| Here we consider the verification and semantic integration for the set of first-order time ontologies by Allen-Hayes, Ladkin, and van Benthem that axiomatize time as points, intervals, or a combination of both within an ontology repository environment. Semantic integration of the set of time ontologies is explored via the notion of theory interpretations using an automated reasoner as part of the methodology. We use the notion of representation theorems for verification by characterizing the models of the ontology up to isomorphism and proving that they are equivalent to the intended structures for the ontology. Provided is a complete account of the meta-theoretic relationships between ontologies along with corrections to their axioms, translation definitions, proof of representation theorems, and a discussion of various issues such as class-quantified interpretations, the impact of namespacing support for Common Logic, and ontology repository support for semantic integration as related to the time ontologies examined. |
