Formalising ontologies and their relations

Abstract

Ontologies allow the abstract conceptualisation of domains, but a given domain can be conceptualised through many different ontologies, which can be problematic when ontologies are used to support knowledge sharing. We present a formal account of ontologies that is intended to support knowledge sharing through precise characterisations of relationships such as compatibility and refinement. We take an algebraic approach, in which ontologies are presented as logical theories. This allows us to characterise relations between ontologies as relations between their classes of models. A major result is cocompleteness of specifications, which supports merging of ontologies across shared sub-ontologies.