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TBox abduction explains why an observation is not entailed by a TBox, by computing multiple sets of axioms, called explanations, such that each explanation does not entail the observation alone while appending an explanation to the TBox renders the observation entailed but does not introduce incoherence. Considering that practical explanations in TBox abduction are likely to mimic minimal explanations for TBox entailments, we introduce admissible explanations which are subsets of those justifications for the observation that are instantiated from a finite set of justification patterns. A justification pattern is obtained from a minimal set of axioms responsible for a certain atomic concept inclusion by replacing all concept (resp. role) names with concept (resp. role) variables. The number of admissible explanations is finite but can still be so large that computing all admissible explanations is impractical. Thus, we introduce a variant of subset-minimality, written ⊆ds-minimality, which prefers fresh (concept or role) names than existing names. We propose efficient methods for computing all admissible ⊆ds-minimal explanations and for computing all justification patterns, respectively. Experimental results demonstrate that combining the proposed methods is able to achieve a practical approach to TBox abduction.