Towards Expressive Metamodelling with Instantiation.
Petra Kubincová, Ján Kľuka, Martin Homola · Description Logics · 2015
In metamodelling we allow concepts and roles to be classified into “meta” concepts and to be reasoned with as if they were individuals. This is useful in modelling of certain complex domains or in reasoning about ontology entities for sake of verification of methodological constraints. What many proposed metamodelling languages lack is the ability to model with instantiation – the relation between an instance and a concept it belongs to – similar to the ability to express restrictions on rdf:type in the undecidable OWL Full. We investigate a variant of higher-order description logics combining various desired metamodelling features, including: (a) a fixly interpreted instanceOf role connecting instances with their concepts, freely usable in modelling; (b) promiscuous concepts that may have individuals, other concepts, and roles as instances at the same time; but also (c) strictly typed concepts allowing only a certain type of instances. We show the decidability of two expressive fragments by means of reduction.