We present a simple and intuitive extension GCWAG of the generalized closed world assumption (GCWA) from positive disjunctive deductive databases to general disjunctive deductive databases (with default negation). This semantics is defined in terms of unfounded sets and possesses an argumentation-theoretic characterization. We also provide a top-down procedure for GCWAG, which is sound and complete with respect to GCWAG. We investigate two query evaluation methods for GCWAG: database partition, and database splitting. The basic idea of these methods is to divide the original deductive database into several smaller sub-databases and the query evaluation in the original database is transformed into the problem of query evaluation in smaller or simplified components. We prove that these two methods of query evaluation are all sound with respect to GCWAG.