Model-theoretic inseparability and modularity of description logic ontologies

The aim of this paper is to introduce and study model-theoretic notionsof modularity in description logic and related reasoning problems. Our ap-proach is based on a generalisation of logical equivalence that is called model-theoretic inseparability. Two TBoxes are inseparable w.r.t. a vocabulary Σif they cannot be distinguished by the Σ-reducts of their models and thuscan equivalently be replaced by one another in any application where onlyvocabulary items from Σ are relevant. We study in-depth the complexityof deciding inseparability for the description logics EL and ALC and theirextensions with inverse roles. We then discuss notions of modules of a TBoxbased on model-theoretic inseparability and develop algorithms for extractingminimal modules from acyclic TBoxes. Finally, we provide an experimen-tal evaluation of our module extraction algorithm based on the large-scalemedical TBox Snomed ct.