Reasoning in DL- \(Lite_R\) Based Knowledge Base Under Category Semantics

We propose in this paper a rewriting of the usual set-theoretical semantics of the Description Logic DL- \(Lite_{\mathcal {R}}\) by using categorical language based on objects and arrows which are the two fundamental elements of category theory. This Description Logic is showed to be useful for extending a relational database (ABox) with an ontology (TBox) for answering conjunctive queries over such an extended database. Based on this rewriting, we define category-theoretical satisfiability of a DL- \(Lite_{\mathcal {R}}\) knowledge base and show that a DL- \(Lite_{\mathcal {R}}\) knowledge base is set-theoreticallly satisfiable iff it is category-theoretically satisfiable. We also introduce a tractable algorithm for checking category-theoretical satisfiability. The simplicity of the construction of such an algorithm shows the power of categorical language in comparison with existing algorithms based on the construction of a model.