Proceedings of the Twenty-First International FLAIRS Conference (2008)
The Categorial Annotation of Coordination in Arabic
Ismaïl Biskri & Boucif Amar Bensaber
Département de Mathématiques et Informatique – Université du Québec à Trois-Rivières
CP 500, Trois-Rivières, (QC) G9A 5H7, Canada
{ismail.biskri ; bensaber}@uqtr.ca
in front of each member of coordination. Correlative
coordination does not seem very current in Arabic, but,
nevertheless, it is not agrammaticale.
Coordination is an explicit or an implicit relation which
links elements of the same sort: sentences, or linguistic
units which have the same function. It is expressed
explicitly by markers (of coordination) which are in fact
conjunctions, such as ‫ و‬wa (and) (In this paper, we
will focus entirely on this marker).
In the scientific literature, several formalization of
coordination was proposed. The syntagmatic models
appeared more promising based on the arguments
advanced by Pollard, Sag, and Beavers for the process
of coordination with ellipses using an HPSG Grammar
(Beavers, Sag, 2004) (Sag, 2003), they do not seem to
yield general rules for treating all types of coordination.
This is why the TCCG was proposed for treating
English coordination (Beavers, 2004). The challenge
facing TCCG is to use certain Categorial Grammars
rules while keeping the HPSG grammar base. The
model of Categorial Grammars in its various versions
offered interesting perspectives but was criticized for
“over-generation” mainly because of type raising rules
and its incapacity to account for certain constructions in
which the elements coordinated are not of comparable
nature or do not fulfill the same function (Sag, 2003),
though we proved in (Biskri, Desclés, 2006) that a
categorial model is able to analyze a coordination of
different categories.
Very few studies were devoted to the correlative
coordination. Some work is, however, listed for English
with the generative current (Sag, 2005; Schwarz, 1999;
Hendriks, 2004) or from the point of view of
translinguistic generalization (Johannessen, 2005;
Zoerner, 1999; De Vries, 2005). We find two diagrams
for the analysis of the correlative coordination: (a) A
symmetrical analysis (Sag, 2003) for which each
member of coordination is introduced by the same
conjunction; (b) An asymmetrical analysis (Johanessen,
2005; Hendriks, 2004) which consists in regarding the
initial conjunction as an adverbial modifier.
Abstract
The model of categorial grammars is a sufficiently flexible
model to give an account of several languages and several
forms of organisation of the linguistic units of these languages
(coordination, subordination, etc). However, the research
tasks were limited almost exclusively to European languages.
A language like Arabic, in spite of the richness of the
tradition of its schools of thought, which go back for several
centuries, remains unexplored by this current. In our article,
we show how the model of Applicative Combinatory
Categorial Grammar can give an account of categorial
annotation of Arabic, in particular of certain forms of Arabic
coordination.
1. Coordination
Let us consider the following statements:
(i) thaâhada ettarafani bi eliîthirafi elmouthabadili wa
bi elimthinaii ân ayi thaharoukathin âskariyathin
‫أي ﺗﺤﺮآﺎت ﻋﺴﻜﺮﻳﺔ‬
‫ﺗﻌﻬﺪ اﻟﻄﺮﻓﺎن ﺑﺎﻻﻋﺘﺮاف اﻟﻤﺘﺒﺎدل وﺑﺎﻻﻣﺘﻨﺎع ﻋﻦ‬
(ii) youkhatibou elibnou abahou bi ihthiramin wa
oumahou bi hananin
‫ﻳﺨﺎﻃﺐ اﻹﺑﻦ أﺑﺎﻩ ﺑﺎﺣﺘﺮام و أﻣﻪ ﺑﺤﻨﺎن‬
(iii) yaakoulou elqirdou elmawza wa eddoubou elâssala
‫ﻳﺄآﻞ اﻟﻘﺮد اﻟﻤﻮز و اﻟﺪب اﻟﻌﺴﻞ‬
(iv) elibnou youkhatibou wa abahou bi ihthiramin wa
oumahou bi hananin
‫اﻹﺑﻦ ﻳﺨﺎﻃﺐ و أﺑﺎﻩ ﺑﺎﺣﺘﺮام و أﻣﻪ ﺑﺤﻨﺎن‬
The statement (i) represents the coordination of two
members of different nature but fulfill the same
function. The statements (ii) and (iii) represent two
different cases of coordination with ellipse. In both
cases the verb is elided and two non-constituents are
coordinated. In the first case (ii) the non-constituents
[abahou bi ihthiramin] and [oumahou bi hananin] are
sequences of an object (abahou and oumahou) followed
by a backward modifier of an intransitive verb (bi
ihthiramin and bi hananin). In the case of (iii) the nonconstituents [elqirdou elmawza] and [eddoubou
elâssala] are sequences of a subject followed by an
object. The statement (iv) represents the case of a
correlative coordination where the conjunction appears
Copyright © 2008, Association for the Advancement of Artificial
Intelligence (www.aaai.org). All rights reserved.
462
Application rules :
2. Categorial analysis
[X/Y : u1] - [Y : u2]
-------------------------->;
[X : (u1 u2)]
The model of Applicative and Combinatory Categorial
Grammar (ACCG) (Biskri, Desclés, 1997) as most of
categorial models (Dowty, 2000 ; Morrill, 1994 ;
Moorgat, 1997 ; Steedman, 2000 ; Baldridge, Kruijff,
2003), assigns syntactical categories to each linguistic
unit in order to express its function. The basic
categories N and S are assigned respectively to noun
phrases and sentences. The orientated categories,
developed from basic types by means of the two
operators of types construction “/” and “\”, are assigned
to the linguistic units which function like operators. For
example, the category (S\N)/N is assigned to transitive
verbs which are seen as operators with two operands,
the first being the object of type N positioned to its
right whereas the second being the subject of type N
positioned to its left. In our paper, a linguistic unit u
with the type X will be noted by [X : u].
According to the postulate that the representation of the
language is with three levels (Desclés, 1996) (Desclés,
1990) (Shaumyan, 1998): (i) the morphs-syntactical
level ; (ii) the predicative level ; (iii) The cognitive
level, the ACCG makes it possible, by means of rules,
to give an account of: (1) to ascertain syntactic
correctness; (2) to progressively construct the semantic
functional interpretation; (3) to allow a functional
analysis of a linguistic marker (example: ‫ و‬wa
(and),…).
The premise of each rule is a concatenation of linguistic
units with oriented types. The consequence of each rule
is an applicative typed expression with possible
introduction of one combinator. The type-raising of one
unit u introduces the combinator C*; the composition of
two concatenated units introduces the combinator B.
[Y : u1] - [X\Y : u2]
--------------------------<
[X : (u2 u1)]
Type raising rules :
[X : u]
---------------------->T
;
[Y/(Y\X) : (C u)]
*
[X : u]
---------------------->Tx ;
[Y/(Y/X) : (C u)]
*
functional composition rules :
[X/Y : u1]-[Y/Z : u2]
------------------------->B
[X/Z : (B u1 u2)]
[X : u]
----------------------<T
[Y\(Y/X) : (C u)]
*
[X : u]
----------------------<Tx
[Y\(Y\X) : (C u)]
*
;
[X/Y : u1]-[Y\Z : u2]
--------------------------->Bx;
[X\Z : (B u1 u2)]
[Y\Z : u1]-[X\Y : u2]
-------------------------<B
[X\Z : (B u2 u1 )]
[Y/Z : u1]-[X\Y : u2]
-------------------------<Bx
[X/Z : (B u2 u1)]
Combinators are used in order to construct semantic
interpretation. Each combinator is introduced or
eliminated by a β-reduction. For illustration, we present
the β-reduction rules of combinators used in this paper
Φ, B and C* (U1, U2, U3, U4 being typed applicative
expressions which function either like operators or like
operands):
(Φ U1 U2 U3) U4
((B U1 U2) U3)
((C U1) U2)
*
Æ
Æ
Æ
U1(U2 U4) (U3 U4)
(U1 (U2 U3))
(U2 U1)
Let us deal now with a simple example in Arabic:
‫( ﺗﺪﻋﻢ اﻟﺤﺮﻳﺔ اﻟﺪﻳﻤﻘﺮاﻃﻴﺔ‬that we will transcribe for the
needs of our paper by means of Latin characters :
Thoudaiimou elhouriathou
eddimouqratiyatha
(Freedom reinforces democracy))
1.
2.
3.
4.
[(S/N)/N : thoudaiimou]-[N : elhouriyathou]-[N : eddimouqratiyatha]
[(S/N)/N: thoudaiimou]-[S\(S/N):(C* elhouriyathou)]-[N: eddimouqratiyatha]
[S/N : (B (C* elhouriyathou) thoudaiimou)]-[N : eddimouqratiyatha]
[S : ((B (C* elhouriyathou) thoudaiimou) eddimouqratiyatha)]
5.
6.
7.
8.
((B (C* elhouriyathou) thoudaiimou) eddimouqratiyatha)
((C* elhouriyathou) (thoudaiimou eddimouqratiyatha))
((thoudaiimou eddimouqratiyatha) elhouriyathou)
thoudaiimou eddimouqratiyatha elhouriyathou
(<T)
(<Bx)
(>)
B
C*
The transitive verb in Arabic is a predicate which needs
its two arguments (the subject and the object) on its left
(its right with the Latin transcription). Contrary to
French and English, Arabic being VSO, the subject is
intercalated between the verb and the object. In the
traditional Arabic grammar, it is easy to differentiate
the subject from the object being given the presence in
the sentence of morphological indices. Concretely, the
categorial syntactical type (S/N)/N is assigned to the
transitive verb thoudaiimou. In other words the verb,
here, is seen as an operator whose first operand is the
object with type N positioned to its right in order to
construct a complex operator whose operand would be
the subject of type N positioned to the right. The
assignment of the types is made at step 1. Steps 2 to 4
occur in the morphs-syntactical level. They consist in
applying categorial rules. The type raising rule (<T) is
applied to elhouriyathou at step 2 in order to obtain the
operator (C* elhouriathou) whose operand would be
the result of the application of the transitive verb to the
object. In Arabic analysis, the strategy of application of
categorial rules should not be the same as in French or
English. For recall, this one consists of the application
of type raising rules only if the other rules are not
463
possible. That would make in the case of Arabic the
subject as the first operand of the transitive verb, what
is against the tradition established in linguistics. The
sentence is seen as syntactically correct at step 4,
because we get the type S. At step 5, a natural
deductive process of combinatory logic is carried out in
the predicative level. At step 8 the functional semantic
interpretation is constructed. It expresses the effective
order operator/operand of the linguistic units of the
initial statement.
The example shown here is a sentence known as verbal
being given that it begins with the verb. In Arabic, the
majority of the sentences start with the verb, however it
is not excluded to have sentences known as nominal
where the subject is placed before the verb :
(elhouriathou thoudaiimou eddimouqratiyatha)
‫ اﻟﺤﺮﻳﺔ ﺗﺪﻋﻢ اﻟﺪﻳﻤﻘﺮاﻃﻴﺔ‬. However, the traditional
grammar of Arabic considers the subject as being the
“moubthada” and the verbal syntagm, formed by the
transitive verb followed by an “erased” pronoun clitic
and an object, as the “khabar”. It is a form of
topicalization of the subject in which the pronoun clitic
which would have to take the place of the subject (to
make a parallel with the French topicalization) on the
right of the verb is erased. The application of the type
raising rule (>Tx) in the analysis which follows takes in
account this fact.
1.
2.
3.
4.
[N : elhouriyathou]-[(S/N)/N : thoudaiimou]-[N : eddimouqratiyatha]
[S/(S/N):(C* elhouriyathou)]-[(S/N)/N: thoudaiimou]-[N: eddimouqratiyatha]
[S/N : (B (C* elhouriyathou) thoudaiimou)]-[N : eddimouqratiyatha]
[S : ((B (C* elhouriyathou) thoudaiimou) eddimouqratiyatha)]
5.
6.
7.
8.
((B (C* elhouriyathou) thoudaiimou) eddimouqratiyatha)
((C* elhouriyathou) (thoudaiimou eddimouqratiyatha))
((thoudaiimou eddimouqratiyatha) elhouriyathou)
thoudaiimou eddimouqratiyatha elhouriyathou
(>Tx)
(>B)
(>)
B
C*
With the model of the ACCG, we consider that the
conjunction applies to two linguistic units fulfilling the
same function and that the linguistic unit which results
from coordination also inherits this function. This
postulate takes form in Lambek’s scheme of type
(X\X)/X associated to the conjunction ‫ و‬wa (and). In
this type the variable X can be unified with any basic or
non-basic type.
To avoid any form of over-generation, within the
ACCG model we provide meta-rules to control the
application of the type raising. Thus, in first case
(respectively the second) the type raising rule (<T)
(respectively (>Tx)) is started by the meta-rule M1
(respectively by M2).
M1 : If u1 is of type (Y/N)/Z and u2 of type N,
then we apply the type raising rule (<T) to u2 :
[N : u1 ==> Y\(Y/N) : (C* u1)]
Let us show the categorial analysis of the sentence (ii) :
M2 : If u1 is of type N and u2 of type (Y/N)/Z,
then we apply the type raising rule (>Tx) to u1 :
[N : u1 ==> Y/(Y/N) : (C* u1)]
1. [(S/N)/N : youkhatibou]-[N :elibnou]-[N :abahou]-[(S/N)\(S/N) :bi-ihthiramin]-[ (X\X)/X : wa]-[N :oumahou]-[(S/N)\(S/N) :bi-hananin]
2. [(S/N)/N : youkhatibou]-[S\(S/N):(C* elibnou)]-[N : abahou]-[(S/N)\(S/N) : bi-ihthiramin]-[(X\X)/X : wa]-[N : oumahou]-[(S/N)\(S/N) :
bi-hananin]
(<T)
3. [S/N : (B (C* elibnou) youkhatibou)]-[N : abahou]-[(S/N)\(S/N) : bi-ihthiramin]-[(X\X)/X : wa]-[N : oumahou]-[(S/N)\(S/N) : bihananin]
(<Bx)
4. [S : ((B (C* elibnou) youkhatibou) abahou)]-[(S/N)\(S/N) : bi-ihthiramin]-[(X\X)/X : wa]-[N : oumahou]-[(S/N)\(S/N) : bi-hananin]
(>)
5. [S/(S/N) :(C* elibnou)]-[S/N:(youkhatibou abahou)]-[(S/N)\(S/N) :bi-ihthiramin]-[(X\X)/X :wa]-[N:oumahou]-[(S/N)\(S/N):bi-hananin]
6. [S/(S/N) : (C* elibnou)]-[S/N : (bi-ihthiramin (youkhatibou abahou))]-[(X\X)/X : wa]-[N : oumahou]-[(S/N)\(S/N) : bi-hananin]
(<)
7. [S : ((C* elibnou) (bi-ihthiramin (youkhatibou abahou)))]-[(X\X)/X : wa]-[N : oumahou]-[(S/N)\(S/N) : bi-hananin]
(>)
(<T)
8. [S : ((C* elibnou) (bi-ihthiramin (youkhatibou abahou)))]-[(X\X)/X : wa]-[(S/N)\((S/N)/N) : (C* oumahou)]-[(S/N)\(S/N) : bi-hananin]
9. [S : ((C* elibnou) (bi-ihthiramin (youkhatibou abahou)))]-[(X\X)/X : wa]-[(S/N)\((S/N)/N) : (B bi-hananin (C* oumahou))]
(<B)
10. [S/(S/N):(C* elibnou)]-[S/N:((B bi-ihthiramin (C* abahou)) youkhatibou)]-[(X\X)/X:wa]-[(S/N)\((S/N)/N):(B bi-hananin (C* oumahou))]
11. [S/(S/N):(C* elibnou)]-[(S/N)/N:youkhatibou]-[(S/N)\((S/N)/N):(B bi-ihthiramin (C* abahou))]-[(X\X)/X:wa]-(B bi-hananin (C* oumahou))]
12. [S/(S/N) :
(C*
elibnou)]-[(S/N)/N
:
youkhatibou][(S/N)\((S/N)/N) :
(B
bi-ihthiramin
(C*
abahou))][((S/N)\((S/N)/N))\((S/N)\((S/N)/N)) : (wa (B bi-hananin (C* oumahou)))]
{X = (S/N)\((S/N)/N)} (>)
13. [S/(S/N) : (C* elibnou)]-[(S/N)/N : youkhatibou]-[(S/N)\((S/N)/N) : ((wa (B bi-hananin (C* oumahou))) (B bi-ihthiramin (C* abahou)))]
(<)
14. [S/(S/N) : (C* elibnou)]-[(S/N) : (((wa (B bi-hananin (C* oumahou))) (B bi-ihthiramin (C* abahou))) youkhatibou)]
(<)
15. [S : ((C* elibnou) (((wa (B bi-hananin (C* oumahou))) (B bi-ihthiramin (C* abahou))) youkhatibou)))]
(<)
16. ((C* elibnou) (((wa (B bi-hananin (C* oumahou))) (B bi-ihthiramin (C* abahou))) youkhatibou)))
17. (((wa (B bi-hananin (C* oumahou))) (B bi-ihthiramin (C* abahou))) youkhatibou))) elibnou)
18. (((Φ ∧ (B bi-hananin (C* oumahou))) (B bi-ihthiramin (C* abahou))) youkhatibou))) elibnou)
…
19. ((∧ (bi-ihthiramin (youkhatibou abahou)) (bi-hananin (youkhatibou oumahou))) elibnou)
464
C*
wa = Φ ∧
The analysis starts with the assignment of the syntactic
categories to the lexemes. For recall, each syntactic
category describes the way in which a lexeme operates
on its arguments. The category (X\X)/X assigned to the
conjunction is in fact a scheme of type which describes
the conjunction like an operator whose first and second
operands, of type X, are respectively the second
member and the first member of the coordination. The
type of the coordination (S/N)\((S/N)/N) which will be
substituted to X is known after the construction of the
second member of coordination (step 9). Steps 1 to 15
represent the application of ACCG rules. With these
steps we verify the correctness of the sentence (the type
S obtained at 15). A first structural reorganization is
applied at steps 5 in order to extract the operand of biihthiramin. A second structural reorganization is
applied at steps 10 and 11 in order to extract the first
member of the coordination. The structural
reorganization (Biskri, Desclés, 1997) is based mainly
on the reduction and/or the introduction of some
combinators into a combinatory expression to give an
equivalent but differently structured combinatory
expression. At the step 2, the type raising rule (<T) is
controlled by the meta-rule M1. But at step 8 the same
rule is controlled by the following meta-rule:
M3 : For a concatenated sequence u1-u2-u3, if u1
is the conjunction ‫ و‬wa, u2 is of type N and u3
of type Z\Y, then we apply the type raising rule
(<T) to u2 : [N : u2 ==> Y\(Y/N) : (C* u2)]
This meta-rule construct, explicitly, starting from the
object oumahou, the complex operator (C* oumahou)
whose operand is the verb youkhatibou. On this basis, it
becomes possible at the following step to compose two
operators (C* oumahou) and bi-hananin.
Steps 16 to 23 are in the predicative level level. They
reduce combinators in order to construct the functional
semantic interpretation (the normal form): ((∧ (biihthiramin
(youkhatibou
abahou))
(bi-hananin
(youkhatibou oumahou))) elibnou), which is structured
like a conjunctive clause. At the step 18 the linguistic
predicate wa (and) is replaced by its meaning in the
cognitive level Φ ∧ in order to express the distributive
and the conjunctive nature of wa (and) by respectively
the combinator Φ and the logical connector ∧.
We are, also, interested by the analysis of (iii). With the
one of (ii) we prove the important cover capacity of
ACCG in the case of coordination of non-constituents
in Arabic.
1. [(S/N)/N : yaakoulou]-[N : elqirdou]-[N : elmawza]-[(X\X)/X : wa]-[N : eddoubou]-[N : elâssala]
(<T)
2. [(S/N)/N : yaakoulou]-[S\(S/N) : (C* elqirdou)]-[N : elmawza]-[(X\X)/X : wa]-[N : eddoubou]-[N : elâssala]
3. [S/N : (B (C* elqirdou) yaakoulou)]- [N : elmawza]-[(X\X)/X : wa]-[N : eddoubou]-[N : elâssala]
(<Bx)
(>)
4. [S : ((B (C* elqirdou) yaakoulou) elmawza)]-[(X\X)/X : wa]-[N : eddoubou]-[N : elâssala]
5. [S : ((B (C* elqirdou) yaakoulou) elmawza)]-[(X\X)/X : wa]-[S/(S/N) : (C* eddoubou)]-[N : elâssala]
(>Tx)
(<Tx)
6. [S : ((B (C* elqirdou) yaakoulou) elmawza)]-[(X\X)/X : wa]-[S/(S/N) : (C* eddoubou)]-[(S/N)\((S/N)/N) : (C* elâssala)]
7. [S : ((B (C* elqirdou) yaakoulou) elmawza)]-[(X\X)/X : wa]-[S\((S/N)/N) : (B (C* eddoubou) (C* elâssala))]
(>Bx)
8. [S : ((B (C* elqirdou) (C* elmawza)) yaakoulou)]-[(X\X)/X : wa]-[S\((S/N)/N) : (B (C* eddoubou) (C* elâssala))]
9. [(S/N)/N : yaakoulou]-[S\((S/N)/N) : (B (C* elqirdou) (C* elmawza))]-[(X\X)/X : wa]-[S\((S/N)/N) : (B (C* eddoubou) (C* elâssala))]
10. [(S/N)/N : yaakoulou]-[S\((S/N)/N) : (B (C* elqirdou) (C* elmawza))]-[(S\((S/N)/N))\(S\((S/N)/N)) : (wa (B (C* eddoubou) (C*
elâssala)))]
{X = (S\((S/N)/N)} (>)
11. [(S/N)/N : yaakoulou]- [S\((S/N)/N) : ((wa (B (C* eddoubou) (C* elâssala))) (B (C* elqirdou) (C* elmawza)))]
(<)
12. [S : (((wa (B (C* eddoubou) (C* elâssala))) (B (C* elqirdou) (C* elmawza))) yaakoulou)]
(<)
13. (((wa (B (C* eddoubou) (C* elâssala))) (B (C* elqirdou) (C* elmawza))) yaakoulou)
14. (((Φ ∧ (B (C* eddoubou) (C* elâssala))) (B (C* elqirdou) (C* elmawza))) yaakoulou)
15. …
16. (∧ ((yaakoulou elmawza) elqirdou) ((yaakoulou elâssala) eddoubou))
It is interesting to notice that, in the analysis of this
statement, the construction of the second member of
coordination requires the application, at steps 5 and 6,
respectively, of two crossed type raising rules (forward
then backward) (>Tx) and (<Tx). The application of
these rules is done thanks to meta-rules M4 and M5.
M4 : For a concatenated sequence u1-u2-u3, if u1
is the conjunction ‫ و‬wa, u2 is of type N and u3 of
type N, then we apply the type raising rule (>Tx) to
u2 : [N : u2 ==> S/(S/N) : (C* u2)]
wa = Φ ∧
The second member of the coordination is a complex
operator (whose operand is the transitive verb) which in
the case of our example can be only one combination of
the type raised subject with the type raised object. The
choice of each type raising is determined by the
position of the operand in the linear structure. Thus,
(<Tx) applied to the object is justified by the fact that
the verb which is the operand of (C* elâssala) precedes
the object in the linear structure, without, however, to
be contiguous for it. (>Tx) applied to the subject is
justified by the fact that its operand would be in the
linear structure a combination of the verb and the type
raised object, this latter being positioned on the right of
the subject. wa, in this case too, is a linguistic operator
M5 : For a concatenated sequence u1-u2-u3, if u1
is the conjunction ‫ و‬wa, u2 is of type S/(S/N) and
u3 of type N, then we apply the type raising (<Tx)
to u3 : [N : u3 ==> (S/N)\((S/N)/N) : (C* u3)]
465
which is expressed at the cognitive level by Φ ∧ (step
14). At step 21, the interpretation of the initial
statement is obtained. This one is in clausal conjunctive
form: ((yaakoulou elmawza) elqirdou) ∧ ((yaakoulou
elâssala) eddoubou).
1
The next example, elibnou youkhatibou wa abahou bi
ihthiramin wa oumahou bi hananin, introduces a
correlative coordination. We note the initial conjunction
by wa1 and the non-initial conjunction by wa2 to avoid
confusing them.
10
11
12
13
[N: Elibnou] - [(S/N)/N : youkhatibou]- [(X/(X\X))/X :wa1]-[N : Abahou] - [(S/N)\(S/N) : bi ihtiramin]-[(X\X)/X : wa2]-[N : Oumahou][(S/N)\(S/N) : bihananin]
[S/(S/N) : (C* Elibnou)] - [(S/N)/N : youkhatibou]-[(X/(X\X))/X : wa1]- [N : Abahou] - [(S/N)\(S/N) : bi ihtiramin] - [(X\X)/X : wa2] - [N
: Oumahou] - [(S/N)\(S/N) : bihananin]
(>Tx)
[S/N : (B (C* Elibnou) youkhatibou)] -[(X/(X\X))/X : wa1] - [N : Abahou] - [(S/N)\(S/N) : bi ihtiramin] - [(X\X)/X : wa2] - [N :
Oumahou] - [(S/N)\(S/N) : bihananin]
(>B)
[S/N : (B (C* Elibnou) youkhatibou)] -[(X/(X\X))/X : wa1] - [(S/N)\((S/N)/N) : (C* Abahou)] - [(S/N)\(S/N) : bi ihtiramin] - [(X\X)/X :
wa2] - [N : Oumahou] - [(S/N)\(S/N) : bihananin]
(<T)
[S/N : (B (C* Elibnou) youkhatibou)] -[(X/(X\X))/X : wa1] - [(S/N)\((S/N)/N) : (B bi ihtiramin (C* Abahou))] - [(X\X)/X : wa2] - [N :
Oumahou] - [(S/N)\(S/N) : bihananin]
(<B)
[S/N : (B (C* Elibnou) youkhatibou)] -[((S/N)\((S/N)/N))/(((S/N)\((S/N)/N))\((S/N)\((S/N)/N))) : (wa1 (B bi ihtiramin (C* Abahou)))] [(X\X)/X : wa2] - [N : Oumahou] - [(S/N)\(S/N) : bihananin]
{X = (S/N)\((S/N)/N)} (>)
[S/N : (B (C* Elibnou) youkhatibou)] -[((S/N)\((S/N)/N))\((S/N)\((S/N)/N)) : (B (wa1 (B bi ihtiramin (C* Abahou))) wa2)] - [N :
Oumahou] - [(S/N)\(S/N) : bihananin]
{X = (S/N)\((S/N)/N)} (>B)
[S/N : (B (C* Elibnou) youkhatibou)] -[((S/N)\((S/N)/N))\((S/N)\((S/N)/N)) : (B (wa1 (B bi ihtiramin (C* Abahou))) wa2)] [(S/N)\((S/N)/N) : (C*Oumahou)] - [(S/N)\(S/N) : bihananin]
(<T)
[S/N : (B (C* Elibnou) youkhatibou)] -[((S/N)\((S/N)/N))\((S/N)\((S/N)/N)) : (B (wa1 (B bi ihtiramin (C* Abahou))) wa2)] [(S/N)\((S/N)/N) : (B bihananin (C*Oumahou))]
(<B)
[S/N : (B (C* Elibnou) youkhatibou)] -[(S/N)\((S/N)/N) : ((B (wa1 (B bi ihtiramin (C* Abahou))) wa2) (B bihananin (C*Oumahou)))]
(>)
[S/(S/N):(C* Elibnou)]-[(S/N)/N:youkhatibou]-[(S/N)\((S/N)/N):((B(wa1 (B bi ihtiramin (C* Abahou))) wa2)(B bihananin (C*Oumahou)))]
[S/(S/N) : (C* Elibnou)] - [(S/N) : (((B (wa1 (B bi ihtiramin (C* Abahou))) wa2) (B bihananin (C*Oumahou))) youkhatibou)]
(<)
[S : ((C* Elibnou) (((B (wa1 (B bi ihtiramin (C* Abahou))) wa2) (B bihananin (C*Oumahou))) youkhatibou))]
(>)
14
15
16
17
18
19
((C* Elibnou) (((B (wa1 (B bi ihtiramin (C* Abahou))) wa2) (B bihananin (C*Oumahou))) youkhatibou))
((((B (wa1 (B bi ihtiramin (C* Abahou))) wa2) (B bihananin (C*Oumahou))) youkhatibou) Elibnou)
(((wa1 (B bi ihtiramin (C* Abahou))) (wa2 (B bihananin (C*Oumahou)))) youkhatibou) Elibnou)
(((C* (B bi ihtiramin (C* Abahou))) (wa2 (B bihananin (C*Oumahou)))) youkhatibou) Elibnou)
(((wa2 (B bihananin (C*Oumahou))) (B bi ihtiramin (C* Abahou))) youkhatibou) Elibnou)
((Φ ∧ (B bihananin (C*Oumahou))) (B bi ihtiramin (C* Abahou))) youkhatibou) Elibnou)
2
3
4
5
6
7
8
9
C*
B
wa1 = C*
C*
wa2 = Φ ∧
…
20 ((∧ (bihananin (youkhatibou Oumahou)) (bi ihtiramin (youkhatibou Abahou))) Elibnou)
The first member of coordination is delimited by the
first conjunction wa1 (initial one) and the second
conjunction (coordinating one) wa2. A consequence of
that: the category of the coordination is obtained after
the construction at step 5 of the first member of
coordination (B bi ihtiramin (C* Abahou)) with the
type (S/N)\((S/N)/N). The category (X/(X\X))/X is
assigned to the initial conjunction wa1 in order to
express its role of operator whose first operand is the
first member [abahou bi ihthiramin] of the coordination
and the second operand is the result of the application
of the coordinating conjunction wa2 to the second
member [oumahou bi hananin]. This category is in
agreement with the fact that the presence of an initial
conjunction is strongly dependent on the presence of a
non-initial conjunction. However, it makes it possible
to classify our analysis neither in the class of the
symmetrical analysis nor in the class of the
asymmetrical analysis as described in the literature.
Indeed, on the one hand this category is different from
the category assigned with the non-initial conjunction
and thus defines the conjunction initial as notcoordinating, and on the other hand it is not compatible
with the category of an adverb. The second conjunction
C*
wa2 which is coordinating still have the scheme of type
Steps 14 to 24 reduce combinators in order to
construct the functional semantic interpretation: ((∧
(bihananin (youkhatibou Oumahou)) (bi ihtiramin
(youkhatibou Abahou))) Elibnou), which is structured
like a conjunctive clause too. This functional semantic
interpretation is exactly the same as the one produced
through the analysis of elibnou youkhatibou abahou bi
ihthiramin wa oumahou bi hananin. At the step 17 the
linguistic predicate wa1 (and) is replaced by its
meaning C* in the cognitive level. wa1 is not a
coordinating conjunction. It is just an operator who
“types raise” the first member of coordination to
produce a complex operator (wa1 (B biihtiramin (C*
Abahou))) whose operand is the result (wa2 (B
bihananin (C*Oumahou))) of the application of the
coordinating conjunction wa2 to the second member of
coordination (B bihananin (C*Oumahou)). At the step
19 the linguistic predicate wa2, because of its
distributive and conjunctive nature, is replaced by its
meaning Φ ∧ in the cognitive level. In short, the initial
conjunction does not function like a simple
conjunction. It is different by its not coordinating
nature. It is mainly useful to reinforce coordination,
(X\X)/X.
466
either by eliminating ambiguity as in French (Biskri,
Rochette, 2007) or by determining the first member of
coordination as well as the type of coordination. The
analysis of correlative coordination is asymmetric, even
if the initial conjunction does not function like an
adverb.
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3. Conclusion
With this work, it arises several fundamental results.
From a theoretical point of view, with the ACCG,
thanks to the use of the combinatory logic, and the
meta-rules we prove, on concrete examples, that it is a
very solid formalism and very flexible device for the
analysis of coordination in Arabic. The analysis carried
out confirms that the categorial operators and the
combinators of the combinatory logic construct, starting
from the concatenated structure, the right
interpretations of the statements; these interpretations
are expressed in functional terms (operator/operand). In
addition, these results show that in spite of criticisms
(even if all are not sufficiently verified) concerning all
categorical models, it remains that the categorial
approach is enough flexible to be adapted to Arabic,
only meta-rules should be exclusive to each language.
On another hand, we prove, in a general way, that
Arabic language is not just a linear succession of
linguistic units. Certain units function like complex
operators. It is useful to formalise their meaning. The
model of representation of the language with three
levels (morphs-syntactical level/predicative level/
cognitive) is in adequacy with this reality.
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