The description logic SHIQ with a flexible meta-modelling hierarchy

This work is motivated by a real-world case study where it is necessary to integrate and relate existing ontologies through meta-modelling. For this, we introduce the Description Logic SHIQM which is obtained from SHIQ by adding statements that equate individuals to concepts in a knowledge base. In this new extension, concepts can be individuals of another concept (called meta-concept) which itself can be an individual of yet another concept (called meta-meta-concept) and so on. We define an algorithm that checks consistency of SHIQM by modifying the Tableau algorithm for SHIQ. From the practical point of view, this has the advantage that we can reuse the code of existing OWL reasoners. From the theoretical point of view, it has a similar advantage of reuse. We make use of the existing results and proofs that lead to correctness of the algorithm for SHIQ in order to prove correctness of the algorithm for SHIQM.