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ONTOLOGY MEDIATION, MERGING, AND ALIGNING
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to be declarative, while procedural mappings can be de ned by means of an XPath expression for the transformation of instance data. C-OWL Another perspective on ontology mapping is given by Context OWL (C-OWL) (Bouquet et al., 2004), which is a language that extends the ontology language OWL (Dean and Schreiber, 2004) both syntactically and semantically in order to allow for the representation of contextual ontologies. The term contextual ontology refers to the fact that the contents of the ontology are kept local and they can be mapped with the contents of other ontologies via explicit mappings (bridge rules) to allow for a controlled form of global visibility. This is opposed to the OWL importing mechanism where a set of local models is globalized in a unique shared model. Bridge rules allow connecting entities (concepts, roles, or individuals) from different ontologies that subsume one another, are equivalent, are disjoint or have some overlap. A C-OWL mapping is a set of bridges between two ontologies. A set of OWL ontologies together with mappings between each of them is called a context space. The local models semantics de ned for C-OWL, as opposed to the OWL global semantics, considers that each context uses a local set of models and a local domain of interpretation. Thus, it is possible to have ontologies with contradicting axioms or unsatis able ontologies without the entire context space being unsatis able.
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6.2.3. Ontology Alignment
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Ontology alignment is the process of discovering similarities between two source ontologies. The result of a matching operation is a speci cation of similarities between two ontologies. Ontology alignment is generally described as the application of the so-called Match operator (cf. (Rahm and Bernstein, 2001)). The input of the operator is a number of ontology and the output is a speci cation of the correspondences between the ontologies. There are many different algorithms which implement the match operator. These algorithms can be generally classi ed along two dimensions. On the one hand there is the distinction between schema-based and instance-based matching. A schema-based matcher takes different aspects of the concepts and relations in the ontologies and uses some similarity measure to determine correspondence (e.g., (Noy and Musen, 2000b)). An instance-based matcher takes the instances which belong to the concepts in the different ontologies and compares these to discover similarity between the concepts (e.g., (Doan et al., 2004)). On the other hand there is the distinction between element-level and structure-level matching. An element-level matcher compares properties of the particular concept or relation, such as the name, and uses these to nd similarities (e.g., (Noy and Musen, 2000b)). A structure-level matcher compares the structure (e.g., the concept hierarchy) of the ontologies to
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APPROACHES IN ONTOLOGY MEDIATION
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nd similarities (e.g., (Noy and Musen, 2000a; Giunchiglia and Shvaiko, 2004)). These matchers can also be combined (e.g., (Ehrig and Staab, 2004; Giunchiglia et al., 2004)). For example, Anchor-PROMPT (Noy and Musen, 2000a), a structure-level matcher, takes as input an initial list of similarities between concepts. The algorithm is then used to nd additional similarities, based on the initial similarities and the structure of the ontologies. For a more detailed classi cation of alignment techniques we refer to Shvaiko and Euzenat (2005). In the following, we give an overview of those approaches. Anchor-PROMPT (Noy and Musen, 2000a) is an algorithm which aims to augment the results of matching methods which only analyze local context in ontology structures, such as PROMPT (Noy and Musen, 2000b), by nding additional possible points of similarity, based on the structure of the ontologies. The algorithm takes as input two pairs of related terms and analyzes the elements which are included in the path that connects the elements of the same ontology with the elements of the equivalent path of the other ontology. So, we have two paths (one for each ontology) and the terms that comprise these paths. The algorithm then looks for terms along the paths that might be similar to the terms of the other path, which belongs to the other ontology, assuming that the elements of those paths are often similar as well. These new potentially related terms are marked with a similarity score which can be modi ed during the evaluation of other paths in which these terms occur. Terms with high similar scores will be presented to the user to improve the set of possible suggestions in, for example, a merging process in PROMPT. GLUE (Doan et al., 2003; 2004) is a system which employs machinelearning technologies to semi-automatically create mappings between heterogeneous ontologies based on instance data, where an ontology is seen as a taxonomy of concepts. GLUE focuses on nding 1-to-1 mappings between concepts in taxonomies, although the authors mention that extending matching to relations and attributes, and involving more complex mappings (such as 1-to-n and n-to-1 mappings) is the subject of ongoing research. The similarity of two concepts A and B in two taxonomies O1 and O2 is based on the sets of instances that overlap between the two concepts. In order to determine whether an instance of concept B is also an instance of concept A, rst a classi er is built using the instances of concept A as the training set. This classi er is now used to classify the instances of concept B. The classi er then decides for each instance of B, whether it is also an instance of A or not. Based on these classi cations, four probabilities are computed, namely, P(A,B), P(A,B), P(A,B), and P(A,B), where, for example, P(A,B) is the probability that an instance in the domain belongs to A, but not to B. These four probabilities can now be used to compute the joint probability distribution for the concepts A and B, which is a user supplied function with these four probabilities as parameters.
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