Contextual Ontologies for the Semantic Web – An Enabling Technology

Ma. Laura Caliusco Ma. Rosa Galli Omar Chiotti CIDISI Research Center

UTN – FRSF mcaliusc@frsf.utn.edu.ar

INGAR CONICET

mrgalli@ceride.gov.ar

INGAR CONICET

chiotti@ceride.gov.ar

Abstract

To realize the goals of the Semantic Web, there is a need of working on approaches focused on the machine processing semantics and approaches to systematically define conceptual models about data semantics. Ontologies are a primary means to deploy the Semantic Web vision, but managing the context-dependent semantics remains an open problem. In this paper we discuss the role of contexts on the Semantic Web and, present a contextual ontology modeling language called C-OML.

1. Introduction

With the purpose of making the current web evolve into the Semantic Web, enormous effort has been made in defining and developing various supporting standards and technologies [1][6]. Some of this effort is carried out by the World Wide Web Consortium (W3C) [18]. But, while standardization can be a reason why adoption of a new technology succeeds, another requirement is easy to use[8]. So, in order to facilitate the adoption of the enabling Semantic Web technologies, a bridge should be created. This could be achieved by using the Model Driven Architecture (MDA) initiative [12].

Although, ontologies play an important role as an enabling technology for the Semantic Web they do not solve the semantics problem at all. Taking into account that the meaning of ontology concepts depends basically on their context, contextual ontologies emerge as an approach for allowing semantic interoperability.

The goal of this paper is to present a metamodel for modeling explicit and formal contextual ontologies based on the MDA initiative. First, we examine the role of contextual ontologies on the Semantic Web area. Then, we show how ontology modeling languages fit into the MDA initiative. Following, we present the main elements of a modeling language called C-OML. Finally, we discuss our conclusions and future works.

2. The role of context on the Semantic Web

To view how the context influence the understanding of the information published by a web site we have to considerer the following aspects: sites often publish a piece of data that is true at the time of publication, the temporal

qualification being implicit; how things are may depend on the site's perspective on them; data published on a site can be partially represented along an implicit spatial dimension. So, if we want to aggregate data from web sites without misunderstanding, we have to make the context explicit. So, the role of contexts on the semantic web is to factor the differences, like the previously described one, between different sites when aggregating data from them. In the next section we discuss how to integrate contexts and ontology in order to achieve semantic interoperability within Semantic Web area.

3. Contextual ontologies and semantics An approach to overcome semantic heterogeneity in the

Semantic Web is to define an ontology [1]. However, to achieve data integration between web sites it is necessary to make the context explicit. So, in this section, we show how contexts could be integrated with ontologies to achieve semantic interoperability in the Semantic Web.

3.1. The notion of ontologies It is possible to find several definitions of ontologies in

the literature [8] [10] [4] [13] [17]. From these definitions, we can identify some essential aspects of ontologies which can be formalized as follows:

Definition 1. An ontology Oi is a 4-tuple <Ti, Pi, Ri,Ai> where:i identifies the domain or source an ontology is associated with, Ti is a set of terms tj of Oi, Pi is a set of properties of terms tj Ti, Ri is a set of relations between tj and tx Ti, Ai is a set of axioms that characterizes each relation of Ri

3.2. The notion of contextual ontologies Taking into account different definitions of context [7]

[3] [15], we can define a context as a collection of relevant conditions or assumptions that make a situation or entity unique and comprehensible. That entity or situation depends on the domain we are. The context definition could be formalized as:

Definition 2. Let J be a set of indexes j , a context CjJj can be defined as a 3-tuple <cj, Dj, Oi,j>,

where: cj is the unique identifier of context j, Dj is a set of assumptions about context j and Oi,j represents ontology i within context j.

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3.2.1. Context mapping

The advent of the Semantic Web has increased the need for efficient and flexible mechanisms to provide semantic mapping among ontologies [14]. The ontology mapping is a well known problem in knowledge engineering [11]. However, if we represent the semantics using a contextual ontology, the mapping has to be made between contexts. That is called context mapping.

A context mapping allows us to state that a certain property holds between elements belonging to different ontologies defined in different contexts [2]. Then, a context mapping is defined by bridge rules as linking rules between contexts [3]. Following, we define context mapping and bridge rules.

Definition 3. A context mapping tsM , can be defined as a 3-tuple <cs, ct, BR> where: cs identifies the context source, ct identifies the context target and BR represents the set of bridge rules that map an element from a source context to elements of a target context.

Mappings are directional, i.e., Ms,t is not the inverse of Mt,s. A mapping Ms,t might be empty [2]. That means that there is no relation between both contexts.

Definition 4. A bridge rule BR can be defined as a 3-tupple Ree ts ,, where: se is an element from source context, te is an element from target context, and R is a rule operator between elements.

A bridge rule is formed as cs:es ct:et where ei and ejare elements from a source context (cs) and a target context (ct) respectively. Examples of bridge rules are: 1) office-equipment:pen school-equipment:penmeans that the concept pen within office-equipment context is similar to the concept pen in school-equipment context. 2) informatics:mouse biology:mouse means that the concept mouse in informatics context is disjoint with the concept mouse within biology context. 3) e-commerce:businessdocument * business:transactionmeans that a businessdocument in e-commerce context, is a compatible concept with transaction in business context. 4) entertainment:artist television:actor means that the concept artist in entertainment context is more general than the concept actor in television context.

4. Contextual ontology modeling languages and the MDA initiative

The objective of this section is to show how contextual ontology modeling languages fit into the MDA (Model-driven architecture) initiative [12]. This initiative is a standard produced by the Object Management Group (OMG), and uses abstract high level models based on a

four-layer architecture. The M3 layer contains the meta-meta-model. The M2 layer contains meta-models. A meta-model defines the structure of a set of models. UML and UML profiles are meta-models. The M1 layer contains models. A model is in conformance with some meta-models. The M0 layer contains the data to be modelled [5].

UML has been proposed to model ontology since UML class diagram can be used to express concepts in terms of classes and relationships among them. But, UML itself does not satisfy needs for representation of ontology concepts and properties that are borrowed from Descriptive Logic and that are included in ontology specification languages [4]. So, other visual modeling language have been defined. However, the main disadvantage of these languages is that they propose to define a context by using annotations that are not easily transformed into a machine processable language.

In short, the need for a dedicated contextual ontology modeling language stems from the observation that a contextual ontology cannot be sufficiently modelled with existing modeling languages. This new modeling language resides in the M2 layer of the MDA initiative and derives from MOF. In the next section we describe the elements of the language metamodel.

5. Contextual ontology modeling language

In order to define the proposed metamodel we have imported some elements from the Core::Abstractions and Core::PrimitiveTypes Packages of the UML 2.0 specification [16]. Furthermore, our metamodel is augmented with OCL constraints with specific invariants that have to be fulfilled by all models that instantiate it.

The metamodel of the C-OML language has been architected with the modularity design principles in mind. So, the metamodel constructs were grouped into packages according to the elements needed to define a contextual ontology.

5.1 Ontology package Classes and associations of the Ontology Package are

shown in the class diagram of Figure 1. The main component of this diagram is the Ontology class that includes definition of concepts used to describe a specific domain. This class is associated with the OntologyElements class, which groups the objects of an ontology metamodel. An ontology could contain definitions whose meanings are defined in other ontologies (imports association). The prior_Version association identifies the referred ontology as a prior version of one ontology. Furthermore, an ontology is described by a set of features represented by the Feature class. Finally, each ontology and its elements could be described by a comment represented by the Documentation class.

R

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NamedElement

name : Stringnamespace : URIreference

(from Kernel)

Element(from Kernel)

Comment

Body : String(from Kernel)

annotatedElement

DocumentationType : String

1

OntologyElements

id : String(from Kernel)

Ontology

0..10..1

prior-Vers ion

0. .n0. .n1..n0..n

ontology1..n

ownedElement0..n

0..n0..n

DataType(from DataType)

FeatureValue : Object0..n0..n

features

1Type

1includes imports

Figure 1. Elements defined in Ontology package.

5.2 Terms and properties package

The metamodel that represents the relation between Property and Term is presented in Figure 2.

ComplexDataType(from DataType)

Simple1type1

OntologyElements

id : String(from Kernel)

ValueSpecification(from Kernel)

Property

1

0..1

specification 1

0..1Instances

non-Relational(from Axioms)

Term0..n 0..1

property0..n

characterizedTerm0..1

11type

0..n+axioms

0..n

Figure 2. Elements defined in Terms and Properties package.

Terms represent a set of concepts and could be simple or complex. Simple terms have literal as their values. Complex terms are composed by simple terms.

Properties describe the features of a term. For example, allowed values, the number of values, and other features of values that a simple or complex term could take.

5.3 Relations package

Relations can be divided into hierarchical relations (is-a and part-of), conceptual relations (synonym and antonym) and particular relations (defined by the ontology designer).

The relations’ metamodel is presented in Figure 3. Terms and Relations classes are associated via the RelationEnd class. An instance of Relations class has to be associated at least with two instances of RelationEnd class, which is indicated with the relations source and target. The RelationEnd contains the information about cardinality, navigability and the role of terms.

One important requirement for ontologies is the ability to structure the relations into hierarchies, i.e., to define sub-relations of a relation (Subrelationof). Furthermore, it

is suitable to define equivalent relations (equivalentto) and inverse relations (inverseof).

Hierarchical Conceptual

Synonym Antonymis-a part-of SimpleRelationCompositeRelation

Particular1..n1..n

0..10..1subrelationof

0..10..1

inverseof0..10..1equivalentto

OntologyElements

id : String(from Kernel)

Attribute

Term(from Terms and Properties)

RelationEndMinCardinality : StringMaxCardinality : StringRole : StringNavigable : Boolean1 1

associatedTerm

1 1

Relational(from Axioms)

Relations

1

1

1

1

source

11

11

target

0..n+axioms

0..n

Figure 3. Elements defined in Relations Package.

5.4 Axioms package

Axioms are properties of relations. They help to constrain the interpretation of concepts and provide guidelines for automated reasoning. In the UML class diagram, axioms could be expressed by OCL [15]. However, describing such constraints may involve writing moderately complex OCL expressions that are not immediately understood by human readers. So, an interesting issue is to model axioms as objects.

Figure 4 represents the metamodel for modeling axioms and their associations with the class Relations.

Axioms

Relational

Symmetric

Transitive

Antisymmetric

Reflexive

OntologyElementsid : String

Functional

PeriodStart : DateEnd : Date

ValueSpecification(from Kernel)

AParticular 0..nValidPeriod

0..n

1+expression

1

Simplenode

OperandSymbol : String

non-Relational

Term(from Terms and Properties)

1

+attribute

1

CompositeNode

1 +symbol1

1..n+expression1..n{ordered}

1

+attributenode

1

Figure 4. Elements defined in Axioms Package.

Axioms can be classified into two subsets: the set of axioms for relational algebra (symmetric, asymmetric, reflexive, transitive and functional), and the set of particular axioms (axioms defined by users). In addition, the metamodel allows us to represent temporal axioms by the Period class. This class represents the period of time in which the axiom is valid.

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5.5 Context package

We associate the Context class with an Ontology class and with one or more Assumptions classes as shown in the class diagram of Figure 5.

NamedElement

name : Stringnamespace : URIreference

(from Kernel)

SimpleContext

Ontology(from Ontology)

CompositeContext

Context1..n 0..1+ownedOntology1..n

+context0..1

0..n0..n

derivedfrom

0..10..1

prior-version

1..n

+composed-by

1..n

ValueSpecification(from Kernel)

Assumption0..n+assumption 0..n

1+specification

1

Figure 5. Elements defined in Context Package.

In addition, a context could be derived from another context (derivedfrom association). Furthermore, contexts dynamically evolve (prior-version association). Finally, a context could be simple or complex. That is, a context could be formed by other contexts.

5.6 Context mapping package

Figure 6 represents classes and associations to model the context mapping, bridge rules and domain space. The DomainSpace class is associated with one or more Contextand Mapping classes.

Finally, we have to define the container of all the above defined elements. This container is the domain space concept.

Element(from Kernel)

NamedElement

name : Stringnamespace : URIreference

(from Kernel)

DomainSpaceDescription

Context(from Context)

1..n

+contexts

1..n

Mapping1..n

+mappings1..n

11

target

11

sourceOntologyElements

(from Kernel)

RuleBridgeRule1..n

+rule1..n

2+ruleElements

2

1+ruleType

1

Equivalence

MoreGeneral LessGeneral

Compatible

Disjunct

Figure 6. Elements defined in Context Mapping Package.

6. Conclusions Semantics representation is a key factor for Semantic

Web success and will bring lots of important applications. While ontologies may play an important role in facilitating integration, they are not the panacea. Taking into account that concepts published by web sites are true or false depending on the context, ontologies and contexts have to

be integrated in order to achieve semantic integration. In this paper we have presented a Contextual Ontology

Definition Metamodel in order to support the semantic modeling process. This metamodel allows us to explicitly model contextual ontologies.

7. Acknowledgments This work has been partially supported by Banco Rio

S.A., Universia Portal, and Univ. Tecnológica Nacional.

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