Combining data from multiple sources involves transforming the ontologies of all the different data sources into a combined ontology describing all the data.Ontology transformations are structure-preserving maps; things that are related in a source ontology need to have the same relationship in the transformed ontology. In the language of category theory, if you consider ontologies as categories then ontology transformations are their associated morphisms.
An epimorphism is a special kind of morphism.
In our context, an ontology transformation is an epimorphism if every statement in the target ontology is a consequence of transformed statements from the source ontology.
So suppose you’re trying to build a particular solution, and you start by creating an ontology that describes the solution domain. You then assemble a collection of fragmentary ontologies and data from various sources, and construct morphisms from all these fragments into your target ontology.
If the collection of morphisms taken together constitutes an epimorphism then the solution you’ve constructed is complete, in the sense that any possible statement in your target ontology is a consequence of statements in the various ontology fragments.
Our goal in Epimorphics is to create epimorphisms from available linked data into ontologies describing domains of value to real people.