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ONTOLOGY MEDIATION, MERGING, AND ALIGNING
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6.3.1. Mapping Language
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An important requirement for the mapping language which is presented in this section is the epistemological adequacy of the constructs in the language. In other words, the constructs in the language should correspond to the actual correspondences one needs to express in a natural way. More information about the mapping language can be found in Scharffe and de Bruijn (2005) and on the web site of the mapping language.1 Now, what do we mean with natural way There are different patterns which one can follow when mapping ontologies. One can map a concept to a concept, a concept with a particular attribute value to another concept, a relation to a relation, etc. We have identi ed a number of such elementary mapping patterns which we have used as a basis for the mapping language. Example. As a simple example of possible mapping which can be expressed between ontologies, assume we have two ontologies O1 and O2 which both describe humans and their gender. Ontology O1 has a concept Human with an attribute hasGender; O2 has two concepts Woman and Man. O1 and O2 use different ways to distinguish the gender of the human; O1 uses an attribute with two possible values male and female, whereas O2 has two concepts Woman and Man to distinguish the gender. Notice that these ontologies have a mismatch in the style of modeling (see Section 6.2.1). If we want to map these ontologies, we need to create two mapping rules: (1) all humans with the gender female are women and (2) all humans with the gender male are men. The example illustrates one elementary kind of mapping, namely a mapping between two classes, with a condition on the value of an attribute. The elementary kinds of mappings can be captured in mapping patterns. Table 6.1 describes the mapping pattern used in the example.
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Table 6.1 Class by attribute mapping pattern. Name: Class by Attribute Mapping Problem: The extension of a class in one ontology corresponds to the extension of a class in another ontology, provided that all individuals in the extension have a particular attribute value. Solution: Solution description: a mapping is established between a class/attribute/attribute value combination in one ontology and a class in another ontology. Mapping syntax: mapping :: classMapping(direction A B attributeValueCondition(Po)) Example: classMapping(Human Female attributeValueCondition(hasGender female ))
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http://www.omwg.org/TR/d7/d7.2/
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MAPPING AND QUERYING DISPARATE
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The pattern is described in terms of its name, the problem addressed, the solution of the problem, both in natural-language description and in terms of the actual mapping language, and an example of the application of the pattern to ontology mapping, in this case a mapping between the class Human in ontology O1 and the class Woman in ontology O2, but only for all humans which have the gender female. The language contains basic constructs to express mappings between the different entities of two ontologies: from classes to classes, attributes to attributes, instances to instances, but also between any combination of entities like classes to instances, etc. The example in Table 6.1 illustrates the basic construct for mapping classes to classes, classMapping. Mappings can be re ned using a number of operators and mapping conditions. The operators in the language can be used to map between combinations of entities, such as the intersection or union (conjunction, disjunction, respectively) of classes or relations. or example, the mapping between Human and the union of Man and Woman can be expressed in the following way: classMapping(Human or(Man Woman) ) The example in Table 6.1 illustrates a mapping condition, namely the attribute value condition. Other mapping conditions include attribute type and attribute occurrence. The mapping language itself is not bound to any particular ontology language. However, there needs to be a way for reasoners to actually use the mapping language for certain tasks, such as querying disparate knowledge bases and data transformation. For this, the mapping language can be grounded in a formal language. There exists, for example, a grounding of the mapping language to OWL DL and to WSML-Flight. In a sense, the grounding of the mapping language to a particular language transforms the mapping language to a language which is speci c for mapping ontologies in a speci c language. All resulting mapping languages still have the same basic vocabulary for expressing ontology mappings, but have a different vocabulary for the more expressive expressions in the language. Unfortunately, it is not always the case that all constructs in the mapping language can be grounded to the logical language. For example, WSML-Flight does not allow disjunction or negation in the target of a mapping rule and OWL DL does not allow mapping between classes and instances. In order to allow the use of the full expressive power offered by the formal language to which the mapping language is grounded, there is an extension mechanism which allows to insert arbitrary logical expressions inside each mapping rule. The language presented in this section is suitable for the speci cation and exchange of ontology mappings. In the next section we present a semi-automatic approach to the speci cation of ontology mappings.
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