A novel method to automatically pass hukm on Hadith

Transcription

1 A novel method to automatcally pass hum on Hadth Aql M. Azm Department of Computer Scence Kng Saud Unversty Ryadh, Saud Araba Amjad M. AlOfadly Department of Computer Scence Imam Mohammad bn Saud Islamc Unversty Ryadh, Saud Araba Abstract The Holy Qur an ordered the Muslms to follow the example of the Prophet Muhammad (PBUH) and so from the very begnnng the Companons concerned themselves wth followng the Sunna (conduct or custom) of the Prophet, whch was emboded n Hadths narratng hs words and deeds. The actual text of the Hadth s nown as the matn whch records the Prophet's acts or sayngs. For the matn to be recognzed as authentc, t needs to have attached to t the lst of people who were transmtters of the matn. The snad chronologcally lsts the narrators nvolved n transmttng the hadth all the way tll t was recorded. Bascally the hadth scholars grade the Hadth based on the strength of the transmsson chan, and s graded usng terms such as sahh (the most relable), hasan (acceptable) etc. In ths paper we propose a novel method that s not machne learnng based to grade the Hadth. Our determnstc scheme maes use of heurstcs and nformaton readly avalable n narrator s bographc data. We tested the system on close to 3000 Hadths from Sahh of Buhar and Sunan al-trmz achevng a success rate of over 99% and 94% respectvely. Keywords Hadth gradng; Islamc nowledge; Algorthm. I. INTRODUCTION Hadths are oral tradtons relatng to the words and deeds of Prophet Muhammad PBUH. The tradtonal Muslm schools of jursprudence regard Hadth as an mportant tool for understandng the Qur an and n all matters relatng to jursprudence. The sanad (سند) or ts synonymous term snad Hadth. are the two man elements of a (المتن) and matn (إسناد) The matn s the actual wordng of the Hadth. Informaton regardng the route by whch a matn has been reached s called sanad. The snad conssts of a chronologcal lst of the narrators, each mentonng the one from whom they heard the Hadth all the way to the prme narrator of the matn followed by the matn tself. Many Orentalsts nsst that Hadths are documents orgnated long after Prophet Muhammd s death, most lely n the second or even thrd century of Hjra. To ths we have the wors of [5], [6] and other Muslm scholars that proved logcally that the Orentalst stand was more mred by poltcal rather than academc honesty. It s wdely beleved that the snad have started around (35H/655CE) durng the ftna followng the demse of the thrd calph, Uthman. Unle Ths wor was funded by Research Center of the College of Computer & Informaton Scences (CCIS) at Kng Saud Unversty under grant number RC-2226 for whch the authors are thanful. the Qur an whch s the unadulterated word of God, the Hadth corpus s huge and represents an entre spectrum of texts whose authentcty ranges between ndsputable to poor. The Hadths were classfed manly on the bass of the qualty and the strength of the snad. For a hadth scholar there are several factors that contrbute to the overall gradng of a Hadth. Hgh on ther lst s the transmsson chan, whch must be unbroen. Next are the ndvdual narrators nvolved n transmttng the Hadth. Also the transmtter must be strctly accurate n reproducng precsely what he had personally acqured from those from whom he transmts [3]. Usually a hadth scholar may spend days consultng narrator s bographc nformaton researchng a sngle Hadth just to valdate the contnuty of the transmsson chan. In wae of ths the Muslms establshed brand new scences, lm al-rjal, lterally meanng nowledge of men, to deal wth hadth crtcsm. For more detals on the subject the reader s advsed to consult [4]. There are many boos whch has large corpus of compled Hadths. Among them are Sahh of Buhar ( البخاري,(صحيح and Sahh of Muslm ( مسلم (صحيح and others. Yet there are other large corpuses, e.g. Sunan of al-trmz ( الترمذي,(سنن Sunan of,(سنن أبن ماجة ( Majah Sunan of Ibn,(سنن أبو داود ( Dawud Abu Sunan of al-nasa ( النسائي (سنن and many others. Wth the advent of the computer systems many people have attempted to record these boos to aval them for consumers n a dgtal form. There s no doubt, searchng these boos have become a clc of a button tas and people are now capable of performng some queres n few seconds that were mpossble thng to do n such a short of tme. There are however some lmtatons, these eboos contan the orgnal text boos contents wthout ntellgence. People can t perform smart queres on them, nferrng some nformaton; n our case for example you can t as the computer to grade (حكم) a Hadth unless of course t was hardwred. For Hadth scholars all the Hadths n the Sahhs of Buhar and Muslm are all consder sahh :صحيح) the most relable). The story s dfferent for the other collecton. They may contan Hadths whch are sahh as well as da f :ضعيف) wea) and many other classfcatons n between. Gradng the Hadth s a laborous manual tas, and hadth scholars are nown to spend ther entre lfe worng on gradng the Hadth. In ths paper we report on a novel algorthm that wll grade the Hadth. The scheme s amazngly smple and t does not requre any nd of machne learnng. 8

2 The only thng we need s nformaton that s avalable n the narrator s bographc boos. We truly beleve that computer can never replace professonal human judgment, and so even though our method s able to pass a judgment (حكم) on a Hadth wth very hgh accuracy, t s not ntended to replace the tradtonal hadth scholars but rather a tool that wll help them n ther tas. II. A PASSING LOOK AT HADITH There are many aspects to the scence of hadth; one of them s the snad whch mpacts the classfcaton of the Hadth: (متواتر) mutawatr, and (آحاد) ahaad. In the former we have a large number of narrators, a nd of many-many relaton; whle n ahaad t s more or less a one-one relaton between the narrators. In a mutawatr hadth the sheer number of narrators maes t nconcevable for them to agree to le,.e. fabrcate a hadth matn. Hadth cover every concevable aspect of lfe and typcally they range n sze from few lnes to few hundred lnes wth the majorty beng fve or sx lnes long. Consder the sample Hadth, حدثنا عائشة قتيبة بن سعيد رضي هللا عنها حدثنا Ths s a smple Hadth from Sahh of Muslm wth a sngle chan of narrators. We can draw a dagram showng the flow of nformaton as: Qutayba bn Sa d Lath Hsham bn Urwa hs father Asha Hamza bn Amr al-aslam. Here the denote narrated from. Based on ths we can say that Hamza bn Amr al-aslam s the prme narrator (the one who heard/saw the Prophet), and Qutayba bn Sa d s the teacher/sheh whom Imam Muslm (the compler of ths collecton) learned ths partcular Hadth from. When complng Hadth collectons, some hadth scholars ngenously combned several snad chans when they all shared an almost dentcal matn. The scholars devsed a conventon of usng the letter (ح) to mar the begnnng of a new snad. The followng example from Sahh of Muslm llustrates ths pont (we braceted the narrator names and mared them usng superscrpted Roman letters), عن ليث هشام بن عروة عن أنها قالت سأل حمزة بن عمرو األسلمي عن أبيه رسول هللا صلى هللا عليه وسلم عن الصيام في السفر فقال إن شئت فصم وإن شئت فأفطر ]صحيح مسلم وحدثني كتاب الصيام/ 7 [. ]حرملة بن يحيى التجيبي[ a أخبرنا ]ابن وهب[ b أخبرني أنه سمع عن ]أبي سلمة بن عبدالرحمن[ e عن ]ابن شهاب[ d ]يونس[ c تقول: سئل رسول هللا... ]عائشة[ f h و]أبو بكر بن أبي شيبة[ g و]سعيد بن منصور[ حدثنا ]يحيى بن يحيى[ l ح وحدثني كلهم عن ]ابن عيينة[ j و]زهير بن حرب[ و]عمرو الناقد[ o n عن ]يعقوب بن إبراهيم بن سعد[ m و]عبد بن حميد[ ]حسن الحلواني[ و]عبد بن ح وحدثنا ]إسحق بن إبراهيم[ r عن ]صالح[ q حدثنا ]أبي[ p v u كلهم عن ]الزهري[ t أخبرنا ]معمر[ s قاال أخبرنا ]عبد الرزاق[ حميد[ بهذا اإلسناد... Fg.. s the full narraton tree of the second Hadth. For those famlar wth the hadth lterature wll understand that both Hadths are related. Towards the end of the second Hadth t says ( اإلسناد (بهذا referrng to the earler snad. The queston of where do both snad chans meet? Ths s determned by a.(الزهري) narrator common to both Hadths, who n our case s He s also nown by the name ( شهاب الزهري,(ابن and roncally.(ابن شهاب) n the frst Hadth he s mentoned as m n s r o t j h g p Fg.. Full narraton tree of a Hadth n Sahh of Muslm. The letters desgnate the narrators. The rghtmost node s the prme narrator of the hadth. Each path from the leaf (leftmost nodes) to the prme narrator consttutes a sngle snad. Ths Hadth has 9 snad chans. III. RELATED WORKS Ths s a crucal subject touchng each and every Muslm s lelhood, but as most of the classcally traned hadth scholars argue that computers can never replace ntellectual judgment. And ths s why there s scarcty n wors related to ths subject. Aldhaln et al [7] devsed a machne learnng based scheme that classfed hadth as beng sahh, hasan, da f, and maudo :موضوع) fae). The classfcaton s based on the characterstcs of the narrators n the snad chan. The rules were extracted usng C4.5 algorthm. That algorthm s used to generate a decson tree from a set of tranng data, whch n turn s used for the classfcaton purpose. Two dfferent algorthms were used for classfcaton: Decson Tree (DT) classfer and Naïve Bayes (NB) classfer. The authors collected 999 Hadths dvdng t nto two datasets: 75% for tranng and 25% for testng. They reported a success rate of 96.69% when usng NB classfer, and 97.59% when usng DT classfer. Razzo [5] suggested usng fuzzy logc to ran/grade the ndvdual narrators. The problem wth the suggeston was the system requred so many nput parameters wth some of the nformaton are hard to get by. In [2][7] the authors used expert system to mplement a fuzzy system to determne the grade of the Hadth. They appled the system on Al-Kaf, a famous Shte hadth boo. It s worth notng that Shte s Hadth collecton s nowhere close to what the Sunn s have nor an ntrcate snad system. Moreover ther narrators ranng system s qute unle the Sunn s, e.g. Shtes dscredt all the Companons except for handful. Next, we lst some of the wors that deals wth the hadth lterature but not to our subject. In [0] the authors devsed a context-free grammar and used t to parse hadth text extractng all the narrators whle eepng trac of how they were connected. Ths was used to automatcally generate a vsual narraton tree. The system was tested on 90 Hadths wth some u l q v e f 9

3 havng extremely complex structure. They acheved a success rate of 87%. In [6] the authors suggested a scheme to vsualze the chan of hadth narrators as an educatonal ad for students learnng the scence of hadth. The paper lacs detal on how the chan tself was constructed. The authors n [3] presented a scheme to show the narraton chan graphcally. They also presented a database structure that suts storng bographcal data. The wor n [] tacles segmentaton of Hadth texts nto sanad and matn usng unsupervsed learnng technque. Interestngly the authors used 95% of a large corpus for teachng and only 5% for testng. Whle [8] developed an algorthm to classfy the Arabc text, and was tested on Hadth wth an objectve of fndng the chapter t belonged to. Ther experments suggest Naïve Bayesan slghtly outperformed the other technques. IV. PRELIMINARIES FOR GRADING A HADITH The Hadth conssts of two dstnct parts: the sanad, whch s a chronologcal lst of narrators who were nvolved n transmttng the Hadth; and the matn, the man text or body of the Hadth. In the mnd of hadth scholars, to accept a Hadth t must satsfy two condtons: () all the narrators n the chan must be (ثقة) trustworthy; and (2) no gaps n the transmsson chan. The trustworthness of a narrator s depended on two crtera: moralty and sound nowledge. The famous scholar, As-Suyut, defned moralty: a Muslm who has reached maturty, s mentally sound, free from causes of obscenty, and abdes by the standards and norms of hs communty [2]. The second crtera, soundness of nowledge s meant to test the lterary accuracy of a narrator. TABLE. The twelve classes of narrators accordng to Ibn Hajar. The lower the ran the better. Rans -6 are consdered as passng mars. Ran Descrpton Sample wordng.(الصحابة) The Companons 2 Narrators wth confrmed exemplary status 3 Those prased wth a sngle adjectve ثقة ( trustworthy Trustworthy and trustworthy wth ;(ثقة.(ثقة حافظ ( memory exceptonal Trustworthy ;(ثقة) steady of.(ثبت) tong and reasonng.(صدوق) 4 Those of slghtly lesser grade. Truthful 5 Of lower ran. Includes those accused of nnovaton (بدع) and t must be explctly lsted. 6 Those wth paltry output and there s nothng nown to dscredt them. 7 Those nvolved n transmsson through more than one channel but have not been assessed. 8 Whose status been gauged by authorty but labeled nadequate. 9 Has not been assessed and has transmtted through sngle channel only. Truthful but wth falterng.(صدوق سيء الحفظ ( memory Here we nclude nnovaton,.(تشيع) e.g. Shtes.(مقبول) Acceptable.(مجهول الحال ( qualty Unnown.(ضعيف) Wea.(مجهول) Unnown.(متروك الحديث ( Abandoned 0 Do not have an assurance. Accused of falsehood..(كذاب) 2 A nown lar The couplng of both crtera and the varyng degree of each crteron wthn a narrator allowed the hadth scholars to create mult-classes/categores a narrator s classfed nto. Ibn Hajar, another famous scholar, grouped narrators nto twelve classes (see Table ) [4]. The frst sx of these classes can be consdered as passng mars. The stress on ranng the narrators necesstated access to the bographes of the transmtters nvolved. For ths the scholars dedcated hundreds of volumes just for bographc nformaton. Followng the narrator s trustworthness we come to the second condton to accept a Hadth. The chan of transmsson must not be broen. We need to confrm that the ndvduals nvolved learned from one another. Suppose we have a hypothetcal chan of three, A B C. If B dd not learn from C, or that A and B never came nto contact, then the chan s obvously defectve. The bographc boos wll note the lst of teacher student par who s nown to have narrated plenty of hadths. But for those wth few hadth to ther credt, ths nformaton wll be hard to confrm and n ths case the hadth scholar wll be suffced f he can prove that the lves of A and B, or B and C suffcently overlap. Ibn Hajar devsed the concept of narrator s generaton الرواة) (طبقات as a mean to solve ths problem. He proposed assgnng a generaton level to each narrator, wth the Companons beng the frst generaton, and al-tab een (التابعين) as the second generaton, and so on. In total Ibn Hajar s scheme has twelve generatons coverng the perod from the days of the Prophet tll approxmately the year 300H, the tme by when all the famous hadth complers, e.g. Imam Buhar, Imam Muslm, etc passed away. So far we are not aware of any wor that actually formulates the exact set of rules used by the classc hadth scholars to pass judgment on Hadth []. V. OUR PROPOSED ALGORITHM A. Our judgment modeled on Sunan al-trmz Our objectve s to devse a system that wll automatcally pass a judgment/grade (حكم) of a gven hadth by formulatng the set of rules as used by the tradtonal hadth scholars. In ths study we pced Sunan al-trmz as a model. When complng hs collecton, Imam al-trmz passed judgment on many Hadths whch he usually reported at the end of the Hadth. For example, حدثنا قتيبة بن سعيد حدثنا أبو عوانة عن سماك بن حرب ح وحدثنا هناد حدثنا وكيع عن إسرائيل عن سماك عن مصعب بن سعد عن ابن عمر عن النبي صلى هللا عليه وسلم قال: ال تقبل صالة بغير طهور وال صدقة من غلول. قال هناد في حديثه إال بطهور. قال أبو عيس هذا الحديث أصح شيء في هذا الباب وأحسن ]جامع الترمذي الطهارة[. We underlned the judgment of the Hadth. In judgng the Hadth, Imam al-trmz used many terms. Bascally he 20

4 classfed a Hadth n three broad terms: sahh, hasan, and da f. Whle descrbng a sahh hadth, Imam al-trmz used,(حسن صحيح غريب (,(صحيح حسن (,(حسن صحيح (,(صحيح) terms: the etc. For da f we found that he used the,(حسن غريب صحيح ( terms:,(غريب حسن (,(حسن غريب (,(غريب),(ضعيف) (منكر) etc. Only n hasan he used term.(حسن) See [9] for detals. Narrators bographc DB ( ) Raw Hadth Extract transmsson chans Identfy narrators n chans Pass hum on Hadths Fg. 2. A basc overvew of the system. The narrators bographc database s based on Ibn Hajar s Taqrb al-tahzb. Fg. 2. s a rudmentary vew of our proposed system. The nput to the system s plan Hadth texts. Each Hadth n the nput s gven a unque number along wth a mnemonc symbol that dentfes the collecton t came from such as Sahh of ت / 25,م / 32,خ / 5 dentfcaton, Buhar. For example the desgnates (respectvely) Hadth no. 5 n Sahh of Buhar, no. 23 n Sahh of Muslm, and no. 3 n Sunan al-trmz. The frst step s to extract all the transmsson chans. These are saved n the followng format (we assume that narrator_ s the prme narrator): narrator_*narrator_2*.*narrator_n[hadthid]. The Hadth dentfer (HadthID) s appended at the end of each chan to help tell whch Hadth the chan came from. For example, below are some sample chans for the Hadth featured n Fg.. Note that they all have the same HadthID,.e. Hadth. snce they all came from the same,<م / 6326 < عائشة*أبو سلمة بن عبدالرحمن*الزهري*معمر*عبد الرزاق *عبد بن حميد >م/ 6206 < عائشة*أبو سلمة بن عبدالرحمن*الزهري*معمر*عبد الرزاق *إسحق بن إبراهيم >م/ 6206 < عائشة*أبو سلمة بن عبدالرحمن*الزهري*ابن عيينة*عمرو الناقد >م/ 6206 < For convenence, all the narrator names have been normalzed n the chan. Due to Arabc grammatcal rules, narrator names that start wth (أبو) may appear as (أبي) or (أبا) n other places. In our case, the latter two forms have been replaced wth.(أبو) The next step s to dentfy the ndvdual narrators n the chan usng the bographc database (Fg. 2). Ths database has all the essental nformaton extracted from Ibn Hajar s monumental wor Taqrb al-tahzb. Each narrator n the database s gven a unque number based on the prnted edton of Taqrb al-tahzb [4]. Ths number wll be treated as an dentfer for the narrator, e.g. the entry for ( الزهري (اإلمام n Taqrb al-tahzb s, After the dentfcaton of the narrators the frst chan wll be (the numbers nsde the square bracet s narrator dentfer), As we are dealng wth Hadth, a subject vtal to every Muslm, so we must safeguard aganst error at each step. The frst two steps n the process (Fg. 2), the extracton of narraton chan and the dentfcaton of ndvdual narrators n the chan are a complcated method and requre extensve checng and verfcaton. We were lucy to be able to use the data from Prof. al-azam s poneer wor [3], for whch we are thanful. All the data we receved were thoroughly checed and so we do not have to worry about ts accuracy. B. Passng the hum on Hadth Our man am s to devse a smple scheme to classfy the hadth broadly as: sahh, hasan, or da f. The system s modeled on the judgments found n Sunan al-trmz, and t has been tested on large sample of Hadths collected from Sunan al-trmz (excludng those used n modelng) and Sahh of Buhar. The scheme depends on the characterstcs of the people nvolved n transmttng the matn. Ths s acheved by assgnng each narrator some nd of a factor that s based on hs/her characterstcs. Algorthm. s the man algorthm to mae the hum on the hadth. Input: Set of narraton chans: c, c, c, K, c for Hadth T 2 3 m Output: Pass a judgment (حكم) on the hadth Begn for each chan c n T do calculate factor j End 6926 محمد بن مسلم بن عبيد هللا بن شهاب بن عبدهللا بن الحارث بن زهرة بن كالب القرشي الزهري أبوبكر الفقيه الحافظ متفق على جاللته وإتقانه وهو من رؤوس الطبقة الرابعة مات سنة خمس وعشرين وقيل قبل ذلك بسنة أو سنتين. ع. عائشة] 3688 [ *أبو سلمة بن عبدالرحمن] 379 [ *الزهري] 6926 [ *معمر] 6382 [ *عبد الرزاق] 86 [ *عبد بن حميد] 966 [ >م/ 6206 < Let F be the hghest judgment among factors j f ( F < F < 0.846) return da f else f (0.808 F < 0.826) return hasan else return sahh Algorthm. The man scheme that accepts the set of all narraton chans of a hadth and then passes a hum. See the text for an explanaton on how the factors are calculated. 2

5 In Algorthm. there are two parts that need further explanaton. The method used to calculate the factors, and how we defned the range that s used for classfyng the hadth nto one of three classes. For factors, they are calculated as follows. Assume the narraton chan c of a hadth contans the narrators r * r * r * K * r, 2 3 n where r s the prme narrator. In computng the factors we requre two peces of nformaton for every narrator n the chan: the generaton (الطبقة) the narrator belongs to, and hs/her ran (see Secton IV). Both peces of nformaton are accessble from the bographc database whch s extracted from Taqrb al-tahzb. Let gen( r ) and ran( r ) denote the generaton and the ran of narrator r ( n). The factor j s zero f the transmsson chan has dscontnuty (broen), otherwse t s gven by, j æ n ö = (ran( r )) (ran( r )) G - D / 2 ç å n çè ø = where the grade functon Gdepends on the ran of the narrator (see Table 2), and D s a penalty functon. The grade functon s roughly set at G: 3 - ran( ). Table 2. Narrator s ran and the correspondng grade functon G. See Table for further detal on the ran. ran grade G The penalty functon D s used to tae care of nown defcences. Suppose we have a narrator whose memory weaened when he/she aged, so n ths case we deduct 0.2 from hs/her grade to reflect ths defcency. Table 3. lsts some of the defcences as reported n Taqrb al-tahzb and our correspondng penalty. Table 3. Some of the defcency assocated wth narrators (as reported by Taqrb al-tahzb) and the correspondng penalty. The more serous the defcency the larger the penalty. Defcency r Penalty Hs/her memory weaened when he/she got older (ربما يخطئ ( mstae Perhaps he made a Spoe about hm/her wthout argument. 0.3 Accused of nnovaton such as Shte,(تشيع) Jahmyya,(الجهمية) or.(القدر) al-qadr To determne f the transmsson chan s unbroen we must satsfy the next two condtons: () gen( r ) 2; and (2) - gen( r ) - gen( r ) 5. The frst condton nssts that + the prme narrator must be ether a Companon (صحابي) or a Tab ee,(تابعي) whle the second condton maes a bound on the generaton dfference between a student and hs/her teacher. Typcally we expect the generaton of the teacher to be lower than hs student s, however; we came across cases that ths was not true. The most common dfference between the generaton 0.5 of the teacher and hs student s 2 3. Fg. 3. shows two boundary examples for the second condton. [783] بالل بن مرداس generaton 7 [373] عبد األعلى بن عامر الثعلبي [58] إبراهيم بن جرير generaton 3 generaton 6 [2787] شريك generaton 8 Fg. 3. Two examples of narrators that we used for settng the bounds for condton two. In the frst example we have the generaton of the teacher (left of the arrow) s less than hs student s; and n the second case the generaton gap between them s 5. The numbers nsde the square bracet s the narrator dentfer. We used a smple mechansm to defne the border range for each judgment n Algorthm. Gven that the factor FÎ [0, ] we ntally splt the range nto ten equal parts,.e.g , ,, Then we pced 50 Hadths from Sunan al-trmz along wth ther nown judgments. As all these Hadths have a nown pre-judgment t allows us to compare between the orgnal hum (of Imam al-trmz) and the numerc value of the factor F (as obtaned usng our scheme). After that we count how many judgments are located n each range. If a range has many judgments, then t s further dvded nto smaller range. The process s repeated tll we reach ranges whch contan at most the same hum. VI. TESTING AND RESULTS As mentoned earler, our system s modeled on ffty Hadths selected from Sunan al-trmz. To test the system we run the algorthm on some other Hadths from Sunan al- Trmz, we exclude those used n developng our model. We also test the system on Hadths from Sahh of Buhar, a collecton that s nown to contan only sahh Hadths. To clarfy our algorthm we would trace t on some sample Hadths. A. Example Consder the Hadth (not part of the sample used for modellng). For convenence we greyed out the text, حدثنا سويد بن نصر أخبرنا ابن المبارك أخبرنا رشدين بن سعد قال حدثني ابن أنعم عن أبي عثمان أنه حدثه عن أبي هريرة عن رسول هللا صلى هللا عليه وسلم قال: "إن رجلين ممن دخل النار اشتد صياحهما فقال الرب تبارك وتعالى أخرجوهما فلما أخرجا قال لهما ألي شيء اشتد صياحكما قاال فعلنا ذلك لترحمنا قال رحمتي لكما أن تنطلقا فتلقيا أنفسكما حيث كنتما من النار فينطلقان. فيلقي أحدهما نفسه فيجعلها عليه بردا وسالما ويقوم اآلخر فال يلقي نفسه فيقول له الرب تبارك وتعالى: ما منعك أن تلقي نفسك كما ألقى صاحبك فيقول يا رب إني ألرجو أن ال تعيدني فيها بعد ما أخرجتني فيقول له الرب تبارك وتعالى: للك رجاؤك فيدخالن الجنة جميعا برحمة هللا". حديث ضعيف من جامع 9922 الترمذي / المعجم 8- صفة جهنم / ب 78 ح/ 22

6 Ths Hadth has a smple sngle chan of narrators. Table 4. lsts all the nformaton needed to calculate the factor of ths Hadth. Table 4. All the nformaton to calculate the factor of the Hadth. The defcency (f any) s talczed. Note that we too of 0.3 as penalty from the grade of the thrd narrator. Narrator s name Ran (textual) Ran (numerc) Grade Generaton Trustworthy سويد بن نصر Trustworthy, steady ابن المبارك of tong and reasonng Wea, mxed n hs رشدين بن سعد Hadth Wea ابن أنعم Acceptable أبي عثمان Companon 2 أبي هريرة The chan s unbroen, and the factor F= So ths Hadth falls nto the da f (wea) category, whch agrees wth the judgment gven to the Hadth. B. Example 2 Consder the Hadth (agan not part of the sample used for modellng). For convenence the text has been greyed out leavng the narrators n blac, Ths Hadth has also a sngle narraton chan. Table 5. lsts all the data necessary to calculate the factor. Table 5. All the nformaton to calculate the factor of the Hadth. The second narrator has been penalzed by 0.2. Narrator s name علي بن حجر إسمعيل بن عياش Ran (textual) Trustworthy wth exceptonal memory Truthful, mxed n hs Hadth when he got older Ran (numerc) Grade Generaton Trustworthy حبيب بن صالح أبي حي المؤذن الحمصي حدثنا علي بن حجر حدثنا إسمعيل بن عياش حدثني حبيب بن صالح عن يزيد بن شريح عن أبي حي المؤذن الحمصي عن ثوبان عن رسول هللا صلى هللا عليه وسلم قال :" ال يحل المرئ أن ينظر في جوف بيت امرئ حتى يستأذن فإن نظر فقد دخل وال يؤم قوما فيخص نفسه بدعوة دونهم فإن فعل فقد خانهم وال يقوم إلى الصالة وهو حقن " قال أبو عيسى حديث ثوبان حديث حسن ]جامع الترمذي - الصالة[ Acceptable يزيد بن شريح Truthful Companon 2 ثوبان The factor for ths Hadth s F= 0.822, whch places t n the category of hasan. Agan t agrees wth the decson made by Imam al-trmz. C. Evaluaton and results We tested our scheme on 752 Hadths from Sunan al- Trmz, and 280 Hadths from Sahh of Buhar whch s about a thrd of the collecton. The reason for pcng Sahh of Buhar should be obvous; the entre collecton s acnowledged to contan sahh Hadths. We defne two measures to evaluate our system, the Success Rate of the Judgment (SRJ), and the Error Rate of the Judgment (ERJ). These are defned as, SRJ ERJ æncj ö = ç * 00% çènoh ø ænij ö = ç * 00% çènoh ø where NCJ, NIJ, and NoH are: number of correct judgments, number of ncorrect judgments, and the number of Hadths, respectvely. For Sunan al-trmz the results were SRJ = 93.62%, and ERJ = 6.38%. Whle for Sahh of Buhar these were 99.60% and 0.40% respectvely. VII. CONCLUSION AND FUTURE WORK In ths wor we proposed a system that judges a Hadth to one of three categores: sahh, hasan, and da f. We devsed a smple scheme and modeled the rules usng 50 sample Hadths from Sunan al-trmz. We beleve our smple calculaton based scheme s smple enough for people to follow wth all the ngredents requred for judgng a Hadth are extracted from Ibn Hajar s Taqrb al-tahzb. The system was appled on over 2900 Hadths extracted from Sunan al-trmz and Sahh of Buhar achevng a success rate of 94% for Sunan al-trmz and over 99% for Sahh of Buhar. We would le to extend the testng to nclude other Hadths collectons as well. ACKNOWLEDGMENT The authors would le to greatly acnowledge the help and support of hadth scholar, Prof. Emertus M.M. al-azam who dd not hestate to share hs huge data. REFERENCES [] M.M. al-azam, Manhajn Naqd nd al-muhaddthn (n Arabc), 3rd ed, Ryadh, 990. [2] M.M. al-azam, Hstory of the Qur anc Text from revelaton to complaton, 2nd ed, Ryadh, Chapter 3,

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