2003 OntologyMappingStateofTheArt

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Subject Headings: Ontology Mapping Task, Ontology Mapping Algorithm, Ontology Mapping System.

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2006

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Abstract

Ontology mapping is seen as a solution provider in today's landscape of ontology research. As the number of ontologies that are made publicly available and accessible on the Web increases steadily, so does the need for applications to use them. A single ontology is no longer enough to support the tasks envisaged by a distributed environment like the Semantic Web. Multiple ontologies need to be accessed from several applications. Mapping could provide a common layer from which several ontologies could be accessed and hence could exchange information in semantically sound manners. Developing such mappings has been the focus of a variety of works originating from diverse communities over a number of years. In this article we comprehensively review and present these works. We also provide insights on the pragmatics of ontology mapping and elaborate on a theoretical approach for defining ontology mapping.

1. Introduction

Nowadays, the interested practitioner in ontology mapping, is often faced with a knotty problem: there is an enormous amount of diverse work originating from different communities who claim some sort of relevance to ontology mapping. For example, terms and works encountered in the literature which claimed to be relevant include: alignment, merging, articulation, fusion, integration, morphism, and so on. Given this diversity, it is difficult to identify the problem areas and comprehend solutions provided. Part of the problem is the lack of a comprehensive survey, a standard terminology, hidden assumptions or undisclosed technical details, and the dearth of evaluation metrics.

This article aims to fill-in some of these gaps, primarily the first one: lack of a comprehensive survey. We scrutinised the literature and critically reviewed works originating from a variety of fields to provide a comprehensive overview of ontology mapping work to date. We also worked on the theoretical grounds for defining ontology mapping, which could act as the glue for better understanding similarities and pinpointing differences in the works reported.

The overall goal of this paper is not only to give readers a comprehensive overview of the ontology mapping works to date, but also to provide necessary insights for the practical understanding of the issues involved. As such, we have been critiquing while reporting these works, and not just been descriptive. At the same time though, we objectively review the works with emphasis given on a practitioner’s interests, and try to provide answers to the following questions:

  • What are the lessons learnt from this work?
  • How easily can this work be replicated in similar domains?

2.a Defining ontology mapping

We shall adopt an algebraic approach and present ontologies as logical theories. An ontology is then a pair O = (S,A), where [math]\displaystyle{ S }[/math] is the (ontological) signature describing the vocabulary — and [math]\displaystyle{ A }[/math] is a set of (ontological) axioms — specifying the intended interpretation of the vocabulary in some domain of discourse. Typically, an ontological signature will be modelled by some mathematical structure. For instance, it could consist of a hierarchy of concept or class symbols modelled as a partial ordered set (poset), together with a set of relations symbols whose arguments are defined over the concepts of the concept hierarchy. The relations themselves might also be structured into a poset. For the purposes of this survey we shall not commit to any particular definition of ontological signature; we refer to the definitions of ‘ontology’, ‘core ontology’, or ‘ontology signature’ in (Kalfoglou and Schorlemmer 2002; Stumme and Maedche 2001; Bench-Capon and Malcolm 1999), respectively, for some examples of what we consider here an ontological signature. In addition to the signature specification, ontological axioms are usually restricted to a particular sort or class of axioms, depending on the kind of ontology.

Ontological signature morphisms. We understand ontology mapping as the task of relating the vocabulary of two ontologies that share the same domain of discourse in such a way that the mathematical structure of ontological signatures and their intended interpretations, as specified by the ontological axioms, are respected. Structure-preserving mappings between mathematical structures are called morphisms; for instance, a function f between two posets that preserves the partial order (a b implies f(a) f(b)) is a morphism of posets. Hence we shall characterise ontology mappings as morphisms of ontological signatures as follows.

A total ontology mapping from O1 = (S1,A1) to O2 = (S2,A2) is a morphism f : S1 → S2 of ontological signatures, such that, A2 |= f(A1), i.e., all interpretations that satisfy O2’s axioms also satisfy O1’s translated axioms. This makes an ontology mapping a theory morphism as it is usually defined in the field of algebraic specification (see, for instance, (Meseguer 1989)).

In order to accommodate a weaker notion of ontology mapping we will say that there is a partial ontology mapping form O1 = (S1,A1) to O2 = (S2,A2) if there exists a sub-ontology O 1 = (S 1, A 1) (S 1 ⊆ S1 and A 1 ⊆ A1) such that there is a total mapping from O 1 to O2.

Populated ontologies. Central to several approaches to ontology mapping is the concept of a populated ontology. In this case, classes of an ontological signature come equipped with their respective instances. A populated ontology can be characterised by augmenting the signature with a classification relation that defines the classification of instances to the concept symbols in the signature. This brings forth issues about the correctness of populated ontologies, namely if the classification of instances respects the structure of the ontological signature. See (Kalfoglou and Schorlemmer 2002) for a use of populated ontologies in the definition of ontology mapping.

Taking into account the population of ontologies when establishing the mapping between ontologies may be useful for relating concepts according to the meaning and use that these concepts are given by particular communities. This idea is theoretically described in (Kent 2000) and (Schorlemmer 2002), for instance, and is fundamental to the information-flow based approaches described in Section 3.f.

Ontology morphisms. So far, we have defined ontology mapping only in terms of morphisms of ontological signatures, i.e., by determining which concept and relation symbols of one ontology are mapped to concept and relation symbols of the other. A more ambitious and practically necessary approach would be to take into account how particular ontological axioms are mapped as well. Formally, this would require ontology mappings to be defined in terms of morphisms of ontologies, i.e., signature + axioms, instead of morphisms of signatures only.

Most works on ontology mapping reported here adopt the more restrictive view of ontology mapping as signature morphism. Nevertheless, some of them consider the alignment of logical sentences, and not of signature symbols only (Calvanese et al. 2001b; Madhavan et al. 2002). Thus, we will use the term ‘ontology mapping’ for mappings as ontological signature morphisms as well as mappings as ontology morphisms.

Ontology alignment, articulation and merging. Ontology mapping only constitutes a fragment of a more ambitious task concerning the alignment, articulation and merging of ontologies. Here we want to clarify our understanding of these concepts within the above theoretical picture. An ontology mapping is a morphism, which usually will consist of a collection of functions assigning the symbols used in one vocabulary to the symbols of the other. But two ontologies may be related in a more general fashion, namely by means of relations instead of functions. Hence, we will call ontology alignment the task of establishing a collection of binary relations between the vocabularies of two ontologies. Since a binary relation can itself be decomposed into a pair of total functions from a common intermediate source, we may describe the alignment of two ontologies O1 and O2 by means of a pair of ontology mappings from an intermediate source ontology O0 (see Figure 1). We shall call the intermediate ontology O0, together with its mappings, the articulation of two ontologies. For an example of ontology articulation see (Maedche and Staab 2000; Madhavan et al. 2002; Compatangelo and Meisel 2002).

Fig. 1. Diagrammatic views of articulation and merging of two ontologies.

  • Articulation: O1 ⇒ O2; O1 ⇒ O3.
  • Merging: O1 ⇒ O2; O1 ⇒ O3; 02 ⇒ O4; 03 ⇒ 04.

Finally, an articulation allows for defining a way in which the fusion or merging of ontologies has to be carried out. The intuitive idea is to construct the minimal union of vocabularies S1 and S2 and axioms A1 and A2 that respects the articulation, i.e., that is defined modulo the articulation (see Figure 1). This corresponds to the mathematical pushout construct, and is exploited, for instance, in the frameworks described in (Bench-Capon and Malcolm 1999; Kent 2000; Schorlemmer 2002). Again, this ‘strong’ notion of merging can be relaxed by taking the articulation of two sub-ontologies of O1 and O2 respectively, and defining the merged ontology O according to their articulation.

A word on translation and integration. Translation is used by different authors to describe two different things. First, there is the translation between formal languages, for example from Ontolingua to Prolog. This changes the syntactic structure of axioms, but not the vocabulary. This is not of our concern in this survey. Second, there is the actual translation of the vocabulary. This is intimately linked to the issue of ontology mapping. Actually, the difference between mapping and translation is that the former denotes the process of defining a collection of functions that specify which concepts and relations correspond to which other concepts and relation, while the latter is the application of the mapping functions to actually translate the sentences that use the one ontology into the other. This presupposes that the ontologies share the domain in which the respective vocabularies are interpreted. Under integration, on the other hand, we regard the composition of ontologies to build new ones, but whose respective vocabulary are usually not interpreted in the same domain of discourse.

4 Examples

Fern´andez-Breis and Mart´ınez-Béjar: In Figure 5 we illustrate the example used in (Fern´andez-Breis and Mart´ınez-Béjar 2002). As we reported in Section 3.a, Fern´andez-Breis and Mart´ınez-Béjar developed an algorithm for integrating ontologies. The algorithm works as follows: it detects synonymous concepts (e.g., BUILDING, SCIENCES FACULTY in both ontologies), as well as exploits nodes in the hierarchy that have the same attributes. The upper part of Figure 5 illustrates two university ontologies describing a faculty of sciences, whereas the lower part illustrates the integrated ontology. The concept PEOPLE has been converted to PERSON since both concepts share the same attributes (AGE, INCOME). The algorithm also integrates attributes of the same concepts (BUILDING in the integrated ontology has the sum of its predecessors’ attributes in the original ontologies).

5 Pragmatics

In Sections 3 and 4 we have described and showed examples of 35 works related to ontology mapping. In this section we will elaborate on important topics that emerged when examining these works. We were selective in choosing the topics that we think are prevailing when practitioners are faced with the subtle task of ontology mapping. While the main section of this article aims to act as a road map of ontology mapping works today, herein, we critically review issues concerned with the relation of ontology mapping and databases schemata integration, the normalisation of ontologies and the creation of formal instances, the role of formal theory in support of ontology mapping, the use of heuristics, the use of articulation and mapping rules, the definition of semantic bridges, find we also discuss the thorny issue of automated ontology mapping.

6 Conclusions

In this article we presented the state-of-the-art in ontology mapping: 35 works have been reviewed and some of them illustrated through example cases. Many more have been left out of this survey: It was not feasible neither practical to include everything that has been done to date. Rather, we selected indicative examples that characterise a range of related works.

We argue that ontology mapping nowadays faces some of the challenges we were facing ten years ago when the ontology field was at its infancy. We still do not understand completely the issues involved. However, the field evolves fast and attracts the attention of many practitioners among a variety of disciplines, the result being the variety of works we presented in this article. As today we know more about ontologies, how to design, develop, and deploy them. We hope that this article contributes to a better understanding of the emerging field of ontology mapping.

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 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
2003 OntologyMappingStateofTheArtYannis Kalfoglou
Marco Schorlemmer
Namyoun Choi		Ontology Mapping: the State of the ArtThe Knowledge Engineering Reviewhttp://eprints.ecs.soton.ac.uk/10519/1/ker02-ontomap.pdf10.1017/S02698889030006512003
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