Paradigmatic Treatment of Arabic Morphology 
Martine Smets 
Cognitive and Computing Sciences 
University of Sussex, Brighton BN1 9HQ, UK 
martines@cogs.susx.ac.uk 
Abstract 
This paper 1 presents a language to express 
morphological processes, concatenative or non- 
concatenative. The language allows the def- 
inition of two kinds of paradigms: helping 
paradigms, which define partial morphological 
forms, and main paradigms, which combine two 
or more helping paradigms to define fully spec- 
ified forms. 
1 Introduction 
This paper presents a language to express mor- 
phological processes and shows how that lan- 
guage applies straightforwardly to Arabic mor- 
phology 2. This approach to morphology is di- 
rectly compatible with unification-based frame- 
works in that lexical entries are feature struc- 
tures, and morphological processes are related 
to unification of feature structures. 
This work departs from two-level morphol- 
ogy, which has been at the center of com- 
putational morphology since the implementa- 
tion of URKIMMO (Koskenniemi 1983) and 
was applied to Arabic morphology first by Kay 
(1987), then by Beesley (1989, 1996), Kiraz 
(1994, 1996a) and to Syriac morphology by Ki- 
raz (1996b). Two-level morphology is charac- 
terized by an emphasis on phonological (or or- 
thographic) rules, and has a rudimentary treat- 
ment of morphology itself. 
The language presented in this paper pro- 
poses a declarative approach to morphology 3 
1The research was supported by a grant from the 
Research Board of the University of Illinois at Urbana- 
Champaign. 
2I would like to thank two anonymous reviewers for 
their helpful comments. 
3Only inflectional morphology is discussed in this pa- 
per; but the approach can be extended to derivational 
morphology. 
in which morphological processes are repre- 
sented as paradigms of relations between fea- 
ture structures and orthographic/phonological 
forms. This approach is inspired from work 
done by Calder (1989) who uses paradigms to 
organize morphological information, and string 
equations to handle string operations. 
2 Organization of the Lexicon 
The language described here supports an orga- 
nization of the lexicon into three components: 
feature component, morphological component 
and lexical entries. 
The feature component is a hierarchy of 
types related by monotonic multiple inher- 
itance. 
The morphological component is a set of 
paradigms which relate feature structures 
of the feature component to inflected forms. 
The lexicon of "stems" is a collection of 
roots which are related to inflected forms 
by the morphological component. As is 
customary in accounts of Arabic, roots are 
ordered lists of consonants. They are asso- 
ciated with relevant idiosyncratic informa- 
tion (mainly semantic, for example the par- 
ticular meaning associated with each root). 
3 Description of the Language 
3.1 The Feature Component 
The feature component consists of a hierarchy 
of grammatical objects constrained by relevant 
features, similar to the type hierarchy of Head- 
driven Phrase Structure Grammar (Pollard and 
Sag 1994). This allows to capture generalities 
common to classes of words and avoid redun- 
dancies in the lexicon of roots. For example, 
verbs are constrained to be of category verb. 
58 
(2) 
H-P mel-perf 5 \]\] 
perf active: Vt = a V2 = a; 
..-, v, :,., v, : i; 
Lperf passive R IX: l 
and to belong to one of ten forms or binyanim. 4 
The first binyan carries the meaning of the 
root and is unmarked morphologically, while 
other binyanim bring modification to the mean- 
ing and to the pattern of vowels and conso- 
nants (though the modification in meaning is 
not systematic and not always predictable: see 
Me Carthy 1981). 
Verbs are also characterized by different vowel 
melodies which vary in function of aspect and 
voice: a verb can be in the perfective, imper- 
fective or participle aspect, and in the active or 
passive voice. 
Additionally, verbs carry affixes which vary in 
function of person, number and gender. All such 
information which is predictable is organized in 
the feature component. 
Thus, for example, the class verb is organized 
along two dimensions, template and melody; the 
class template has ten subclasses, one for each 
of the binyaxtim; the class melody is organized 
along two dimensions, aspect and voice, which 
have themselves subclasses. Classes of the hier- 
archy define appropriate constraints in a mono- 
tonic fashion. 
Lexical items inherit predictable informa- 
tion either directly (appartenance to a specific 
class is stated in the lexical entry) or through 
the morphological component (the lexical entry 
specifies to which paradigm a lexeme belongs). 
3.2 Morphological Component 
The morphological component is a set of 
paradigms 6. There are two kinds of paradigms: 
4Mc Carthy (1981) distinguishes 15 forms, but for the 
purposes of this paper, I will consider only the first ten 
ones, which are the productive forms. 
SActually, there are three different melodies for the 
perfective aspect of verbs of the first form (a a, a i and 
a u), but only one of the melodies is given here, as an 
illustration of helping paradigms. 
6The notion of paradigm defined here is closely re- 
lated to the traditional paradigm: paradigms are sets of 
words related to the leading form which is the conven- 
tional representation of the lexeme; words are considered 
main paradigms, which specify fully inflected 
forms, and helping paradigms, which introduce 
partially specified forms. The latter introduce 
information specific to particular morphological 
relations, and this information is used by main 
paradigms to define fully inflected word forms. 
The fact that helping paradigms can express 
information independently of a particular word 
form a/lows that information to be inherited in 
distinct environments, and to combine with in- 
formation from other helping paradigms. Help- 
ing paradigms can then be seen as capturing 
generalizations about morphological relations, 
and main paradigms as expressing specific mor- 
phological forms. 
As for the interface between syntax and mor- 
phology, each entry of a helping paradigm as- 
sociates relevant features to the appropriate 
phonological realization through references to 
types of the sort hierarchy: the name or label of 
each entry of a helping paradigms directly refers 
to class(es) in the type hierarchy. 
3.2.1 Helping Paradigms 
Helping paradigms are sets of pairs (F,S), 
where S is a string specification and F a fea- 
ture structure associated with the string speci- 
fication. The string specification is a partial de- 
scription of string which may contain variables 
(Calder 1989). The feature structure is inher- 
ited from types in the feature component. Thus, 
each helping paradigm is a subset of the Carte- 
sian product of the set of feature structures con- 
sistent with the type hierarchy, and the set of 
strings of the language. 
Syntax of Helping Paradigms. Helping 
paradigms have the concrete syntax in (1): 
H-P Name 
(I) PHON String of characters & 
{Type labels: variable instantiation} 
as wholes, and affixes do not have any meaning indepen- 
dently of a root (Matthews 1991). 
59 
(3) 
"H-P mel-imperf 
\[PHON \[V1, (C,Va*)*, Va,C\]\] & 
"imperf active n I: Vt = a V2 = nil Va = i; 
active rl {II, III, IV}: V1 = u Va = a V3 = i; imperf 
imperf active I"1_ { V, VI}: V1 = a V2 = a Va = a; 
imperf active N { VII, VIII, IX, X}: V1 = a V2 = a V3 = i; 
imperf passive I'i I: Vt = u V2 = nil V3 = a; 
imperfpassive NII, IlI ... VIlI, X: V1 = u V2 = a V3 = a; 
imperf passive n IX: ± 
The name of helping paradigms is followed 
by the phonology, 7 a partial description of a 
string, s The curly brackets denote a set of 
paradigm entries, and Type Labels refers to 
types in the feature component. 
Examples of Helping Paradigms. Exam- 
ples of helping paradigms are given in (2) and 
(3): these are two of the melody paradigms. 
As said earlier, aspect and voice in Arabic are 
expressed through the choice of a particular 
melody: jalas is the perfective active of the verb 
to sit down/, while ajlis is the imperfective ac- 
tive of the same verb. The root consonants 
are similar, but the melody differentiates per- 
fective from imperfective. This is expressed by 
defining melody paradigms which specify which 
melody is associated with which features; the 
melody is intertwined with an abstract root in 
the paradigm. 
Capital letters in the phonology stand for 
variables: C is any consonant, V any vowel; 9 
lower case letters are constants. 
The symbol n means unification, while the 
symbol & following the phonology means that 
the phonology feature is distributively associ- 
ated with each of the entries (there are as many 
specializations of the phonology as there are en- 
tries). 
The value nil means that this position in the 
string is empty; during unification, a variable 
unifying with nil is removed from the pattern. 
rPhonology means the concrete representation of a 
string, the orthography or the phonology. 
Sin the helping paradigms which define vowel melody, 
the phonologies are actually regular expressions (where * 
means as usual zero or more occurences of a character). 
9If two variables of the same type bear the same in- 
dex, it means that they stand for the same constant. 
Finally, a paradigm entry specified as 2. is un- 
defined. 
Variables of the phonology are instantiated 
in the paradigm entries, according to syntactic 
features: the first entry of the paradigm called 
mel-imperf specifies the value of the vowels in 
the pattern \[ 1/'1, (6, V2 *) *, V3, C \] , for the im- 
perfective active of verbs belonging to the first 
form. 
The label preceding the colon, active n I, 
refers to names of classes in the feature com- 
ponent, so that the constraints defined in these 
classes are inherited by the partial form speci- 
fied by this paradigm entry. 
Sometimes, the label contains a disjunc- 
tion: for example in the paradigm mel- 
irnperf, the label of the second entry is 
imperf active n {II, III, IP~; the disjunction 
{II, III, IY} means that the melody character- 
izing this paradigm entry is associated with any 
of these derived forms (II, III or IV) in the im- 
perfective active. 
The helping paradigms in (2) and (3) only 
partially specify the phonology and features of 
Arabic verbs: the melody has to be correctly 
intertwined with a particular pattern of conso- 
nants TM. The pattern for verbs in the perfective 
aspect is defined in helping paradigm (4). 
The template of triliteral verbs in the per- 
fective aspect is given in the PHON attribute 
of the paradigm perf-temp: \[P, C1,X, Cz, Y, C3 \]. 
The value of the consonants 6"I, C2 and Ca is 
determined by particular lexical entries, while 
entries of the paradigm specify what kind of ma- 
1°Verbs are also inflected for person, number and gen- 
der. This can be readily expressed by defining more help- 
ing paradigms. 
60 
(4) 
H-P perf-temp 
"PHON \[P, CI, X, C2, Y,C3\]\] & 
"I:P= niIX=V1 Y=V2; 
II: P = nil X = \[V1,C2\] Y = V2; 
III: P = nil X = \[Vx,V1\] Y = V2; 
IV: P = \[h,V1\] X = nil Y = V2; 
V: P = \[t,Vx\] X = \[V1,C2\] Y = V=; 
YI: P = \[t,V1\] X = \[VI,V1\] Y = V2; 
VII: P = n X = VI Y = V2; 
VIII: P = nil X = \[t,V1\] Y = V2; 
IX: P = nil X = nil Y = \[V,I,C3,V2\]; 
IV: P = \[s,t,V1\] X = nil Y = V2; 
terial comes in between those root consonants: 
for form V, the prefix is made of the consonant 
t and a vowel (whose value is determined by 
a melody paradigm); after the first consonant, 
there is a vowel (the same as the one of the pre- 
fix), and the second consonant is duplicated; fi- 
nally, the third consonant is preceded by a vowel 
(which can be different from the first one). Each 
entry partially specifies the general pattern, and 
associates the resulting string with a label cor- 
responding to a class of the feature component. 
Again, the resulting entries are partial de- 
scriptions of strings associated with partial syn- 
tactic/semantic characterisations, and these de- 
scriptions of strings have to be combined with 
other partial descriptions of strings in order 
to yield fully specified verbs. This is the 
task of main paradigms. Before turning to 
main paradigms, a last characteristic of helping 
paradigms needs to be presented. 
Inheritance. Helping paradigms can be re- 
lated by monotonic inheritance. Similarities be- 
tween paradigms can thereby be captured, and 
the encoding be more concise. For example, the 
template of verbs in the imperfective differs only 
slightly from the template of verbs in the perfec- 
tive: a vowel is prefixed to the latter. This can 
be expressed very concisely with inheritance (5). 
The paradigm imperf-temp inherits all the infor- 
mation specified in the entries of the paradigm 
per f-temp. 
H-P imperf-lemp: II-P perf-temp\] 
(5) \[\[PHON Iv, P, C,, X, C2, Y,C3I\] J 
Inheritance also provides an elegant way of ex- 
pressing subregularities: for example, if a class 
of verbs is almost completely regular, except for 
a few entries, the entries which are common to 
the regular and the irregular paradigms are ex- 
pressed in one paradigm; both the regular and 
irregular paradigms inherit these entries, and 
specify only entries which are not common to 
both paradigms. 
3.2.2 Main Paradigms 
Main paradigms relate lexemes (lexical entries, 
so in the case of Arabic, consonantal roots) 
to fully specified forms, through reference to 
helping paradigms: which helping paradigms 
are combined together is defined by each main 
paradigm. 
The operation which combines helping 
paradigms together is an extension of Cartesian 
product, denoted by the symbol (X). 
Helping paradigms are sets of pairs 
(PHON, FS> (pairs of phonology and fea- 
ture structure); when two helping paradigms 
are combined together, each pair of the first 
paradigm is unified with each pair of the second 
helping paradigm: the PHON attributes are 
combined together, and the feature structures 
are combined together, resulting in a new pair 
(PHON, FS) if unification succeeds. If the 
values of some feature are not compatible, 
unification fails, and that particular pair is not 
returned11. 
11The way paradigm entries combine is reminiscent of 
Kay (1984) who mentions unification of patterns (which 
constrain the order in which syntactic constituents must 
appear) alongside unification of other types of features. 
61 
(7) M-P ver5-3 (\[G,C2,C3 \],FS): FS \[l \[H-P mel-perf 
FS \[3 \[ H-P mel-imperf 
(x) H-Pperf-temp(PHON \[P,C1,X,C2,Y,C3\])\]; 
(x) H-P imperf-temp (PHON \[V,P,C~,X,C2,Y,C3\]) \]; 
Syntax of Main Paradigms. Main 
paradigms have the syntax in (6): 
(6) M-P Name(Phon,FS): FS n {(H-P, (x) 
H-P2 (x) ...), (H-P3 (x) H-P4 (x)...), ...} 
In (6), Name is the name of the paradigm, 
and its argument is a lexical entry, which has 
two components, a phonology and a feature 
structure. The feature structure of the lexical 
entry is distributively unified with the elements 
resulting from the combination of the helping 
paradigms. 
Thus, if an entry of a main paradigm refers to 
two helping paradigms, H-P1 and H-P2, each 
of the entries of H-P1 is unified with each of 
the entries of H-P2: 
H-Pa = {(Fa, Pa), (F2, P2), ..-, (Fk, Pk)}. 
H-P2 = {(F'x, P'I), (F'2, P'2), ..., (F'k, P'k)}. 
H-P1 (x) H-P2 = {(Fa, P1), ..-, (Fk, Pk)} (x) 
{(F'I, P'I), ..., (F'i, P'i)} = 
{(F1 n F'I, P, I"1 P'I), ..., (Fk \[3 F'j, Pk N P'j)} 
The result is a new paradigm, a set of 
pairs (PHON, FS), but this time, the phonol- 
ogy does not contain any more variables, and 
the feature structure of the lexical entry is 
unified with the second member of each pair. 
To illustrate, the main paradigm in (7) com- 
bines the helping paradigms defined in (2), (3), 
(4) and (5). The first entry of (7) combines the 
perf-temp helping paradigm with the mel-perf 
helping paradigm so that each entry of the first 
helping paradigm tries to unify with each entry 
of the second paradigm. For example, the third 
entry of the perf-temp paradigm unifies with 
the first entry of the meI-perf paradigm: 
PHON \[\[C1,Va,Vx,C2,V2,C3\] n \[(C,a*)*,a,C*\]\] 
& \[III n perf active n {II, III, IV}\] 
The PHON values are unified by string unifi- 
cation (Calder 1989), the feature structures by 
standard unification of features. The form III 
unifies with the disjunction {II, III, IV} because 
III belongs to the disjunction. The result of 
unification is given in (8),with the class names 
expanded in feature structures (in HPSG style). 
(8) 
PHON 
HEAD 
CONT 
Cl,a,a,C2,a,C3\] 
"verb 
ASPECT imperfect 
VOICE active 
FORM III 
This is not a complete characterization of an 
Arabic verb of the third form in the imperfec- 
tire active; it is just an illustration of how par- 
tial descriptions get combined to yield complete 
descriptions. 
String Unification. String unification is the 
unification of two partial descriptions of strings 
which represent the same object. As shown by 
Siekmann (Calder 1989), string unification is 
decidable and has a finite number of substitu- 
tions if repeated variables are only permitted on 
one side of the equation. An example of string 
equation with the variable assignments result- 
ing from string unification is given in (9). 
(9) jVVlWs = RaaSaT 
RIj Via S/l W/a T/s 
String unification is a powerful tool which al- 
lows other kinds of morphological relations to 
be specified, besides concatenation: words are 
defined as lists of elements, which can be par- 
tial strings or individual characters. Some el- 
ements of the list are variables, which can be 
located in any position of the list representing 
the word, and get specified through unification 
with a complementary list. The ability to iso- 
late particular positions in the word, together 
with the ability to define in helping paradigms 
specific substrings, allows the description of any 
type of morphological relation. 
3.3 The Lexicon of Roots 
Lexical entries are tuples (P, F, M) where P is 
the phonology (a consonantal root, as is cus- 
tomary in Arabic dictionaries), F the feature 
62 
structure and M, the morphological informa- 
tion. The morphological information is the 
name of the main paradigm(s) to which the en- 
try belongs. 
The feature inventory of lexical entries is re- 
duced, and contains only features that cannot 
be inferred from morphological processes rele- 
vant for the entries (typically, semantic infor- 
mation). 
4 Comparison with other 
Frameworks 
4.1 Calder's Paradigmatic Morphology 
The approach described in this paper is di- 
rectly inspired by Calder's paradigmatic ap- 
proach (1989); however, there are major differ- 
ences between the two approaches. 
First, lexical rules constitute the interface 
between syntax and morphology, in Calder's 
approach, while there are no lexical rules in 
the present framework: lexical entries are not 
specified for features predictable from the mor- 
phology, and these are inherited from the fea- 
ture component through specification of types 
in paradigm entries. 
Second, there is no definition of partial spec- 
ification of strings, in Calder (1989), while 
the distinction between helping and main 
paradigms is one of the main features of the 
present approach: it allows to define morphemes 
independently of any specific root, and thereby 
to capture generalizations about morphemes. 
Thus, in the case of Arabic, both the melody 
and the pattern of consonants are defined inde- 
pendently of a root in helping paradigms, while 
in Calder's approach, one has to be arbitrarily 
chosen as basic (as belonging to the root), and 
regularities about that morpheme are lost. 
4.2 Two-level Morphology 
The most successful approach to morphology 
in computational linguistics has been the two- 
level approach started by Koskenniemi (1983). 
Although particularly suited to concatenative 
morphology, this approach has been extended to 
other types of morphologies, and more precisely 
to templatic morphology first by Kay (1987), 
then by Beesley (1991,1996) and Kiraz (1994, 
1996) among others. But even though two-level 
systems are successful in practice, they suffer 
from a number of shortcomings: they are not 
really morphological systems, but phonological 
systems, as theyfocus on the phonology (or or- 
thography) of words, and not on the morphol- 
ogy; morphotactics is usually implemented us- 
ing continuation lexicons 12 (which implies that 
bound morphemes are lexical entries like stems, 
a disputable assumption); it assumes a linear 
view of phonology, which has been shown since 
the late seventies to be inadequate for the de- 
scription of natural language phonology (Gold- 
smith 1990). Also, since this approach to mor- 
phology is particularly suited to concatenative 
morphology, new systems have to be built in or- 
der to account for non-concatenative languages 
(with the exception, maybe, of Beesley's sys- 
tem which can reuse the runtime code used for 
other languages; but compilation necessitates 
new code specific to Arabic). 
I will not try to argue that the framework 
I advocate will produce better results in terms 
of speed and efficiency: the advantages of fi- 
nite state techniques in that respect have been 
shown countless times. But there are other as- 
pects to consider, besides efficiency: type of 
linguistic analysis allowed by the framework; 
whether different types of morphological pro- 
cesses can be accounted for; interface with other 
components of an NLP system (such as a syn- 
tactic parser), since morphological analysis is 
usually not an end in itself. 
The language presented in this paper is 
declarative: paradigms relate partial strings 
to relevant features, and richer descriptions of 
strings derive from the combination of two or 
more helping paradigms. The ability to define 
partial strings in isolation, and then to combine 
several partial descriptions of strings through 
unification entails that this framework is not 
biased towards a specific type of morphological 
process. 
Also, this approach to morphology is similar 
to and therefore can readily interface with a syn- 
tactic theory like HPSG, which is used widely 
in computational linguistics. 
Finally, this approach does not restrict the 
grammar writer to the framework of linear 
phonology, and allows for the testing of a cer- 
tain type of morphological theories, which claim 
that bound morphemes do not exist as lexicon 
l~There are a number of exceptions, Bear (1986), 
Ritchie et al. (1992), Kiraz (1996). 
63 
entries, but exist only in morphological relations 
(and more particularly the Word and Paradigm 
approaches (Matthew 1991, Anderson 1992, By- 
bee 1985 and many others)). 
4.3 DATR 
There have been other approaches to morphol- 
ogy than the two-level approach in computa- 
tional linguistics; Gazdar and Evans have de- 
veloped DATR (1996), a knowledge represen- 
tation language, which has been used to write 
fragments of the morphology of a number of 
languages, among them Arabic (Gibbons 1990, 
Cahill 1990). But as is the case with other ap- 
proaches, DATR is more suited to express con- 
catenative processes than other types of mor- 
phological processes: Cahill shows that DATR 
in itself cannot account for non linear morphol- 
ogy, and she creates a new module, MOLLUSC, 
to use in conjunction with DATR, whose pur- 
pose is to account for the phonology of morpho- 
logical processes. 
5 Future Work 
This language has not been implemented yet, 
and implementation is the next goal. The oper- 
ations that the language supports are well de- 
fined and well known: they are monotonic in- 
herltance, unification of feature structures and 
string unification. Inheritance (monotonic and 
non-monotonic) is a feature of object-oriented 
programming languages, and both kinds of uni- 
fication have been extensively used, unifica- 
tion of feature structures in the NLP commu- 
nity, string unification in the field of automatic 
theorem proving (Calder 1989); thus we can 
hope that implementation will be straightfor- 
ward and results acceptable in terms of effi- 
ciency. 

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