| Abstract / Kurzbeschreibung: |
Several modularity concepts for ontologies have been studied in the
literature. Can they be brought to a common basis? We propose to use
the language of category theory, in particular diagrams and their
colimits, for answering this question. We outline a general
approach for representing combinations of logical theories, or
ontologies, through interfaces of various kinds, based on diagrams
and the theory of institutions. In particular, we consider theory
interpretations, language extensions, symbol identification, and
conservative extensions. We study the problem of inheriting
conservativity between sub-theories in a diagram to its colimit
ontology. Finally, we apply this to the problem of conservativity
when composing DDLs or E-connections.
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