Conservative Rewritability of Description Logic TBoxes

Boris Konev, Carsten Lutz, Frank Wolter, Michael Zakharyaschev

Abstract: We investigate the problem of conservative rewritability of a TBox T in a description logic (DL) L into a TBox T′ in a weaker DL L′. We focus on model-conservative rewritability (T′ entails T and all models of T are expandable to models of T′), subsumption-conservative rewritability (T′ entails T and all subsumptions in the signature of T entailed by T′ are entailed by T), and standard DLs between ALC and ALCQI. We give model-theoretic characterizations of conservative rewritability via bisimulations, inverse p-morphisms and generated subinterpretations, and use them to obtain a few rewriting algorithms and complexity results for deciding rewritability.