  We address the problem of Conjunctive Query Answering (CQA) for the
description logic $\dlssx$ ($\shdlssx$, for short) which extends the logic
$\dlss$ with Boolean operations on concrete roles and with the product of
concepts.
  The result is obtained by formalizing $\shdlssx$-knowledge bases and
$\shdlssx$-conjunctive queries in terms of formulae of the four-level
set-theoretic fragment $\flqsr$, which admits a restricted form of
quantification on variables of the first three levels and on pair terms. We
solve the CQA problem for $\shdlssx$ through a decision procedure for the
satisfiability problem of $\flqsr$. We further define a \ke\space based
procedure for the same problem, more suitable for implementation purposes, and
analyze its computational complexity.
