Constructing Topos from RDF Data

A significant component of data analysis is related to study relations between pieces of data -- something that is the very fabric of Resource Description Framework (RDF). In such a context, there is a need for a formal methodology of building structures reflecting logical aspects of RDF data, and reasoning about them. Category theory, a branch of modern mathematics, has been seem by many as an abstract description of relations between entities. Multiple constructs and tools provided by category theory allow for modelling and analyzing any phenomena. A topos is a category with an extra structure representing elements of logic. This structure allows for applying categorical semantics to study logic encoded by topos. The paper proposes a methodology for representing RDF data as a topos. It presents required mechanisms of category theory and shows the process of creating components of topos based on RDF triples. The elements of the logic of a topos in the context of RDF are presented and discussed.