Institutes: A simpler semantics for heterogeneous ontologies

We consider heterogeneous ontologies, i.e. ontologies whose specifications allow to blend different ontology languages such as propositional logic, OWL, first-order logic, Common Logic, or various extensions of these. In order to give such ontologies a precise formal semantics, we need a suitable notion of abstract logic. We here introduce a new framework, called institute theory, that extends abstract entailment and satisfaction systems with signatures while staying much simpler than the well-known framework of institutions. In particular, we abstain entirely from the usage of category theoretic machinery. The introduced framework is intended to give the logical and semantical underpinning for a forthcoming ISO standard for heterogeneous ontologies and ontology interoperability, OntoIOp.