Current Description Logic reasoning systems provide only limited support for debugging logically erroneous knowledge bases. In this paper we propose new non-standard reasoning services which we designed and implemented to pinpoint logical contradictions when developing the medical terminology DICE. We provide complete algorithms for unfoldable ¢¡¤£ -TBoxes based on minimisation of axioms using Boolean methods for minimal unsatisfiability-preserving sub-TBoxes, and an incomplete bottom-up method for generalised incoherence-preserving terminologies.