The use of logic-based representations in distributed environments such as the semantic web has lead to work on the representation of and reasoning with mappings between distributed ontologies. Up to now the investigation of reasoning methods in this area was restricted to the use of mapping for query answering or subsumption reasoning. In this paper, we investigate the task of reasoning about the mappings themselves. We identify a number of properties such as consistency and entailment of mappings that are important for validating and comparing mappings. We provide formal definitions for these properties and show how the properties can be checked using existing reasoning methods by reducing them to local and global satisfiability testing in distributed description logics.
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