Revision of a description logic-based ontology deals with the problem of incorporating newly received information consistently. In this paper, we propose a general operator for revising terminologies in description logic-based ontologies. Our revision operator relies on a reformulation of the kernel contraction operator in belief revision. We first define our revision operator for terminologies and show that it satisfies some desirable logical properties. Second, two algorithms are developed to instantiate the revision operator. Since in general, these two algorithms are computationally too hard, we propose a third algorithm as a more efficient alternative. We implemented the algorithms and provide evaluation results on their efficiency, effectiveness and meaningfulness in the context of two application scenarios: Incremental ontology learning and mapping revision.