=Paper=
{{Paper
|id=Vol-1427/paper7
|storemode=property
|title=Binary Relations in Educational Ontologies
|pdfUrl=https://ceur-ws.org/Vol-1427/paper7.pdf
|volume=Vol-1427
}}
==Binary Relations in Educational Ontologies==
https://ceur-ws.org/Vol-1427/paper7.pdf
Binary Relations in Educational Ontologies
Seremeti Lambrini Aggelopoulou Nikolitsa Pierrakeas Christos Kameas Achilles
Mathematician, Researcher Mathematician, Researcher, Lecturer, Dept. of Business Associate Professor, School
Hellenic Open University Hellenic Open University Administration, of Science and Technology,
(HOU) (HOU) Technological Educational Hellenic Open University
+30 2610 367 963 +30 2610 367 963 Institute (TEI) of Western (HOU)
seremeti@cti.gr naggelop@eap.gr Greece and +30 2610 367 735
Hellenic Open University kameas@eap.gr
(HOU)
+30 2610 367 730
pierrakeas@eap.gr
ABSTRACT conceptualization is based on subjective statements of the kind
Educational ontologies are classified into οnthologies of Student (subject, verb, object) triples that experts provide, it describes the
Learning Outcomes (SLO), Learning Objects (LO) and Cognitive basic concepts of each CoD and the relations among them
Domains (CoD). In contrast to the conceptualization and between concepts. The classification of these statements in a
implementation of SLO and LO ontologies, based on standards specific ontology could help to avoid polysemy and ambiguity of
available in the literature, the CoD ontologies involve subjectivity relations used to describe CoD. These relations are binary and
derived from the analysis of basic concepts of each CoD and their formal representation by means of ontology will restrict the
relational expressions that experts use in order to associate these use of inappropriate definitions of relations during the
basic concepts. This subjectivity can create inconsistent implementation of CoD ontologies.
ontologies. The aim of this paper is to establish a set of binary Several existing ontology population techniques able to extract
relations to be used in the official representation of CoD. These arbitrary semantic relations from text corpora focused exclusively
relations consist of triples (subject, verb, and object) and can be in binary relations. Ontologies present binary relations (called
classified into a Binary Relation (BR) ontology. properties in OWL).
In this paper, we conceptualize an ontology Binary Relations
Keywords (BR), which officially represents the relations needed to describe
Educational Ontologies, Binary Relations CoD concepts, under the HOU framework. The ultimate goal is to
provide a minimum set of binary relations that are necessary to
1. INTRODUCTION implement CoD ontologies. In this way, experts should restrict to
In the last ten years technology offers opportunities to the proposed binary relations in order to conceptualize CoD.
Universities to reconsider how to extend the teaching, to students The remainder of the paper is organized as follows: Section 2
beyond the traditional teaching and not limited by boundaries. explains the need for formally describing relational expressions
Hellenic Open University (HOU) aims to bring together leading used in CoD’s description. Section 3 focuses on binary relations
technologies and pedagogical approaches to implement e-learning by giving their mathematical definition and their usage in
environments, specialized to the needs of adult users with ontology engineering and Section 4 describes related work for
different knowledge background, skills and biases. In the binary relations. Section 5 describes the main points of BR
realization of this objective, ontologies play a key role. They are ontology engineering, and Section 6 concludes the paper.
machine readable representations of the content of educational
material, users’ profiles, and taxonomy of learning outcomes,
which enables to the creation of individualized learning paths [1]. 2. COGNITIVE DOMAIN (CoD)
For this purpose the educational ontologies constructed for HOU ONTOLOGIES
[2], [3], [4], [5], [6], can be divided into ontologies for Learning Initially, domain experts define the basic concepts of cognitive
Objects (LO), ontologies for Student Learning Outcomes (SLO) domain and create relationships between basic concepts of CoD
and ontologies for Cognitive Domains (CoD). Regarding the ontologies. Afterwards, they develop concept maps based on the
engineering of SLO and LO ontologies, problems do not exist. concepts and relationships that have defined. [6]
The conceptualization of LO ontologies is based on standards
available in the literature such as the official description of IEEE These relations are been expressed through individual relations,
LOM standard [7]. Tthe conceptualization of SLO ontologies is known as properties. Properties are divided as object and datatype
based on the Bloom’s taxonomy [8], a widely accepted taxonomy properties. Datatype properties link an individual to a specific
of learning domains that is often used in the design of educational value, namely an XML Schema datatype or an RDF literal. [2]
processes. −1
More specifically, the pair-wise inverse properties X and X
In contrast, when designing CoD ontologies, because their are used to declare a parent-child relation between two concepts.
They can be a) functional, meaning it is a property that can have
Copyright © 2015 for the individual papers by the papers' authors.
Copying permitted only for private and academic purposes. only one (unique) value y for each instance x, b) transitive,
meaning that if a pair (x,y) is an instance of P, and the pair (y,z) is
In: A. Bădică, M. Colhon (eds.): Proceedings of the 2015 Balkan also instance of P, then we can infer the pair (x,z) is also an
Conference on Informatics: Advances in ICT
45
instance of P or c) symmetric meaning if the pair (x,y) is an criterion, which is described in subsection 5.2, of the extracted
instance of P, then the pair (y,x) is also an instance of P. The binary relations. This can facilitate ontology experts and domain
instance property connects class with its members, whilst Y experts to avoid mistakes in coding CoD.
correlates any individual with a certain modifier. Finally, to define
The resulting ontology can also promote interoperability of
the particular relation of a concept with a reserved keyword, the Z
educational ontologies and support automated reasoning in e-
property is used.
learning environments.
Figure 1 presents as an example, based on a part of the concept
map that has been created for the cognitive domain CoD: PLI30
3. BINARY RELATIONS
as we can see in [6].
The relational expressions that domain experts use to provide the
This conceptual map represents 32 identified basic relevant formal description of a CoD as we saw previously are sentences
concepts (see the nodes of Fig. 1) and 5 relations (see the edges of that simply indicate a relation between two basic concepts of the
Fig. 1; for example, “Associative Network includes Node”). same cognitive domain, without any further information. These
sentences are typically described by binary relations.
3.1 Definition of Binary Relations
We will give a formal definition for binary relation. Binary
relations are important, since relations of arity greater than 2 can
be studied in terms of binary relations.
Mathematically speaking, if X and Y are non-empty sets, a
binary relation from X to Y is a subset R ⊆ X × Y . We write
( x, y ) ∈ R or xRy to denote that ( x, y ) ∈ X × Y and we
say that X is related to Y through R . For example, in the
accounting CoD, the natural language expressions “Slot
represents Concept”, “Slot represents Object”, “Slot represents
Event” can be formulated as the binary relation
R = {represents} from the set X = {Slot} to the set
Y = {concept , object , event} . For some binary
−1
relation R ⊆ X × Y , we can define its inverse R ⊆Y×X ,
−1
such that yR x ⇔ xRy .
An interesting point to consider about binary relations is their
composition which is defined as follows: let R ⊆ X × Y and
S ⊆ Y × Z binary relations. Their composition is a binary
relation S oR ⊆ X ×Z defined by
x ( S o R ) z ⇔ ∃y ∈ Y such that xRy and ySz .
Figure 1: Part of the concept map expressing concept “Frame We are also interested in certain properties satisfied by these
Systems”
relations, such as: (a) reflexivity ( xRx for all x in X ), (b)
It is necessary to formalize the terms of relations (verbs), which
are binary relations, in a rigorous machine readable format, with symmetric ( xRx′ implies x′Rx for all x, x′ in X ), and (c)
the aim of understanding the knowledge expressed by domain transitivity ( x′′Rx′ and x′Rx imply x′′Rx for all x, x′, x′′
experts in concept maps. There are several ontology development
tools that implement concept model ontology in different in X ).
languages. Ontology experts can apply Protégé [9] to convert a
The main point is that to uniquely describe a relation R , the
conceptual map produced by the experts into a formal model by
using the formal OWL language. To evaluate the graphic collection of all ordered pairs ( x, y ) such that x is related to
representations of the concepts of the course through the concept
maps in OWL.Then, they can use off-the-shelf automated y by R , must be listed.
reasoning tools.
3.2 Binary Relations in Ontologies
Note that the same natural language relation (verb) can be used by The relations contained in ontologies are usually binary. They
experts to connect different concepts in the same field or in have two arguments; the first is called the domain of relation, and
different cognitive domains. One way to develop consistency and the second is called range. These relations are mainly related to
clear standard definitions of relational expressions used in the classes of the ontology and usually initialized using the
educational ontologies concerning CoD, is to develop an ontology knowledge from the domain representing the ontology. For
providing definition and classification, according to a certain example, to express that “the x processor executes the y software”,
46
the relation “executes” should be designed and should have a 5. BR ONTOLOGY ENGINEERING
class “Processor” as the domain and a class “software” as the The main questions arising when engineering the ontology of
range. On occasion, the same relations used to relate classes, are binary relations used in the HOU context are: Which are the
also used to express attributes of specific classes. These are also intended uses of the BR ontology? Which are the entities that
the binary relations, where domain is a certain class and their require a unique categorization? According to what criterion?
range is a datatype, such as string, number, etc. What kinds of binary relations are used in the literature? What
In the case of n-ary relations, that is, relations which link an kind of relations can we formally describe? What are the
individual to more than one individual or values are represented properties of the described relations? The BR ontology is
by creating an intermediary entity that serves as the subject for the engineered according to commonly accepted engineering
entire set of all relations [9]. In our approach, we refer only to methodologies, based on specification, conceptualization,
binary relations, which are the most common type of relation implementation and evaluation phases, where all the questions
mapping a single subject to a value. stated above are answered [10].
4. RELATED WORK 5.1 Specification of the BR Ontology
The most common type of relation is a binary relation that The CoD ontologies in the framework of HOU are designed to
connects two concepts. Discussions for binary relations have been provide reference points for the expression of the basic concepts
researched in [9], [11], [12], and [13]. The problem of of each cognitive object in a machine readable format. Their
representing a binary relation is not new. construction is based on natural language statements gathered by
In 2014 [9] Vinu, Sherimon, Krishnan and Tarkoni discuss the the domain experts, which are expressed in sentences of the form
issues in modelling n-ary relations. They support that the main (subject, verb, object). These sentences of the kind “A -relation-
elements of ontology are concepts, relations and individuals. W3C B” (where A and B are concepts belonging to the same CoD
provides several patterns to represent n-ary relations. They ontology and “relation” symbolize connects for associating these
examine the issues in n-ary relations, the concept of RDF concepts) can be considered as binary relations between semantic
reification and provide an appropriate pattern to represent the n- concepts in a vocabulary that is specified for a certain cognitive
ary relations. The examples of n-ary relations are taken from domain.
Seafood Ontology they developed. In contrast to our work, they Our task is to develop a minimum set of coherently define binary
focus on the issues of n-ary relations. It explains the ontology relations involved in the formal representation of cognitive
languages followed by the n-ary relation, the issues in n-ary domains through ontologies and the scope to capture the relations
relations,reification and its drawbacks and outline an appropriate currently expressed in the context of the CoD ontologies. This is
pattern to represent the n-ary relations. important, since (a) the inability to distinguish relational
Welty and Fikes in [11] discuss the standard approach to deal expressions which are close in meaning, results in an erroneous
with relationships that change over time, such as OWL that are reasoning process, and (b) the polysemy of relational expressions
biased towards binary relations. Their approach involves treating impedes interoperability between educational ontologies
entities in the domain of discourse as four dimensional with developed in the HOU.
temporal parts that participate in the relation, corresponds to and
stablished ontological position in analytical metaphysics called 5.2 Conceptualization of the BR Ontology
perdurantism. In the literature, binary relations are distinguished in the following
Martin and Benard in [12] propose an ontology design pattern for three kinds. The categorization of binary relations based on their
leading knowledge to represent knowledge in a more normalized domain and range.
way. This pattern is: “using binary relation types directly derived
from concept types, especially role types or types of process with • class, class : for example, statements such as the
nominal expressions as names”. It provides an ontology deriving class “Slot” represents (relation) the class “Object” or
relation types from concept types; this derivation reduces having the class “Slot” represents (relation) the class “Event”.
to introduce new relation types. It explains, formalizes and
illustrates the different parts of ABP (advocated best practice) and • ins tan ce, class : for example statements such as
relates this practice to other ODPs (Ontology Design Patterns).
the instance “current assets” includes (relation) the class
In contrast to our work, in [13] Banek, Juric and Skocir introduce “requirements” or the instance “current assets” includes
an unsupervised method for learning domain n-ary relations from (relation) the class “inventories” and
Wikipedia articles. They claim that providing ontologies with n-
ary relations instead of the standard binary relations built on • ins tan ce, ins tan ce : for example, statements
subject –verb- object paradigm results in preserving the initial
context of time, space, cause, reason that otherwise would be lost. such as the instance “unit of manure” contains (relation)
They discuss the use of n-ary relations for discovering richer the instance “80 Kg N” , since they cannot be
semantic context, the relation extraction process and the considered as sets of objects.
evaluation of this approach.
5.2.1 BR Ontology
Our work is consistent with Martin and Bernard in [12]. We By following our ontology engineering methodology [6], we
attempted to define the relations created from concept maps as constructed an ontological model for the relations of the cognitive
binary relations in order to enable us to better construction of domains in HOU. The BR ontology was constructed with the aid
educational ontologies. of Protégé based on the most recent version of the Web Ontology
Language (OWL) and W3C standard, OWL 2.
47
The main classes of the BR ontology (see in Figure 2) are:
• the class “Relation”, which is divided into three
different subclasses: “ClassClassRelation”,
“ClassInstanceRelation” and “InstanceInstanceRelation”
illustrates the main types of relations. Specific relations
such as “Contains”, “Involves”, “Uses”, “Determines”,
etc. are subclasses of the class “ClassClassRelation”.
• the class “DomainRange”, which is divided into two
subclasses: “Class” and “Instance”, and
• the class “CognitiveObject” Figure 4: The binary relation “represents” from the BR
ontology
This structure categorizes the relation “Represents” as a binary
relation with domain and range classes. It corresponds to a
specific cognitive domain and has properties, such as transitive,
functional and symmetric. Synonyms and description of its
semantics are also provided.
5.2.3 Description of Instances in BR ontology
The natural language statement
“knowledge_representation_language_represents_sentence_of_
propositional_logic” is an instance of the class “Represents” of
Figure 2: The class hierarchy of the BR ontology the BR ontology. Although this statement is understandable by
humans, it has no meaning for a machine. Using the structure of
5.2.2 Description of Properties in BR ontology the BR ontology, the meaning of this statement can also become
The various types of interaction among ontology concepts are machine readable. We can see the instance
expressed through respective relations, known as properties (see “knowledge_representation_language_represents_sentence_of_
in Figure 3). propositional_logic” in Figure 5.
We have defined six (6) object properties and five (5) datatype
properties. More specifically, the class “Relation” relating with
the class “CognitiveObject” with the object property
correspondsTo, the class “InstanceInstanceRelation” relating
with the class “Instance” with the object property
hasDomainInstance etc. The data property isSymmetric determine
if the “Relation” is symmetric or not.
Figure 5. The statement “Knowledge representation language
Represents Sentence of propositional logic” as an instance of
the class “Represents”
According to the structure of the BR ontology, the natural
Figure 3: The properties hierarchy of the BR ontology
language statement “Knowledge representation language
The structure of the BR ontology, conceptualizing a specific Represents Sentence of propositional logic” is conceptualized as
binary relation is depicted in Figure 4. an instance of the class “Represents”.
5.3 Implementation of the BR Ontology
The idea behind the structure of the BR is that the various
statements considered as instances of the relation can be
considered as a binary relation, and are categorized depending on
the domain and range. For example, an instance of the relation
“Determines” implemented in Protégé [14] is depicted in Figure
6.
48
Figure 11: Competency question answers if the relation
“uses_for_resolution” is Functional
The second example is for a ClassInstanceRelation the relation
represents. In the next Figures we can see the individual:
“knowledge_representation_language_represents_sentence_of_
propositional_logic”. This individual hasDomain:
knowledge_representation_ language (Figure 12), correspondsTo:
pli31_CoD1 (Figure 13), hasLabel: αναπαριστώ (Figure 14),
Figure 6. An instance of the class “Determines” implemented hasRange: sentence_of_propositional_ logic (Figure 15) and
in Protégé isSymmetric relation (Figure 16).
The BR ontology can be found at
http://ontologies.eap.gr/webprotege/#Edit:projectId=4be4a475-
b9ff-4b46-ab40-b884c0bf18fa.
5.4 The BR Ontology
Figure 12: Competency question which answers what is the
The BR has been assessed, using the same competency questions,
domain of the relation “represents”
as in the specification phase. The questions answered concern
finding the inverse of a relation, its instantiations, its domain and
range, etc.
We present two examples of competency questions submitted to
BR. The first example is for an InstanceInstanceRelation the
relation usesForInstanceInstance. In the next Figures we can see Figure 13: Competency question answers to what cognitive
the individual domain belongs the relation “represents”
“backward_chaining_uses_for_resolution_conjuctive_normal_for
m”. This individual hasDomain: backward_chaining (Figure 7),
correspondsTo: pli31_CoD1 (Figure 8), hasLabel: χρησιµοποιεί
(Figure 9), hasRange: conjuctive_normal_form (Figure 10) and
isFunctional relation (Figure 11).
Figure 14: Competency question answers which is the label of
the relation “represents”
Figure 7: Competency question which answers what is the
domain of the relation “uses_for_resolution” Figure 15: Competency question answers what is the range of
the relation “represents”
Figure 8: Competency question answers to what cognitive
domain belongs the relation “uses_for_resolution” Figure 16: Competency question answers if the relation
“represents” is Symmetric
6. CONCLUSION
In this paper we aim at systematically representing the binary
Figure 9: Competency question answers which is the label of relations involved while coding CoD ontologies in the HOU
the relation “uses_for_resolution” context, in order to avoid polysemy (the interpretation of a
specific relation must be clear and unambiguous) and homonymy
(different nomenclature may refer to the same relation).
To this end, we have developed the BR ontology which is used to
solve interoperability issues, as well as a reference point from
Figure 10: Competency question answers what is the range of where a minimum set of binary relations, that are used in machine
the relation “uses_for_resolution” readable relational expressions of cognitive objects are extracted.
49
7. ACKNOWLEDGMENTS of the 14th IEEE International Conference on Advanced
This research described in this paper has been co-financed by the Learning Technologies, 2014, pp. 716-718.
European Union (European Social Fund – ESF) and Greek [7] D. Roy, S. Sarkar, S. Ghose. A comparative study of learning
national funds through the Operational Program "Education and object metadata, learning material repositories, metadata
Lifelong Learning" of the National Strategic Reference annotation & an automatic metadata annotation tool. In:
Framework (NSRF) (Funding Program: “HOU”). Joshi, Boley, Akerkar (Eds.), Advances in Semantic
Computing, 2010, pp. 103-126.
8. REFERENCES [8] D.R. Krathwohl. A revision of Bloom’s taxonomy: an
[1] P. Monachesi, K. Simon, E. Mossel, P. Osenova, L. overview. Theory Into Practice, Vol. 41, No. 4, 2002, pp.
Lemnitzer. What ontologies can do for eLearning. 212-264.
Proceedings of the IMCL International Conference on [9] P.V. Vinu, P.C. Sherimon, K. Reshmy, S.T. Youssef. Pattern
Mobile and Computer aided Learning, 2008, pp. 1-10. representation model for n-ary relations in ontology. Journal
[2] A. Kouneli, G. Solomou, C. Pierrakeas, A. Kameas. of Theoretical and Applied Information Technology, Vol. 60,
Modeling the knowledge domain of the Java programming No. 2, 2014, pp. 231-237.
language as an ontology. Proceedings of the International [10] R. Iqbal, M. Murad, A. Mustapha, N.M. Sharef. An analysis
Conference on Advanced Learning Technologies, LNCS, of ontology engineering methodologies: a literature review.
Vo. 7558, 2008, pp.152-159. Research Journal of Applied Sciences, Engineering and
[3] G. Solomou, A. Kouneli, A. Kameas. Using ontologies for Technology, Vol. 6, No. 16, 2013, pp. 2993-3000.
modeling knowledge domains in distance learning. [11] Welty, C., Fikes, R., & Makarios, S. (2006, May). A reusable
Proceedings of the 6th International Conference in Open & ontology for fluents in OWL. In FOIS (Vol. 150, pp. 226-
Distance Learning, 2011, pp. 728-741. 236).
[4] I. Panagiotopoulos, A. Kalou, C. Pierrakeas, A. Kameas. An [12] Martina, P., & Bénard, J. Directly deriving binary relation
ontology-based model for student representation in types from concept types, especially process or role types.
intelligent tutoring systems for distance learning. Artificial
Intelligence Applications and Innovations 2012, Vol. 381, [13] Banek, M., Jurić, D., & Skočir, Z. (2010, January). Learning
pp.269-305. semantic n-ary relations from Wikipedia. In Database and
Expert Systems Applications (pp. 470-477). Springer Berlin
[5] A. Kalou, G. Solomou, C. Pierrakeas, A. Kameas. An Heidelberg.
ontology model for building, classifying and using learning
outcomes. Proceedings of the 12th IEEE International [14] J.H. Gennari, M.A. Musen, R.W. Fergerson, W.E. Grosso,
Conference on Advanced Learning Technologies 2012, M. Crubezy, H. Erikson, N.F. Noy, S.W. Tu. The evolution
pp.61-65. of Protégé: an environment for knowledge-based systems
development. International Journal of Human-Computer
[6] N. Aggelopoulou, C. Pierrakeas, A. Artikis, D. Kalles. Studies, Vol. 58, No. 1, 2003, pp. 89-123.
Ontological modeling for intelligent e-learning. Proceedings
50