Abstract Finding justifications for an entailment is one of the major missions in the field of ontology research. Recent advances on finding justifications w.r.t. the light-weight description logics focused on encoding this problem into a propositional formula, and using SAT-based techniques to enumerate all MUSes (minimally unsatisfiable subformulas). It’s necessary to import more optimized techniques into finding justifications as emergence of large-scale real-world ontologies. In this paper, we propose a new strategy which introduces local search (in short, LS) technique to compute the approximating core before extracting an exact MUS. Although it is based on a heuristic and LS, such technique is complete in the sense that it always delivers a MUS for any unsatisfiable SAT instance. Our method will find the justifications for large-scale ontologies more effectively