Abstract. Generalized closed world reasoning allows for the assumption of a specified maximal set of negated atomic assertions retaining the consistency of an indefinite knowledge base. In this paper, a generalized closed world assumption (GCWA) is specified for the description logic ALCN and all of its sublanguages, provided that the terminological component is eliminable. In certain situations, by applying the GCWA, queries are often answered as intended by users. Opposed to queries with an epistemic operator K, querying with this approach provides the information which of the corresponding assertions can consistently be assumed to be true. Further, the GCWA can be applied locally.