  In this paper we consider the most common ABox reasoning services for the
description logic $\mathcal{DL}\langle
\mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$
($\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$, for short) and prove their
decidability via a reduction to the satisfiability problem for the
set-theoretic fragment \flqsr. The description logic
$\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$ is very expressive, as it admits
various concept and role constructs, and data types, that allow one to
represent rule-based languages such as SWRL. Decidability results are achieved
by defining a generalization of the conjunctive query answering problem, called
HOCQA (Higher Order Conjunctive Query Answering), that can be instantiated to
the most wide\-spread ABox reasoning tasks. We also present a \ke\space based
procedure for calculating the answer set from
$\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$ knowledge bases and higher order
$\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$ conjunctive queries, thus providing
means for reasoning on several well-known ABox reasoning tasks. Our calculus
extends a previously introduced \ke\space based decision procedure for the CQA
problem.
