Conjunctive Query Answering via a Fragment of Set Theory (Extended   Version)
  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. 
Domenico Cantone, Marianna Nicolosi-Asmundo, Daniele Francesco   Santamaria
cs.LO