CONSTRAINT-BASED AND FUZZY LOGIC STUDENT MODELING FOR ARABIC GRAMMAR

International Journal of Computer Science & Information Technology (IJCSIT) Vol 12, No 4, August 2020
DOI: 10.5121/ijcsit.2020.12404 35
CONSTRAINT-BASED AND FUZZY LOGIC STUDENT
MODELING FOR ARABIC GRAMMAR
Nabila A. Khodeir
Informatics Department, Electronic Research Institute, Cairo, Egypt
ABSTRACT
Computer-Assisted Language Learning (CALL) are computer-based tutoring systems that deal with
linguistic skills. Adding intelligence in such systems is mainly based on using Natural Language
Processing (NLP) tools to diagnose student errors, especially in language grammar. However, most such
systems do not consider the modeling of student competence in linguistic skills, especially for the Arabic
language. In this paper, we will deal with basic grammar concepts of the Arabic language taught for the
fourth grade of the elementary school in Egypt. This is through Arabic Grammar Trainer (AGTrainer)
which is an Intelligent CALL. The implemented system (AGTrainer) trains the students through different
questions that deal with the different concepts and have different difficulty levels. Constraint-based student
modeling (CBSM) technique is used as a short-term student model. CBSM is used to define in small grain
level the different grammar skills through the defined skill structures. The main contribution of this paper
is the hierarchal representation of the system's basic grammar skills as domain knowledge. That
representation is used as a mechanism for efficiently checking constraints to model the student knowledge
and diagnose the student errors and identify their cause. In addition, satisfying constraints and the number
of trails the student takes for answering each question and fuzzy logic decision system are used to
determine the student learning level for each lesson as a long-term model. The results of the evaluation
showed the system's effectiveness in learning in addition to the satisfaction of students and teachers with its
features and abilities.
KEYWORDS
Language Tutoring Systems, Student Model, Constraint-Based Modeling, Fuzzy logic
1. INTRODUCTION
Computer-Assisted Language Learning (CALL) is a research discipline that concerned with using
computers, new media, and information technologies for language learning [1], [2]. The
integration of artificial intelligence and adaptive technologies into CALL is called Intelligent
Computer-Assisted Language Learning (ICALL) [3]. Such technologies provide different
adaptation dimensions to the language learning system. They are based on observing learners
through system use and build an updating model of student knowledge and characteristics.
Intelligent Tutoring Systems (ITSs), Adaptive Hypermedia systems (AHSs), Collaborative
environments (CE), and computer-supported ubiquitous learning (CSUL) are the common
adaptive approaches that have been used in ICALL [4]. The ITS approach is used in supporting
the student problem-solving. That is through diagnosing the student answers and identifying the
embedded errors and their origin. That allowing providing immediate and tailored feedback to the
learner [5]. In addition, ITS approach is used in controlling the sequencing of learning items
and/or tasks to reach a specific learning goal.
The focus of this paper is using ITS technology to support the student in solving grammar
problems. AI techniques such as natural language processing (NLP), fuzzy logic, and student

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modeling techniques are used. Fuzzy logic incorporates precise techniques for talking vague
information in the knowledge representation and decision making. It is one of the choices for
appropriate evaluation of a learner’s performance among the existing approaches such as neural,
Baysian networks [6]. Karaci presented an example in using a fuzzy logic decision system to
determine the learning level based on MYCIN certainty factor and the number of times the
student takes for answering the question [6]. Another example presents developing parsers to
identify grammatical errors by incorporating NLP techniques in analyzing student input [7]. Then
the analyzed and interpreted observed student behaviors are mapped onto the student model.
There are different student modeling techniques which are generally classified into two
categories: cognitive science and machine learning approaches [8]. Cognitive Science approaches
modeled how humans learn based on domain modeling and expert systems. Model-tracing (MT)
and constraint-based modeling (CBM) are the two common techniques in the cognitive science
approach. Model-tracing is based on using production rules, where rules that have been applied
by the student with a high success rate are assumed to be learned [9]. This technique requires
modeling of all alternative solutions and specifying each solution path using production rules
[10][11].
Ohlsson proposed CBM as an approach to avoid some limitations of model-tracing, such as
having runnable models of the expert and the student in addition to identifying and augmenting
the student bugs. CBM is based on capturing the domain principles using a set of constraints. A
constraint is represented by the tuple <Cr, Cs>, where the relevance condition Cr is the condition
under which the constraint is applicable, while the satisfaction condition Cs is the condition that
should be satisfied such that the constraint is not violated [12][13]. Identifying errors, in this case,
is based on tracking the violated constraints. In such a situation, the tutoring system can respond
by giving advice to the student about the error, even without being able to replicate it.
Representing domain is typically achieved by breaking the domain knowledge into smaller
elements (concepts) [14]. Neglecting relations between concepts lead to a set or vector model.
Using such a model as a user model restricts updating techniques to only one concept or node at a
time. Relations between domain concepts are considered in different manners. The network
model is one of them where the items are arranged into a network and are interconnected by
different types of links, specifically prerequisite links, is-a or part-of links, and remedial links.
The hierarchy model is also considered in considering relations between concepts where the
items are arranged to make a tree-like hierarchical structure. In such a model the more general
items are placed higher in the hierarchy and are decomposed into simpler ones nearer to the
bottom. The hierarchy model and the network model are the more appropriate models for
grammar-oriented systems to define relations between items/terms as remedial or prerequisite [4].
Arabic is a Semitic native language of hundreds of millions of people worldwide, especially in
the Middle East. Arabic morphology is considered to be one of the main elements that cause the
language to be a very derivational and well-structured language [15]. Over the past decade,
Arabic NLP (ANLP) has gained the interest of many researchers. Moreover, several systems have
been developed for a multitude of applications for various purposes, including ICALLs [16] [17]
This paper presents the design of an ICALL, for 4th grade Arabic grammar skills, that diagnoses
students’ answers and gives adaptive feedback to them. The domain knowledge is described as a
hierarchical structure of grammatical skills, based on which a set of constraints in (Cr, Cs) form
is described for constraint-based student modeling (CBSM). The main contribution is the
proposed mechanism for efficiently checking constraints by utilizing the hierarchical structure of
the domain knowledge. Such a technique facilitates diagnosing student errors and their origins. In
addition, a fuzzy logic decision system is integrated to deal with uncertainty in the determination
of the student learning level for each lesson.

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The rest of the paper is organized as follows: Section two presents related work to highlight the
contributions of the paper. Section three and four give a brief demonstration of AGTrainer and its
questions bank respectively. Section five addresses the domain hierarchal representation.
Sections six, seven, and eight respectively explain student modeling, feedback, and student
learning level in AGTrainer. Finally, sections nine and ten respectively present the evaluation and
the conclusion.
2. RELATED WORK
ICALLs have been implemented for various languages including English, German, Chinese, and
Arabic. Those systems vary in their capabilities, linguistic skills they focus on, the student
modeling techniques, and the learning strategies. We address some of the prominent ICALL in
the following subsections. We also discuss the state of the art in Arabic LTSs.
ICALL that based on intelligent tutoring system technology has the ability to diagnose students’
answers and gives adaptive feedback to them.
Heift et al. present German Tutor which is an Intelligent Language Tutoring System that has been
specifically designed for Web delivery [18]. The system can handle different possible errors
through a series of progress bars attached to concepts from the learning domain. The NLP
component of the system consists of a grammar and a parser which analyzes sentences from the
student and detects grammatical and other errors. The feedback modules of the system then
correlate the comprehensive output of the parser with an error-specific feedback message.
Individualization and adaptively is achieved with techniques of learner modeling by keeping
score across a number of error types, or, nodes such as grammar, vocabulary, punctuation, etc.
According to the learner’s model, the amount and wording of the feedback are adjusted.
Costa et al. present an integrated rule-based machine translation approach to disambiguate
students' intended meaning in a CALL system [19]. They aimed to provide precise feedback to
correct ungrammatical input by using Machine Translation technology to check the student's
intended. Mal-rules are a specific kind of rules that extend a descriptive grammar to make it
accept ungrammatical phenomena. These mal-rules are used both to identify grammar errors and
to reconstruct the semantics of ungrammatical inputs which lead to triggering helpful messages to
language learners The Student Model is the center of information. It contains vocabulary known
by each student, the grammatical complexity the student is expected to work with, and the entire
history of the student’s interaction with the system such as previously completed exercises,
previous mistakes, and time spent with each exercise.
Troussas et al. identify misconceptions, originating from neglect, lack of knowledge, or language
transfer between simultaneous learning of multiple foreign languages. They present a model for
misconception detection and identification (MDI) [20]. The MDI mechanism integrates the Fuzzy
String Searching and The String Interpreting Resemblance algorithms in order to reason between
possible learners’ misconceptions. The system relays on a database with possible students’
misconceptions. This database was constructed using anonymous learners’ data which is served
as training data for the proposed algorithm. They classify misconceptions into three types. The
first error category is the spelling mistakes which can be the result of negligence or ignorance.
The second category is the mistakes in the use of tenses and the third category is the mistakes in
the use of auxiliary verbs. Fuzzy string searching is used to identify the first error category by
detecting the pattern of strings that correspond to the possible answers that are stored in the
system’s database. On the other hand, the string interpreting resemblance techniques is used to
identify spelling misconceptions due to language transfer and misconceptions in the use of tenses

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and auxiliary verbs. It tries to find a translation of the learner’s given answer and compares it
with the stored possible matches. The results of the error diagnosis are used to automatically
model the learning process through four fuzzy sets to represent the student’s knowledge level of
each domain concept.
Several Arabic LTSs have been developed over the years. Tutoring Arabic grammar and syntax
are the main focus of most of those systems. One of the earliest Arabic grammar tutoring systems
included an expert system developed in Prolog for representing Arabic syntax using a set of
production rules for detecting some syntax errors [21].
The more advanced Arabic ICALL system has been developed through a number of versions for
tutoring the Arabic language to primary school students in Egypt in addition to foreigners
learning Arabic as a second language [17] [22]. ICALL is based on NLP tools containing
morphological and syntax analyzer to detect student errors. In addition, the system augmented the
Arabic grammar with mal-rules that are capable of parsing ill-formed input when the grammatical
rules fail. The main limitation of ICALL is the lack of a student model.
Shaalan et al. included a student model in a system for analysis and feedback of erroneous Arabic
verbs [23]. The student learning skill levels are represented in terms of the frequency of an error
that the student has made while satisfying its related concept. It is a form of a perturbation model.
In addition, the system offers adaptive feedback for improving learner’s linguistic knowledge
according to the student level.
The main drawbacks of the presented systems are their dependency on pre-stored answers or mal-
rules or database with possible students’ misconceptions. This requires defining a list of possible
errors in addition to using different mechanisms to correctly interpret a student's error when there
is confusion with potential errors.
Generally the knowledge-based and corpus-based approaches are commonly used in ICALL [24].
The knowledge-based approach depends on morphological and grammatical rules that are written
by linguists. Such an approach assists diagnosing learner errors and provides highly accurate
feedback for these errors. That is usually based on defining a list of possible errors that are
described as mal-rules.
On the other hand, the corpus-based approach utilizes learning algorithms that require large
tagged learner corpus for training and testing to generate statistical models. Such a model can be
used for learner’s error prediction. The corpus-based approach is characterized by its adaptability
in minimal time when sufficient large datasets are available which is not enough in the Arabic
language.
We adopt knowledge-based in addition to utilizing a hierarchal representation of the system
domain knowledge. Since Arabic linguistic grammar skills can be arranged hierarchically, and
the relations between different skills can be defined. Another contribution is using such skill
structure in addition to the CBM representation in diagnosing the students' errors. In other words,
the hierarchical representation is used as a mechanism for efficiently checking constraints to
model student knowledge and diagnosing student errors. In addition, that short student model,
that represented by satisfied and unsatisfied constraints, is utilized with the trail number of
solving the presented question to build a long-term model based on a fuzzy logic decision system.

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3. AGTRAINER SYSTEM
We developed AGTrainer which is an ICALL system [25][25]. It dedicated to training students at
the primary level in Egyptian schools on Arabic language grammar. The system covers the basic
concepts in Arabic grammar through a number of lessons. These lessons include demonstratives
(‫اسماء‬ ‫;)االشارة‬ parts of speech (words type), which include nouns (‫,)االسماء‬ verbs (‫,)االفعال‬ and
particles (‫;)الحروف‬ and pronouns (‫,)الضمائر‬ which contain 1st person pronoun (‫ضمير‬ ‫)المتكلم‬ 2nd
person pronoun (‫,)ضميرالمخاطب‬ and 3rd person pronoun (‫ضمير‬ ‫.)الغائب‬ Other lessons are deal with
dual (‫,)المثنى‬ plural including broken plural (‫الجمع‬ ‫متضمنا‬ ‫جمع‬ ‫,)التكسير‬ nominal sentence ( ‫الجمل‬‫ة‬
‫,)اإلسمية‬ verbal sentence (‫الجملة‬ ‫,)الفعلية‬ noun of place (‫ظرف‬ ‫,)المكان‬ noun of time (‫ظرف‬ ‫,)الزمان‬
interrogative tools (‫أدوات‬ ‫,)االستفهام‬ negation tools (‫أدوات‬ ‫,)النفي‬ and subject and verb agreement
(‫مطابقة‬ ‫الفعل‬ ‫مع‬ ‫.)الفاعل‬ Those lessons are listed on the left-hand side of the system interface as
shown in Figure 1 in the order with which they are taught to the students at the school. However,
the student can choose any lesson without being bound by the order.
When a specific lesson is selected, different question types in the required grammatical skills will
be offered successively. The student can proceed with the same question type by clicking "Next
Question" or "Previous Question" buttons. Different types of questions can be selected using the
"New Question" button.
The system responses to the student's answer by two levels of feedbacks. General feedback is
presented to indicate if the question is correctly answered or not. Besides, informative feedback is
given in case of totally or partially student wrong answer.
Another trail is then given to the student to correct his/her answer. Student can also go back to the
related lesson that is explained through the tutor module by selecting the "Return to the lesson"
button.
Figure 1. Screenshot of the AGTrainer Interface
4. QUESTION BANK
Questions bank is a database implied different types of questions that cover the listed lessons. For
each lesson, all related grammatical concepts are addressed through different questions. For
example; demonstrative lesson has questions that test the student's knowledge of different
demonstratives, other questions consider agreement demonstrative with the noun it refers to in
gender and number with considering exception in irrational plural. The degree of difficulty of the

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questions depends on the number of grammatical concepts to be addressed and whether the
question is subject to exceptions to those concepts.
Each question in the database is defined by its header, statement, and available choices. The
header defines the lesson it belongs to and the grammatical skills it addresses. The difficulty level
of the header is based on the number of grammatical skills it tackles. The statement determines if
the question is subject to grammatical exceptions or not which define the difficulty level of the
statement.
4.1. Question Forms
There are two forms of the questions; selection-form for identifying one or more words that
satisfy the required criteria(s) such as Fig 2 (a, b), or multiple-choice such as Fig. 2 (c, d). Some
questions combine the two forms, for example, Fig. 2 (e, f). Although these forms do not allow
the student to key in an Arabic sentence freely, they make the diagnosis of errors focused on
correcting the basic concepts of this young student ages instead of being distracted in correcting
spelling errors.
Figure 2(a) Figure 2(b)
Figure 2(c) Figure 2(d)
Figure 2(e) Figure 2(f)
4.2. Questions Difficulty levels
Questions are varying in their difficulty levels. The main parts of the question are an explanation
of a question header, a given statement, and choices. Each question part contributes to defining
the grammar concept the question addressed and the question difficulty level it has. For example;
question in fig.2 (a) header is "‫أضغط‬ ‫على‬ ‫إسم‬ ‫اإلشارة‬ ‫فيما‬ ‫"يأتي‬ ("Click on the demonstratives as
follows") that addresses identifying word type and subsequently identifying noun subcategory.
Such skills are used to characterize the noun and the subcategory of that noun. The question

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choices are "‫،هذه‬ ‫،ذهب‬ ‫"التلميذ‬ ("This is, student, went") which are different in their type (noun and
verb). So, the choices added another dimension which is the difference in word type.
Question 2 (c) and (d) have the same header " ‫أختر‬ ‫اسم‬ ‫اإلشارة‬ ‫المناسب‬ ‫فيما‬ ‫"يأتي‬ (Choose the
appropriate demonstratives as follows) and choices which are demonstratives. The skill needed is
the agreement of demonstrative with the noun it refers to in gender and number. The difference
between the two questions is the given statement. The first given statement uses single masculine
noun "student" while the next question uses irrational plural ‫"حميدة‬ ‫أخالق‬ " (good ethics) which is
subject to an exception in the needed skill. So, a further complication is added by the given
statement.
Another example is the question (f) which has the header “‫أجعل‬ ‫اسم‬ ‫اإلشارة‬ ‫للجمع‬ ‫المذكر‬ ‫وغير‬ ‫ما‬ ‫"يلزم‬
(change the demonstrative noun from the singular form into the plural form and change what is
necessary to make it grammatically correct sentence.). One of the nouns in the given sentence has
broken plural that does not follow the rule of conversion to plural.
5. DOMAIN REPRESENTATION
We consider Arabic basic grammar to be modeled in a hierarchal structure. For each domain
concept or skill, there is a set of constraints that cover the corresponding grammar rules including
the existing exception of each one. The application of these constraints shall take into account a
defined hierarchical structure in addition to the possibility of applying them
5.1. Arabic Basic Grammar
The considered basic grammar rules expose to identifying word type and features, some
morphological skills especially agreement between two words in different contexts, and a small
part of the syntactic skill. The next sections will explore the considered skills and the hierarchy
they implied. In addition, grain constraint representation for each skill will be explored through
such representation.
Identifying word type and features are the basic Arabic grammar skill that taught at the early
stage. It is a pre-request for many complicated grammatical skills and it is required in system
grammatical lessons. Identifying word features starts by defining the word type if it is a noun or
verb or particle. Based on the word type, more word features can be identified. For example, the
verb tense is a feature associated with the verb word category. Other examples are identifying the
noun and particle subcategories if the word category is noun or particle respectively. In other
words, there is a hierarchy relationship between identifying word type and subcategories of type
as shown in Figures 3. Such hierarchy facilitates the diagnosis of student errors and gives the
possibility to know their underlying cause. For example, if the question asking about checking
the verbs in the present tense and the student submit a wrong answer. Then we start by checking
the word type to check if the student answer is a verb or not. If not, the student will be alerted to
the basic error. Otherwise, the student answer (verb tens) will be tested.
Morphological skills are a science that discusses the change or conjugating of a word into various
forms in order to achieve the desired meaning. Morphology is only applicable to nouns and verbs
because they are able to be conjugated to different forms, unlike particles.
Morphology is applied to verbs by conjugating them from one tense to another or from one
gender to another. On the other hand, it can be applied to nouns to conjugate them into the dual
and plural forms.

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AGTrainer has two lessons "dual and plural" that dedicated to applying some of the
morphological rules and changing the morphology of words to be inflected according to its role.
In addition, broken plural is also considered. The remainder lessons expose to the morphological
agreement between two words in different cases. Generally, many consecutive words need to be
agreeing on one or two grammatical features with exceptions for some cases. That implies the
dependency between words grammatical features and morphological agreement.
Syntactic skills refer to knowledge of grammar rules or the skills of constructing grammatically
correct sentences in Arabic. Those skills include identifying word constituents according to
certain syntactic features, identifying a sentence type, and converting from a given sentence type
to another.
Figure 3. Identifying word grammatical features
5.2. Constraint Based Modeling
As we indicated in the last sections, we have three main skills: identifying word type and
features, morphological and syntactic skills. Each skill is represented by a set of constraints with
considering the different hierarchy levels. For example, figure 4 indicates part of constraints that
represent Identifying masculine demonstrative noun. They are arranged according to the level it
belongs to. As shown in fig. 5 constraints 15, 16, and 17 have different hierarchy levels.
Constraint 15 checking if the selected answer is a noun. If this constraint is satisfied, the next
constraint which has the same relevance condition and higher hierarchal level is checked.

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Constraint 16 checks the subcategory of the selected answer which is a noun. If constraint 16 is
satisfied the next constraint with the highest hierarchal level is checked. It is worth to mention
that, violation of a constraint blocking checking other constraints with the same relevance
conditions and have higher hierarchy levels.
Another example is shown in figure 5 where some constraints of morphological agreement skill
are indicated. That skill needs to another prerequisite skill where we have to ensure the student
answer is a noun before we check the similarity of the features between the two words.
Accordingly, the first constraint that deals with a case of the agreement (demonstrative with a
word it refers to) defined as a prerequisite constraint that based on identifying word grammatical
features skill with the first level that identifies if the word is a noun. Next constraints 36, 37
define agreement rules of gender and count. On the other hand, constraint 38 defines the
exception of those constraints in case of irrational plural nouns.
Figure 4. Identifying features constraints
Figure 5. Agreement constraints
Identifying features constraints
Constraint 15:
Cr: Identifying masculine demonstrative noun is required
Cs: the student answer should be a noun
Constraint 16:
Cs: the student answer subcategory should be a demonstrative noun
Constraint 17:
Cs: the student answer subcategory gender should be masculine
Agreement Constraints
Constraint 35:
Cr: [Identifying noun], the skill is agreement and the student answer includes a demonstrative
and a word it refers to
Cs: the word it refers to should be a noun
Constraint 36:
Cr: the skill is agreement and the student answer includes a demonstrative and the noun it
refers to is sane
Cs: the gender of the noun should be similar to that of the demonstrative
Constraint 37:
refers to is sane
Cs: the count of the noun should be similar to that of the demonstrative
Constraint 38:
refers to is an irrational plural noun
Cs: the demonstrative should be ‫هذه‬ (singular feminine demonstrative)

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6. STUDENT MODELING
The student modeling process aims to detect student mistakes and figure out their cause. This
detection is achieved by matching each submitted student's answer against constraints with
satisfied relevance conditions. If the student answer violates one or more constraints, the system
supports the student with informative feedbacks that are attached to violated constraints.
Each question is defined by a set of grammar skills needed for correctly solving it. Accordingly,
to check the submitted answer to a presented question, only the constraints corresponding to its
skill set are checked. This speeds up the process and increases its efficiency. The student answer
is correct if all the relevant constraints are satisfied. Errors are figured out based on the violated
constraints.
Some questions need more than one skill to be correctly solved. Those skills can belong to the
same grammar skills category or different skill categories. Moreover, the skills of the same
category can belong to different levels of the skills hierarchy. This affects the sequence of
constraints checking as explained in the following sub-sections.
6.1. Different Levels in the Same Skill
As explained earlier, skills in each category are arranged hierarchically. Constraints can exist at
each level and each node in the hierarchy. For example, at the first level of the identifying word
features skills hierarchy, three constraints check the word type (whether the word is a noun, a
verb, or a particle). Assuming a given word is a noun, at the second level of the hierarchy, there
are constraints to check the noun subcategory (whether the noun is a demonstrative, a pronoun
(1st person, 2nd person, or 3rd person), a noun of place or a noun of time). It is worth mentioning
that checking those constraints is blocked if checking the word category does not indicate a noun.
In other words, checking some constraints is conditioned by the satisfaction of higher-level skill
constraints. This speeds up the process and increases its efficiency. For example, the question in
figure 2(a) that asks the student to click on the demonstratives noun, the correct answer is this
"‫هذا‬ " since it is a demonstrative noun. If the student selects the verb go " ‫ذهب‬ ", the answer word
category will be check if it is a verb. That will violate the higher-level constraint which leads to
blocking the higher-level constraint to check the subcategory.
6.2. Same Levels in the Same Skill
In case the checked constraints belong to the same skill and at the same level in that skill
hierarchy, all constraints should be checked. For example, referring to Figure 4, agreement in
grammatical features such as count and gender are at the same level of the hierarchy. Where the
student answer has to agree in both gender and count with the matched word in the question
statement. Referring to the question in Figure 7, which asks the student to choose the appropriate
demonstrative for nurses "‫,"ممرضات‬ the correct answer is "these" "‫,"هؤالء‬ since it agrees with
"nurses" "‫"ممرضات‬ in both gender (feminine) and count (plural). In that case, we must test all
constraints with satisfied relevance conditions, regardless of whether or not one is satisfied or
violated. The violation of one of the constraints does not block the testing of the rest, such as if
the levels are different.
6.3. Prerequisite Skill
Some questions need skills from different categories to be correctly solved. Such constraints are
arranged such that each constraint follows its prerequisite ones. For example, the question in

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figure 8 that asks the student to select a suitable noun that agrees with 2nd person pronoun. The
prerequisite condition for such a question is the selected word has to be a noun. This means
applying the constraint of checking the word category to be sure it is a noun. If it is a noun the
system will proceed in considering the agreement between the selected pronoun and the noun in
the question statement. Accordingly, if checking the selected word category indicates that the
student selected a word of a wrong category (verb or particle), AGTutor does not proceed to
check the agreement conditions. That means violating the identifying word category constraints
blocks checking the morphological skills constraints. This feature of AGTutor also speeds up the
process and increases its accuracy in the diagnosing process.
Figure 6. Applying constraints in the same hierarchically level in the same skill
7. FEEDBACK GENERATION
Different feedback strategies have been used for lexical and grammatical errors at the sentence
level [26]. Providing the student with the correct solution is direct feedback while underlining his
error(s) is indirect feedback. A metalinguistic explanation that providing grammar rules or the
cause of the student errors is also considered. Recently more discursive forms of feedback such
as providing model texts for the essay questions are addressed [27].
Figure 7. Question needs prerequisite skills
AGTrainer system supports the student through three types of feedback; general feedback which
indicates the status of the student's answer if it is correct or wrong, direct corrective feedback
(correct answer), and informative feedback. Informative feedback supports the student with
diagnosing his/her error(s) and it is only generated if the student fails to submit the correct
answer after two trials. Informative feedback could be considered as a metalinguistic or causal
explanation. It is worth mentioning that, the system has not a runnable model to generate the
correct answer as well as it does not store the questions model answers. So, checking and giving

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the general feedback of correct or wrong answer is based on satisfaction or violation of all or
some constraints with satisfied relevance conditions.
Student answer has the potential to be partially correct which means a violation of some of the
constraints with satisfied relevance conditions. So, we attach positive and negative feedback for
each constraint to be presented in satisfaction and violation of that constraint. Positive feedback
indicates the success of the application of the corresponding constraint and vice versa. The
positive feedback is used only in the student's partial correct answer to indicate the correct part of
the student answer. It is written in a way that allows the aggregation of messages that indicate the
correct and wrong parts in the student answer. In addition, the stored constraints attached
feedback messages include parameters that are substituted by the actual words mentioned in the
question. That gives an adaptable message for each question.
For example, Identify demonstrative Noun constraint has the following feedback messages:
Positive feedback:
‫ضمير‬ ‫المتكلم‬ (‫ضمير‬ ‫ال‬‫متكلم‬ ‫)المختار‬
1st person (selected 1st person)
Negative feedback:
‫كلمة‬ (‫الكلمة‬ ‫)المختارة‬ (‫نوع‬ ‫اإلسم‬ ‫)المختار‬ ‫وليست‬ ‫ضمير‬ ‫متكلم‬
The word (selected word) is (word subcategory) and not a 1st person
Another example, Agreement 1st person pronoun with a noun in count constraint has the
following feedback messages:
Positive feedback:
‫يستخدم‬ ‫لل‬ (‫النوع‬ ‫المناسب‬ ‫في‬ ‫العدد‬ ‫لضمير‬ ‫)المتكلم‬
is used for (correct selected 1st person pronoun count)
Negative feedback:
‫يستخدم‬ ‫لل‬ (‫النوع‬ ‫المناسب‬ ‫في‬ ‫العدد‬ ‫لضمير‬ ‫المتكلم‬ ‫)المختار‬ ‫بينما‬ ‫الكلمة‬ (‫الكلمة‬ ‫المشار‬ ‫)إليها‬ ( ‫ن‬‫وع‬ ‫الكلمة‬ ‫)التالية‬
is used for (selected 1st person pronoun count) while (the word it refers to) is (count of the noun
it refers to).
The word descriptions between brackets are replaced by the actual words in the question. Since
checking satisfaction of each constraint requires retrieving the features of the student answer
from system lexicon. That is used later in the substitution process.
In case of violation of some constraints and the satisfaction of other constraints, aggregation of
positive feedback messages with negative feedback messages is presented. As shown in Figure
9, the student is informed that he/she satisfied the selection of noun subcategory 1st person as
asked in the question and violated the agreement in count constraint where he selects plural 1st
person pronoun while the consequent noun is a singular form of Arabic verb "like" ‫أحب‬ .
The messages before substitution:
First message:

47
‫ضمير‬ ‫المتكلم‬ (‫ضمير‬ ‫المتكلم‬ ‫)المختار‬
1st person (selected 1st person)
Second message:
‫يستخدم‬ ‫لل‬ (‫النوع‬ ‫المناسب‬ ‫في‬ ‫العدد‬ ‫لضمير‬ ‫المتكلم‬ ‫)المختار‬ ‫بينما‬ ‫الكلمة‬ (‫الكلمة‬ ‫المشار‬ ‫)إليها‬ ( ‫ن‬‫وع‬ ‫الكلمة‬ ‫)التالية‬
is used for (selected 1st person pronoun count) while (the word it refers to) is (count of the noun
it refers to)
The messages after substitution:
First message: 1st person (we)
‫ضمير‬ ‫المتكلم‬ (‫)نحن‬
Second message:
is used for (plural) while (like) is (singular)
‫يستخدم‬ ‫لل‬ (‫)جمع‬ ‫بينما‬ ‫الكلمة‬ (‫)أحب‬ (‫)مفرد‬
After substitutions the two messages are aggregated to be:
‫ضمير‬ ‫المتكلم‬ (‫)نحن‬ ‫يستخدم‬ ‫لل‬ (‫)جمع‬ ‫بينما‬ ‫الكلمة‬ (‫)أحب‬ (‫)مفرد‬
1st person (we) is used for (plural) while (like) is (singular)
The second example indicates the case of violation of more than one constraint, the aggregation
of negative feedback messages is presented to the student as shown in Figure 7, where the student
is informed that he/she violated the plural ‫جمع‬ and female ‫مؤنث‬ constraints. It is worth to
mention that, in the aggregation process, we eliminate the repetition of words to produce a
readable message.
Figure 8. An example question with combined constraints
8. STUDENT LEARNING LEVEL

48
CBM represents the short-term student model where the assessment process is based on student
response to a specific question. That model stores the satisfied constraints, violated constraints,
and the number of trails for each question. To assess the learning level of the student in a specific
lesson, we have to consider the student responses to all questions in that lesson. Karaci proposed
ITS that is based on the overlay student model and CBM [6]. He considered each constraint as a
separate problem and calculated MYCIN certainty factor for each one. That is based on grouping
positive and negative points for constraint's satisfaction and violation respectively. In addition, he
considered the trail number in estimating the learning level using a fuzzy logic decision system.
Fuzzy logic was introduced by Zadeh and has been used in different fields implied educational
grading [28]. A Fuzzy logic decision system is based on representing imprecise knowledge. It
starts by fuzzifications of numerical inputs and mapping it to membership functions which is a
range of inputs. This means the inputs are converted to verbal variables according to their
respective values. Different forms of input membership functions are used such as; triangles,
trapezoids, and Gaussian functions. Then some rules are proposed and evaluated using fuzzy
reasoning. Then the result of the rules is combined and defuzzified.
In AGTrainer system we consider the satisfied constraints in addition to the number of trails to
assess student's learning level. Moreover, the constraint's depth level in the hierarchal structure is
also considered as an indication of the difficulty level of each constraint. We consider all these
parameters in assessing the student learning level using fuzzy logic.
8.1. Fuzzy logic input–output variables and fuzzy sets
Two input variables are utilized in the fuzzy logic decision System; the constraints covering and
trail numbers. The output variable is the learning level that represents a long-term student model.
For each lesson, there is a set of constraints that must be satisfied in order for the student's
learning level to be high. The same constraints can be used frequently with various questions. For
this, we calculate each constraint satisfaction percentage compared to times the possibility of
application.
To consider the hierarchal depth level in the long-term evaluation process, we set different
satisfaction percentages for each constraint according to its hierarchal depth level. Satisfaction
percentages are set to 70%, 60%, 50% for first, second, and third depth levels respectively. For
constraints that deal with exceptions, the satisfaction percentage level is set to 40%. These
percentages are taken into account when calculating the number of constraints that were covered
by the student in his solution to the problems.
The fuzzy sets for covering as an input variable are indicated in Fig. 3. It is an example of the
first lesson that deals with demonstratives. Six constraints from different grammatical skills are
required to check a student's answer to lesson questions. The fuzzy sets are defined as three
trapezoids membership functions. The fuzzy sets and boundary values for the constraints
covering the input variable are given in Fig. 9 and Table 1 respectively.
The second input is the trail number where more trail means that the student gets an explanation
of his mistakes, which affects the calculation of his learning level. The fuzzy sets for the trail
input variable and boundary values are shown in Fig. 10 and Table 2 respectively. The output
variable is the learning level which is defined using four fuzzy which are indicated in Table 3
The inference rules to define the learning level in the AGTrainer system are shown in Table 4.
All rules are evaluated in parallel using fuzzy reasoning. The most commonly used Mamdani’s
fuzzy inference mechanism (Mamdani, 1974) and the center of gravity (COG) defuzzification
techniques are applied.

49
Figure 9. Fuzzy sets for covering input variable.
Table 1. Fuzzy sets and boundary values for Covering input variable
Fuzzy set Limits
Low 0 ≤ covering ≤ 2
Medium 1.5 ≤ covering ≤ 4.5
High 4 ≤ covering ≤ 6
Figure. 10. Fuzzy sets for trail input variable.
Table 2. Fuzzy sets and boundary values for trail input variable
Fuzzy set Limits
Low 0 ≤ covering ≤ 30
Medium 20 ≤ covering ≤ 60
High 50 ≤ covering ≤ 86
Figure. 11. Fuzzy sets for learning level output variable.
Table 3 Fuzzy sets and boundary values for Learning level output variable

50
Fuzzy set Limits
Poor 0 ≤ covering ≤ 0.45
Acceptable 0.3 ≤ covering ≤ 0.75
Good 0.6 ≤ covering ≤ 0.9
Very-Good 0.75 ≤ covering ≤ 1
Table 4 Rule base used in the fuzzy logic decision system
Low Medium High
Low
Poor
Good Very-Good
Medium Acceptable
Good
High Low
Fig. 12 System interface that indicates the student learning level
The output is the learning level that is presented to the student at the end of each lesson. Fig. 12
shows the system interface that indicates the student learning level in percentage which is 93.95%
with the corresponding verbal value "very good".
9. EVALUATION
The evaluation process targets the system effect, and satisfaction of the students and the teachers
with AGTrainer. In addition, we conduct an experiment to get the learning level using AGTrainer
with different inputs values for the fuzzy system.
9.1. System Effect
To assess the effect of AGTrainer in tutoring the students, 18 volunteer 4th-grade students at the
primary level in Egypt were asked to get trained using the system as much as they wished for a
period of two weeks. Their performance was recorded in terms of the violated and the satisfied
constraints. For each student, we computed the average percentage of violated constraints the nth
time each constraint was applicable. The global averages were then computed across all the
students. The resulting power curve is depicted in Figure 13. The tutoring effect of AGTutor is
obvious due to reducing the average percentage of violated constraints with learning. Power
curves are increasingly used for evaluating ITSs provided that the assessed variable is represented
by a set of constraints and that its value should be improved by learning [28].
9.2. Satisfaction
Trails
Covering

51
A satisfaction questionnaire formed of eight questions was prepared in order to assess the
satisfaction of the students and the teachers with AGTrainer. We asked the respondents to
provide their answers based on a Likert scale ranging from one to five, such that one refers to
extreme dissatisfaction and five refers to the reverse. We computed the average for each
respondent and then computed the global average. We obtained a value of 4.2 and 4.3 for the
teachers and students respectively indicating a very high degree of satisfaction of both teachers
and students with the capabilities and features of AGTrainer. We also confirmed the credibility of
the questionnaire results using Cronbach's alpha as we obtained a value of α equal to 0.73.
9.3. Learning Level Experiment
The percentages of satisfaction of each constraint are considered with the trail number to
determine the learning levels for a number of students using the fuzzy logic decision system.
Different covering and trail values are indicated in table 5. We consider the demonstratives lesson
where there are six constraints with different depth levels and 43 questions with the possibility to
repeat the attempt to answer each question twice. We can notice that when trail number increases
the learning level decrees even the constraints coverage is high.
10. CONCLUSIONS
This paper presented AGTrainer, an ILTS for tutoring Arabic grammar skills to grade-four
students at the primary stage in Egyptian schools. In AGTrainer, the basic different grammar
skills are categorized and represented hierarchically within each category. Additionally,
AGTrainer utilizes CBM to model domain knowledge using a set of constraints corresponding to
the various skills. The hierarchical domain structure is used as a mechanism for efficiently
checking constraints which facilitates diagnosing student errors and their origins. The system
provides the student with parametrized feedback that indicates the correct and wrong parts of the
student's answer.
The short-term student model is based on defining satisfied and violated constraints. The long-
term model is proposed based on the short model information along with lesson interactions. The
fuzzy logic decision system is integrated to deal with uncertainty in the determination of the
student long term model or learning level model for each lesson. The system effect and
satisfaction of the students and the teachers are considered in the evaluation process. In addition,
an experiment to get the learning level is conducted based on different inputs values for the fuzzy
system.
Each question in the database is defined by its header, statement, and available choices. The
header defines the lesson it belongs to and the grammatical skills it addresses. The difficulty level
of the header is based on the number of grammatical skills it tackles. The statement determines if
the question is subject to grammatical exceptions or not which define the difficulty level of the
statement.
Table 5 Experimental study on fuzzy logic decision system

52
Number of
covered
constraints
Tail number
Learning
level
1 8 0.187
1 46 0.187
1 80 0.187
2 8 0.75
2 43 0.524
2 80 0.2
3 4 0.75
3 49 0.52
3 80 0.168
4 4 0.76
4 25 0.58
4 80 0.22
5 13 0.914
5 44 0.75
5 80 0.75
6 12 0.915
6 42 0.75
6 86 0.75
Fig. 13. Power curve depicting the tutoring effect of AGTrainer.
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AUTHORS
Nabila Khodeir is a researcher in the Informatics department at the Electronics Research Institute, Cairo,
Egypt. Her research interests include intelligent tutoring systems, user modelling and natural language
processing. She earned her Ph.D. and ME from the Electronics and communications department at Cairo
University.

CONSTRAINT-BASED AND FUZZY LOGIC STUDENT MODELING FOR ARABIC GRAMMAR

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