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.Comment: Extended version of the paper entitled "Conjunctive Query Answering via a Fragment of Set Theory" submitted to the Conference ICTCS 2016. arXiv admin note: text overlap with arXiv:1505.0207