A Set-Theoretic Approach to ABox Reasoning Services

  • Domenico Cantone
  • Marianna Nicolosi-Asmundo
  • Daniele Francesco Santamaria
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10364)


In this paper we consider the most common ABox reasoning services for the description logic \(\mathcal {DL}\langle \mathsf {4LQS}^{\mathsf{R},\!\times }\rangle (\mathbf {D})\) (\(\mathcal {DL}_{\mathbf {D}}^{4,\!\times }\), for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment \(\mathsf {4LQS^R}\). 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 (CQA) problem that can be instantiated to the most widespread ABox reasoning tasks. We also present a KE-tableau 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-tableau based decision procedure for the CQA problem.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Domenico Cantone
    • 1
  • Marianna Nicolosi-Asmundo
    • 1
  • Daniele Francesco Santamaria
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of CataniaCataniaItaly

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