The Web of Linked Data is characterized by linking structured data from different sources using equivalence statements, such as owl:sameAs, as well as other types of linked properties. The ontologies behind these sources, however, remain unlinked. This paper describes an extensional approach to generate alignments between these ontologies. Specifically our algorithm produces equivalence and subsumption relationships between classes from ontologies of different Linked Data sources by exploring the space of hypotheses supported by the existing equivalence statements. We are also able to generate a complementary hierarchy of derived classes within an existing ontology or generate new classes for a second source where the ontology is not as refined as the first. We demonstrate empirically our approach using Linked Data sources from the geospatial, genetics, and zoology domains. Our algorithm discovered about 800 equivalences and 29,000 subset relationships in the alignment of five source pairs from these domains. Thus, we are able to model one Linked Data source in terms of another by aligning their ontologies and understand the semantic relationships between the two sources.
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