Making Ontology Relationships Explicit in a Ontology Network

Abstract

The development of ontologies to the Semantic Web is based on the integration of existing ontologies favoring the modularization and reuse of them. These ontologies are used together in complex applications. However, how they are combined is usually hidden in the application code. The lack of an approach for explicitly expressing the way how ontologies are combined for a speci c purpose, leads to think on ontology networks as a new ontology engineering concept. This paper formally de nes the di erent relationships among the networked ontologies and shows how they can be modeled as an ontology network in a case study of the health domain.

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Tom Gruber [ 1 ] has de ned \ontology" as a \formal, explicit speci cation of a shared conceptualization", what means that ontologies are very useful for structuring and de ning the meaning of the metadata terms that are collected inside a domain community.

Nowadays, autonomously developed ontologies emerge quite naturally in different domains (health, tourism, learning, quality of services, etc.). These ontologies, each one built for di erent purpose, are used together in complex applications. However, how they are combined is usually hidden in the application code, without explicitly expressing the way how ontologies are combined for a speci c purpose. This situation leads to think on ontology networks as a new ontology engineering concept, which is being increasingly applied, instead of custom-building new ontologies from scratch. An ontology network di ers from a set of interconnected single ontologies, due to in it the meta-relationships among the di erent ontologies involved are explicitly expressed [ 2 ]. As part of the NeOn methodology [ 3 ], di erent scenarios for building ontology networks were identied, ranging from the construction of an ontology network from scratch up to the reuse of ontological and non-ontological resources.

The main contribution of this paper is a rst de nition, based on the Description Logics formalism, of the di erent relationships among networked ontologies. Our work attempts to assuring the consistency of the ontology network speci cation.

The remainder of this paper is organized as follows. Section 2 gives an overview of ontology-network and the theoretical background of this work. Section 3 introduces the ontology relationship de nitions. Section 4 brie y describes a case study in the health domain, more speci cally a recommendation system. Section 5 details the modelling of an ontology network, applying the speci ed ontology relationships among the ontologies of the case study. Finally, Section 6 gives some conclusions and future works. 2

Background

An ontology network can be de ned as a collection of ontologies related together through a variety of di erent relationships such as mapping, modularization, and versioning, among others [ 4 ]. Distributed and collaborative methodologies of ontology design, such as DILIGENT [ 5 ] and the NeOn project approach [ 2 ], allows the design of local models based on a core model which integrates the local ones.

Intuitively, de ning an ontology network is to select a set of networked ontologies, by identifying the di erent kinds of relationships between the networked ontologies. There are some models that cover both the syntactic aspects of ontology relationships and the semantic aspects of interpreting ontology networks and their relations. For instance, the Collaborative Ontology Design Ontology (C-ODO) [ 6 ] is an ontology network that describes design entities (ontologies, modules, activities, etc.). In [ 4 ], Allocca et al. present general relations between ontologies, such as includedIn, equivalentTo, similarTo and versioning, describing them in the DOOR (Descriptive Ontology of Ontology Relations) ontology. Grau et al [ 7 ] propose a work that adapts important notions of software engineering, such as module and black-box behavior, to be applied in the reuse and integration of ontologies. In [ 8 ], Zimmermann et al. introduce the concept of Distributed System as a set of ontologies interconnected by ontology alignments, describing semantic relations between ontologies, such as: cross-ontology concept subsumption or cross-ontology role subsumption, among others.

There also exist several works that propose formal de nitions of the ontology mapping (or ontology alignment) concept, such as [9{12]. Most of them formalize the idea of mapping between concepts, relations and instances (so called entities by [ 12 ]) of two ontologies. They also address the problem of nding these correspondences between entities of di erent ontologies. But in the real world, we nd other ontology relationships beyond mapping, that is, it is not always the case that two ontologies are related through an alignment between concepts, relations or instances. Except for the works [ 4 ] and [ 10 ], which de nes bridge axioms to express di erent relationships between ontologies in a general way, these proposals do not address a formalization which explicitly states the possible di erent relationships between two ontologies. Our approach is similar to [ 4 ] because it de nes ontology relationships. But our proposal di ers from [ 4 ] in two main aspects: { DOOR's relationships were extended by adding the usesSymbolsOf relationship. { Our work is an introduction of a formalization of the inter-ontology relationships. 3

Ontology Relationships in a Ontology Network

Based on the NeOn Methodology [ 13 ], we have analized how to perform the combination of di erent types of knowledge resources for building an ontology network, formalizing a selected set of ontology relationships. This set of relationships allowed us to design an ontology network, expressing explicitly the semantics of the relationships in a particular set of ontologies. This paper is a rst intend of formalization towards the obtaining of a complete and minimal set of ontology relationships necessary and su cient to build an ontology network.

We have considered four ontology relationships: isTheSchemaFor, isAConservativeExtentionOf and mappingSimilarTo, taken from the DOOR ontology and one relationship named usesSymbolsOf, identi ed in the present work. Below we present a conceptual and a formal de nition of each relationship. These definitions are based on the Description Logics formalism (DLs) [14{16], applying the concepts: Signature of a DL [ 7, 17 ], concept description, concept de nition, general concept inclusions (GCIs), TBox [ 14, 16 ], interpretation [ 16, 17 ], ABox [ 16 ], consistency of an ABox w.r.t. a TBox [ 16 ], model of an ontology [ 7 ] and logical consequence of an ontology [ 7 ].

To introduce the ontology relationship de nition we assume we have two ontologies O and O0 formalized by a DL L, formally represented by (T , A, I; N) and (T 0, A0, I0, N 0) respectively, where: T and T 0 are the TBox, A and A0 are the ABox consistent w.r.t. T and T 0, for the models I = ( I ;:I ) and I0 = ( I0 ;:I0 ) respectively, N and N 0 are the sets of individual names of the domains I and I0 respectively. isTheSchemaFor relationship

Conceptually, this relationship keeps the link between a model and its metamodel. A formal de nition is: nameg, GI0 = fCi0I0 j Ci0 I0 g, RI0 = fri0I0 j ri0I0 g O is the Schema for O 0 (isTheSchemaFor(O, O0)) if there exists: Let O and O0 be two ontologies.

Let G = fCi0 j Ci0 2 T 0 is a concept descriptiong, R = fri0 j ri0 2 T 0 is a role

I0 I0 I0 { a function s : A ! G [ R that maps each concept assertion C(i) to a concept description Ci0 or a role name ri0 and { a function sI : I ! GI0 [ RI0 that maps each domain element iI to the set Ci0I0 or to the binary relation ri0I0 , where:

C 2 T is a concept description, i 2 N , C(i) 2 A, iI 2 CI since A is consistent w.r.t. T for the model I, Ci0 2 T 0, ri0 2 T 0 isAConservativeExtensionOf relationship

This relation describes an extension of a given ontology by a number of additional axioms, which describe what has not been covered yet by the existing ontology. Formally:

Let O and O0 O be two ontologies.

Let sig(O0) be the signature of O0 over L; O is a Conservative Extension of O 0 (isAConservativeExtensionOf(O, O0)) w.r.t. L if for every axiom over L with sig( ) sig(O0), we have O j= i O0 j= [ 7, 17 ]. mappingSimilarTo relationship

An ontology O isSimilarMappingTo an ontology O0 if there exists an alignment from O to O0 and this alignment covers a part of the vocabulary of O. The formal de nition is:

Let O and O0 be two ontologies.

Let K fC j C 2 T is a concept descriptiong, K0 fC0 j C0 2 T 0 is a concept descriptiong, KI = fCI I j C 2 Kg, K0I0 = fC0I0 I0 j C0 2 K0g O is Mapping Similar to O 0 (isMappingSimilarTo(emphO, O0)) if there exists: { a function m : K ! K0 that maps each concept description C 2 K to a concept description C0 2 K0 and { K0I0 KI , that means the subset KI I , in the model I for the ontology O, includes the set K0I0 I0 of individuals in the model I0, for the ABox A0 in the ontology O0, that asserts the concepts of the set K0 which are mapped to the concepts of the set K by the function m.

This de ni on is based on the concepts of morphism [ 9 ], ontology alignment [ 10 ], mapping function [ 11 ], mapping source and target ontologies [ 18 ] and ontology alignment function [ 12 ]. usesSymbolsOf relationship

The usesSymbolsOf relationship happens when the properties at an ontology O involves individuals from another ontology O0, in such a way that the ontology O de nes some properties that take value in individuals that are classi ed by classes of the ontology O0. The usesSymbolsOf relationship links ontologies O and O0 in such a way that it abstracts from the particular ontology O0 to be imported and focuses instead on the symbols from O0 that are to be reused. Previously to introduce the de nition of the usesSymbolsOf relationship, it is necessary to de ne the safety of an ontology for a signature :

Let O and O0 be two ontologies.

Let S a signature over L.

We say that O is safe for S w.r.t. L, if for every ontology O0 with Sig(O) \ Sig(O0) S, we have that O is a conservative extension of O0 w.r.t. L [ 7 ]. Now, we can introduce a formal de nition of the usesSymbolsOf relationship: Let O and O0 be two ontologies with Sig(O) and Sig(O0) over L and Sig(O) \ Sig(O0) Sig(O0) .

O uses Symbols of O 0 (usesSymbolsOf(emphO, O0)) if O is safe for Sig(O0).

In the next section, we will introduce a case study of a recommender information system in the health domain. This case study will help to identify the di erent domain ontologies and how they must be combined in order to obtain the underlying model of this application. For this case study, the set of ontology relationships previously formalized was enough to explicitly express the links among the di erent domain ontologies. 4

A Case Study: Modelling a Health Information

Recommender System

The use of the web as a knowledge repository where common people can nd information, especially in the health area, increases drastically day by day. This is a very worrying reality because many of health websites do not contain data of good quality: precise, believable and relevant to user's pro le. In this sense, a decentralized, intelligent recommender system can automatically give an evaluation about the quality of the sources according to the consumer's needs. Apart of the quality data issue, it is necessary to consider other aspects related to the context in which the user makes the query, like query goals and relevance feedback. All these issues lead to shape our health recommender system as based on quality assurance and context features, to give a reading recommendation of health resources for a particular user. Our approach involves several knowledge domains that have to be modeled and integrated as whole. These knowledge domains are health domain, website domain, quality assurance domain, context domain and recommendation domain. Below We will describe these knowledge domains, being each domain independent from each other, favouring the reuse of models. Particularly, in this paper we conceptualize each domain as an independent ontology as it will discuss in Section 5.

The Health Domain refers to terminology about health topics. It models for example the treatment, risk factors, diagnostic and e ects of a disease. These concepts can be re ned in terms of a speci c disease i.e Alzheimer, and thus can be modeled the concepts Alzheimer Treatment or Alzheimer Diagnostic.

The WebSite Domain conceptualize the domain of webpages and particularly describe their contents. The main concepts are: web content, web page and web site, which can be characterized by other concepts such as source and author, depending on the application environment based on the Web Site domain.

Regarding the Quality Assurance Domain , there exists a scienti c approach that de nes data quality dimensions rigorously, as dimensions that can be intrinsic or not intrinsic to an information system [ 19 ]. Some intrinsic data quality dimensions are: believability, accuracy and objectivity. Eysenbach et al. [ 20 ] present a study of how quality on the Web is evaluated in practice, comparing di erent methodologies of quality assessment.A domain expert must decide which dimensions are relevant for a speci c domain and must de ne metrics in order to measure them. Then, the Quality Assurance Domain conceptualize metrics, quality assurance speci cations and quality assessments. Metrics are formulas de ned based on the properties of resources. For example, a metric can measure if a web page has an author, or count its number of words, etc. A quality assurance speci cation describes the di erent quality dimensions ; for instance, readability, precision or believability. In order to make a quality assessment, one or more suitable metrics must be applied. For example a metric to evaluate the believability dimension of a web resource can be based on the resource's author. A quality assessment models the evaluation of a particular web content (i.e. a web page about Alzheimer) for a particular quality dimension through a speci c metric. It is obtained a quality level, which represents the result of the quality assessment, for example, "high" or "low" believability.

The Context Domain describes user pro les, query situations and user actions. The user pro le features user properties, such as age range or role (for instance patient or relative). The query situation models the concept of query goal, that is, explicitly ask users about their goal for each speci c query in order to aid in the recommendation process. This can be done at two levels: type of query, which represents the possible intentions of a user when makes a query (informational, navigational or transactional) or topic, which is the issue of the query, for example Alzheimer. The user action represents the action of the user when makes a query for a speci c task. Once the system had presented the user with an initial set of documents, the user can usually indicate those documents that contain useful information, giving his/her relevance feedback, which will be used as input to produce a reading recommendation of a content.

The Recommendation Domain describes the reading recommendation of a resource for a user. It models two aspects: the recommendation speci cation and the recommendation itself. The former speci es the recommendation de nition, which describes the criterion upon which it relies to make a recommendation (i.e, a quality dimension), the context aspects and the possible recommendation levels. The recommendation models concrete recommendation assessments, based on a recommendation speci cation.

Making Explicit Ontology Relationships in a Ontology

Network: a Case Study

In this section we explain how to build an ontology network, applying the ontology relationships de ned in Section 3, for linking a set of ontologies that conceptualize the di erent and independent knowledge domains corresponding to the recommender system case study described in Section 4. More precisely, this ontology network is a network of ontology networks; this means that each knowledge domain involved is itself an ontology network and all of them are related among each other. Figure 1 outlines this approach; the di erent ontology networks are arranged by columns and the relation inter-ontology networks are shown by arrows crossing columns. In Section 5.1 the ontology relationships will be used to describe the speci c-domain ontology networks and in Section 5.2 the ontology network is shaped as a network of ontology networks. This section describes some of the di erent speci c-domain ontology networks, designed by using the relationships between ontologies introduced above.

Health Domain ontology network comprises the Health and the Speci c Health ontologies. The former conceptualize any diseases, while the last one is more speci c, for instance the Alzheimer ontology.

Both ontologies are related by the isAConservativeExtentionOf relationship. The Alzheimer ontology isAConservativeExtentionOf the Health ontology, since, for instance, the concept Treatment of the Health ontology is extended by subsumption by the concept AlzheimerTreatment of the Alzheimer. This relationship is applied because in the health domain, there are some concepts that are general for all diseases (Diagnostic, Treatment), which can be reused in the knowledge base for a speci c disease, such as alzheimer. Thus, this is the case where the knowledge expressed in the more generic Health ontology must be entirely reused in the more specialized Alzheimer ontology. Looking at the de nition of isAConservativeExtentionOf relationship, the Health ontology should not be compromised by the new axioms. In particular, the extended ontology should not entail new subsumptions between concepts that are in the original one.

WebSite ontology network is composed by three ontologies: WebSite Speci cation, WebSite and WebSite Specialization (Figure 2). The main concepts of the WebSite Speci cation ontology are WebResource and WebResourceProperty. A web resource is any resource which is identi ed by a URL; for instance a webpage. Web resource properties models the properties that can be attached to a web resource, for instance, hasContent, hasSource, hasAuthor, etc. The WebSite ontology has as main concepts: WebContent, WebPage and WebSite, that are more speci c. The WebSite Specialization ontology adds properties to these main concepts, such as hasAuthor and hasSource depending on the application environment.

In this ontology network, the most interesting feature is the use of the isTheSchemaFor relationship. The WebSite Speci cation ontology plays the role of metamodel for the Website and WebSite Specialization ontologies. Thus, the concepts and relations of these two ontologies are instances of the concepts WebResource and WebResourceProperty in the WebSite Speci cation ontology. This matchs the formal de nition of the isTheSchemaFor relationship, where a mapping is de ned between instances that asserts the concepts (ABox) in the metamodel (WebSite Speci cation ontology) and concepts and relations (TBox) in the model (WebSite and WebSite Specialization ontologies).

Quality Assurance ontology network is composed by three ontologies: Metric Speci cation, Quality Speci cation and Quality Assessment, as shown in Figure 3. These ontologies conceptualize metrics, quality assurance speci cations and quality assessments, respectively, as is detailed in Section 4.

As is showed in Figure 1, the Quality Speci cation ontology is related with the Metric Speci cation ontology through the usesSymbolsOf relationship; since a dimension of quality is always based on a metric. In this case, the occurrence of the usesSymbolsOf relationship is given by the assessedBy property that associates to each quality dimension the corresponding metric. It is the case where although two ontologies (Quality Speci cation y and Metric Speci cation) must be kept separate, there exists one ontology that needs to be linked to one or more concepts of another ontology, because some properties (in this case: assessedBy property) of it take values in individuals classi ed by classes in the used ontology (concept Metric of the Metric Speci cation ontology). If we review the given de nition of the usesSymbolsOf relationship, the Quality Speci cation ontology "abstracts" from the particular ontology reused (Metric Speci cation ontology), focusing in the symbols to be reused (Metric concept), assuring the safety of the ontology reused.

Here it is important to clearly establish when to apply the isAConservativeExtensionOf relationship and when to apply the usesSymbolsOf relationship. Reviewing their de nitions, the former could be considered as a particular case of the latter, since in the isAConservativeExtensionOf relationship a ontology is enterely included in another one, while for the usesSymbolsOf relationship an ontology includes some elements of another ontology. But there exist a conceptual di erence, which is important to consider when both relationships are used in a concrete case study. Below we explain the di erence.

For the usesSymbolsOf relationship, although the domains of the involved ontologies are sematically related, the ontologies play di erent roles (for example a ontology models dimensions and another one models metrics). Thus, it can be inferred that for the usesSymbolsOf relationship the related ontologies are kept as separate ontologies, despite of one ontology is linked to the other by the need of reusing some concepts and individuals. However, for isAConservativeExtensionOf, the idea is that an ontology extends all the model of the other, specializing the represented knowledge.

In this work, the Context and Recommendation ontology networks are omitted, they are modeled through the isTheSchemaFor and usesSymbolsOf relationships. 5.2

The Health Ontology Network as a Network of Ontology Networks The above presented ontology networks are also interrelated among each other. Mainly, they are related by the usesSymbolsOf and mappingSimilarTo relations (Figure 1).We have just illustrated the usesSymbolsOf relationship in the domain ontology networks (Section 5.1). The usesSymbolsOf relationship links a ontology to individuals of concepts of another ontology, in such a way that although they are separate ontologies, one ontology depends on the other, since it has properties that involves individuals of it. On the other hand, the mappingSimilarTo relationship, keeps the related ontologies even more independent. As was formalized in the de nition, a mapping is de ned between concepts of two ontologies, but none of them depends on the other, sharing a subset of instances that assert the mapped concepts. This is the reason why mappingSimilarTo is the relationship that ts in most of the links identi ed between ontologies from di erent domains, as Figure 1 shows.

For instance, the mappingSimilarTo relationship is used between Quality Assessment and WebSite ontologies of the Quality Assurance and WebSite domains respectively. It was de ned an alignment between the Resource and WebContent concepts, in this particular case study of the health domain. But if our case study were about quality assessment of leaning objects, in the educational domain, we would de ne a alignment between the Resource and LearningObject concepts, and so on, depending on the nature of the individuals to be assessed.

The mappingSimilarTo relationship is also used between Metric Speci cation and WebSite Speci cation ontologies of the Quality Assurance and WebSite domains respectively. It was de ned an alignment between the Feature and WebResourceProperty concepts. Thus, it is possible to specify that a metric is based on some property of a web resource. Here, it is possible to appreciate the convenience of having some ontologies that plays the role of metamodel for others, because the instances (ABox) of the WebResourceProperty concept of the WebSite Speci cation ontology are relations (TBox) of the WebSite ontology (properties of web contents).

The usesSymbolsOf relationship, can be identi ed (Figure 1) between WebSite Specialization and Alzheimer ontologies of the WebSite and Health domains respectively. For instance, the hasTopic property, from the WebSite Specialization ontology takes values in the Alzheimer ontology. 6

Conclusions and Future Research Directions

In this paper we have explicitly de ned a set of ontology relationships which allow us to express di erent links among the ontologies of a ontology network. We give a formal de nition of each relationship, based on the Description Logics formalism, which prevents from contradictory inferences tailored in an ontology network.

In addition, we have used the de ned relationships to describe an ontology network that models the di erent domains related to a health recommender system. Thus, we have explicited the relationships among the ontologies that compose each domain ontology network as well as those which link the domain ontology networks to make up the Health ontology network.

The present work is a rst theoretic approach which aims to keep the logical consistency of the ontology network model and its directions is towards the obtaining of a complete and minimal set of ontology relationships necessary and su cient to build an ontology network.

Starting from the presented design, good practices on Ontology Engineering lead to evaluate the model in an interaction between ontology engineers and domain experts. From this evaluation, it is expected to reach a nal re nement of the structures which compose the ontology network, capitalizing it in methodological results.

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