A Matrix Representation Of The Inflectional Forms Of Arabic Words: A Study Of Co-Occurrence Patterns

s e q u e n c e of t h r ee l e t t e r s , called a t r i l i t e ra l root . A p r o p o s e d "Matrix" method fo r the r e p r e s e n t a t i o n of the inf lect ional p a r a d i g m s of Arabic words is p r e s e n t e d . This r e p r e s e n t a t i o n r e s u l t s in a c lass i f ica t ion of Arabic w o r d s into a t ree s t r u c t u r e ( F i g ( l ) ) whose leaves r e p r e s e n t u n i q u e conjuga t iona l or de r iva t iona l p a r a d i g m s , each r e p r e s e n t e d in the p r o p o s e d "Matrix" form. A study of about 2,500 stems from a high frequency Arabic wordList due to Landau has revealed a systematic set of co-occurrence patterns for the encLitic pronouns of Arabic verbs and for the possessive pronouns attached to Arabic nouns. Each co-occurrence pattern represents a subcategorization frame that reflects the underlying semantic relationship. The key f e a t u r e tha t d i s t i n g u i s h e s these semant ic p a t t e r n s has been o b s e r v e d to be w h e t h e r the a t t a ched s u f f i x e s re la te to the animate or inanimate . In some cases fo r v e r b s , the n u m b e r of the sub j ec t is also a s ign i f i can t f e a t u r e . These semant ic f e a t u r e s also e x t e n d to n o n a t t a c h e d s u b j e c t s and objec ts ( fo r v e r b s ) and to p o s s e s s i v e noun complements ( f o r n o u n s ) . T h e r e f o r e the semant ic c l a s ses p r e s e n t e d in this p a p e r also a s s i s t in syntactic/semantic analysis. The first application that Was developed, based upon the proposed representaion is a stem-based Arabic morphological ans/yser, from which a spell checker (on a PS/2 microcomputer) emerged as a by-product. Currently, the system is being used to interact with an Arabic syntactic parser and there are plans to use it in a machine assisted translation system. i . INTRODUCTION Over the p a s t few y e a r s t he r e has been a marked i nc r ea se in the use of c o m p u t e r s in the Arabic s p e a k i n g c o u n t r i e s . Many app l ica t ions p r o g r a m s in Arabic have been deve loped , b u t the field of compu ta t i ons / l ingu i s t i c s is r e l a t ive ly new in Arabic and p r e s e n t s a u n i q u e cha l lenge , due to the h i gh ly inf lec ted n a t u r e of the Arabic l a n g u a g e . In the p r e s e n t work , we have a t t e m p t e d to r e p r e s e n t the morphologica l r u l e s g o v e r n i n g the inf lec t ions of Arabic w o r d s in a compact form which can s impl i fy the p r o c e s s i n g of Arabic words b y c o m p u t e r s and which is i n d e p e n d e n t of the a p a r t i c u l a r appl ica t ion . T h e r e have been o t h e r a t t emp t s to show the con juga t ions of Arab ic v e r b s <2> b u t the t r e a t m e n t does not delve into su f f i c i en t d e p t h and not all enc l i t ics , which a re an e s sen t i a l p a r t of Arabic v e r b s , a re c o n s i d e r e d . Moreover , the t r e a t m e n t in <2> does not e x t e n d to n o u n s . By s t u d y i n g some 2,500 s tems out of a h i g h f r e q u e n c y Arabic word l i s t due to Landau <1>, ce r t a in sy s t ema t i c c o o c c u r r e n c e p a t t e r n s g o v e r n i n g v e r b encl i t ics and n o u n p o s s e s s i v e p r o n o u n s have been o b s e r v e d . These p a t t e r n s are wha t we call "Matr ices" in this p a p e r ; each u n i q u e "Matr ix" r e f l ec t s a d i f f e r e n t semant ic b e h a v i o u r . To summar ize Arab ic m o r p h o l o g y in a n u t s h e l l , a b o u t 80 ~, of Arabic words can be d e r i v e d f rom a For example , i f we c o n s i d e r the root ~ ,~ (K T B) , we can form words s u c h as . l -, .r _..£~ (?aKTuB I wr i t e ) and , ~ (KiTa:B b o o k ) , b y s u b j e c t i n g the root to v a r i o u s " forms" or "moulds" and b y u n d e r g o i n g ce r t a in m o r p h o p h o n e m i c ( and p o s s i b l y also m o r p h o g r a p h e m i c ) c h a n g e s . For a full d i s c u s s i o n of t rad i t iona l Arabic morpho logy see <9> and <10>. In this p a p e r , we shall def ine s u c h an inf lected form to be a "STEM". Thus a stem may contain infixes and certain prefixes which are part of the "mould" but may not contain any suffixes. Suffixes for verbs are subject and object pronouns, while for nouns they are possessive pronouns. One further definition which is used in the proposed representaion is the "Core"; this is simply the inflected form with all prefixes and suffixes stripped off. The core may or may not be a valid word. In compar i son wi th o t h e r work in the a r ea of t radi t ional Arabic m o r p h o l o g y (<3>,<4>), where the c o n c e r n is wi th the ru le s which cause the inf lec ted form to be de r i ved f rom the ROOT, we have s t ud i ed the rules governing the derivation of all possible inflected forms from the STEM, as defined above. 2. THE MATRIX REPRESENTATION Sample "MATRIX PARADIGMS" are shown in Fig(2) for verbs and Fig(3) for nouns. Table(1) gives the keys in English to the columns on the Matrix Paradigms. The inflected form for a given Person/Number~Gender/Mode combination for verbs (obtained from the relevant "row" of the Matrix Paradigm) is constructed by concatenating the prefix, core and both subject and object pronoun column entries. The inflected forms for nouns are sinfilarly c o n s t r u c t e d for a p a r t i c u l a r N u m b e r / G e n d e r / C a s e combinat ion . The various "cells" of the object pronoun columns indicate whether a particular entry is valid (indicated by "U', an Arabic numeral one). Invalid entries are indicated by a " '" , an Arabic zero. It is due to this matrix of ones and zeros that the representation was named the "Matrix Paradigm". 3. TAXONOMY OF ARABIC WORDS F i g ( l ) shows a t ree d iagram r e p r e s e n t i n g the taxonomical c lass i f ica t ion of Arab ic v e r b s and n o u n s . T h e r e a re d i f f e r e n t " levels" in the t ree c o r r e s p o n d to d i f f e r e n t t y p e s of va r i a t i ons of the inf lec ted form from one c lass to a n o t h e r . The f i r s t t ype of va r ia t ion co inc ides more or less wi th the t rad i t iona l c lass i f ica t ion and is r e s p r e s e n t e d at levels 2 and 3 fo r v e r b s and at level 2 fo r n o u n s . Each Matrix Paradigm also reflects two further types of variation, which can be considered separately from one another. The first is the variation in the core with the different rows; this dimension c o r r e s p o n d s , fo r example , to the t rad i t iona l s t u d y of v e r b con juga t ions ( see <2>). I -