distributions) as well as testimonies. equations. Based on the newly introduced While Al-Khwarizmi’s proposition algebraic method, the by far most consisted of reducing selected Fiqh- important part of Kitab Al-Jabr wa-l- problems to linear equations, the here Muqabala deals with Islamic heritage introduced Algorithm of Islamic law which is complex with regard to as Jurisprudence proposes to cover the well as both, number of variables and complete corpus juris of Islamic number of Fiqh-rules (axioms). Jurisprudence. Accordingly, Al-Khwarizmi’s Algebra is However, the most important just what its author says in the proposition underlying the Algorithm of introduction: "[a] work on algebra, Islamic Jurisprudence consists of one confining it to the fine and important single statement: parts of its calculations, such as people constantly require in cases of There exits a complete legislation. inheritance, legacies, partition, law- suits, and trade, and in all their dealings Its mathematical and algorithmic with one another, or where surveying, formalization will be presented in part B the digging of canals, geometrical of this paper. computation, and other objects of 2 J.Acad.(N.Y.)4,2:52-87 2014 (36 pages) Abdelwahab et al. 3 This statement implies that every Fiqh- rulings on different matters, problem has a solution, i.e., that every synthetically relying on their personal religious case has a ruling,1 which is the discretion. Their rulings were of three traditional conviction from its inception: types: A) interpretation of the Quran and the Fiqh developed in two stages: Firstly 3 during the time of Prophet Sunnah Muhammad’s (saw)2 companions when B) analogy that draws on similarities Fiqh did not rely on explicit rules. between cases (i.e., qiyas), and Rather, it relied on synthetic C) discretion that does not rely on any understanding by the Prophet’s (saw) particular text companions as they witnessed the revelations of the Quran with a When the major works on Fiqh- situation- and procedural awareness of methodology, such as Al-Shafi'i’s Al- Islamic law. Risalah (204AH / 820AD) [Sahfii] and As the Islamic influence and Al-Ghazali’s Al-Mustasfa (504AH / responsibility grew, the Muslim 1110AD) (cf. [Hammad]) appeared, community was embraced by diversity scholars had different views on the as well as both, culturally and validity of the second type of scholarly intellectually. At the same time, the discretion, i.e., on analogy. personal connection of Fiqh to the Many of the works on Islamic Prophet (saw) and his companions Jurisprudence that discuss analogy 4 became more and more remote. This let include questions concerning logic . Fiqh to be studied analytically. It also Other scholars who deny the relevance required in-depth studies of the Arabic of logic to Islamic Jurisprudence language and logic that were relevant to consistently rejected the very concept of the study of the major sources of analogy. They deprecated the Islamic law, namely the Quran, the introduction of methods that are alien to Sunnah, ijma’, i.e., the unanimity of the the genuine, Arab Muslim mind. community, and ijtihad, i.e., the Nevertheless, a number of leading scholarly discretion. scholars of usul al-Fiqh, such as Al- Ijtihad, which means the exercise of Ghazali and Al-Razi (240-312AH / 854- scholarly endeavor to generate the right 925AD) opposed this position (cf. rulings in different situations, started during the lifetime of Prophet 3 Sunnah is a general term that refers to the Muhammad (saw), but it was limited in Prophet’s (saw) example and guidance, whether scope and remained within the area of verbal or practical. personal matters, mainly with regard to 4 Their understanding of logic was solely based transactions and commitments (cf. [Al- on the well-known syllogisms of the Greek Dawalibi]). After the Prophet (saw) had which were studied in the – then new – context passed away, his companions produced of Fiqh resulting in selections of appropriate "ways of analogy". Muslim scholars invented the idea of expressing syllogistic methods and their explanations is poetic form as can be found 1 Its inversion (complete induction) would in, e.g.: Al-Akhdary – Al sullam al Munawraq simply imply that every religious ruling has a fil Fiqh (cf. Al-Akhdari. (2014, March 26). In reason. Wikipedia, The Free Encyclopedia. Retrieved 2 saw = sall Allahu 'alay-hi wa-salaam = may 21:36, April 7, 2014, from God pray on him and grant him peace (a http://en.wikipedia.org/w/index.php?title=Al- traditional saying after mentioning his name) Akhdari&oldid=601304682) 3 J.Acad.(N.Y.)4,2:52-87 2014 (36 pages) Abdelwahab et al. 4 [Hammad]), citing evidence from the We need to make certain definitions in Quran and the Sunnah to confirm the order to distinguish between the three validity of analogy as a source of disciplines: language, jurisprudence and rulings on questions that are not directly logic: addressed in the Quran or the Sunnah.5 1. A Logical Question (Qgic) is a syntactic problem that cannot be A. FIQH-METHODOLOGY (USUL) solved except through a mental link Our purpose in this part is to present between the realities of the outside some questions of Fiqh-methodology world and the natural human concepts, (hereafter referred to as Arabic: usul al- which is totally independent of agreed Fiqh)6 and explain their relevance and terminology and belief.