Category-based Equational Reasoning: An Approach to Ontology Integration

Incorporating dynamic, general computational knowledge into Semantic Web ontologies is becoming increasingly important. The Semantic Web is now being used to model the behaviour of highly dynamic domains such as web-services, but current approaches to ontologies [such as Web Ontology Language (OWL)] are static and crisp. This article develops a new semantics for Resource Description Framework (RDF) based upon ideas from category theory. In so doing, we not only decouple RDF's semantics from crisp set theory, opening the door to easy adoption of models of uncertainty, but also allow the use of equational reasoning in a principled fashion within RDF. We demonstrate the abilities of equational reasoning, whilst explaining its semantic principles in terms of our RDF category, using an example from the domain of genealogy. We further develop an algebra of (equational) ontologies which allows us to express fine relations between ontologies and to build more complex ontologies out of simpler ones.