Ontology Constraints in Incomplete and Complete Data

Ontology and other logical languages are built around the idea that axioms enable the inference of new facts about the available data. In some circumstances, however, the data is meant to be complete in certain ways, and deducing new facts may be undesirable. Previous approaches to this issue have relied on syntactically specifying certain axioms as constraints or adding in new constructs for constraints, and providing a different or extended meaning for constraints that reduces or eliminates their ability to infer new facts without requiring the data to be complete. We propose to instead directly state that the extension of certain concepts and roles are complete by making them DBox predicates, which eliminates the distinction between regular axioms and constraints for these concepts and roles. This proposal eliminates the need for special semantics and avoids problems of previous proposals.