Some algebraic results in Description logics : Free model and inclusions, finite basis theorem, and completion of knowledge bases

We propose a method to complete description logic (DL) knowledge bases. For this, we firstly build a canonical finite model from a given DL knowledge base satisfying some constraints on the form of its axioms. Then, we build a new DL knowledge base that infers all the properties of the canonical model. This latter DL knowledge base necessarily completes (according to the sense given to this notion in the paper) the starting DL knowledge base. This is the use and adaptation of results in universal algebra that allow us to get an effective process for completing DL knowledge bases.