A Set-Theoretic Approach to ABox Reasoning Services

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.


  1. 1.
    Calvanese, D., De Giacomo, G., Lenzerini, M.: On the decidability of query containment under constraints. In: PODS, pp. 149–158 (1998)Google Scholar
  2. 2.
    Calvanese, D., De Giacomo, G., Lenzerini, M.: Conjunctive query containment and answering under description logic constraints. ACM Trans. Comput. Log. 9(3), 22:1–31 (2008)Google Scholar
  3. 3.
    Cantone, D., Longo, C., Nicolosi-Asmundo, M., Santamaria, D.F.: Web ontology representation and reasoning via fragments of set theory. In: Cate, B., Mileo, A. (eds.) RR 2015. LNCS, vol. 9209, pp. 61–76. Springer, Cham (2015). doi: 10.1007/978-3-319-22002-4_6 CrossRefGoogle Scholar
  4. 4.
    Cantone, D., Nicolosi-Asmundo, M.: On the satisfiability problem for a 4-level quantified syllogistic and some applications to modal logic. Fundamenta Informaticae 124(4), 427–448 (2013)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Cantone, D., Nicolosi-Asmundo, M., Orłowska, E.: Dual tableau-based decision procedures for some relational logics. In: Proceedings of the 25th Italian Conference on Computational Logic, CEUR-WS, vol. 598, Rende, Italy, 7–9 July 2010 (2010)Google Scholar
  6. 6.
    Cantone, D., Nicolosi-Asmundo, M., Orłowska, E.: Dual tableau-based decision procedures for relational logics with restricted composition operator. J. Appl. Non-Classical Logics 21(2), 177–200 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cantone, D., Nicolosi-Asmundo, M., Santamaria, D.F.: Conjunctive query answering via a fragment of set theory. In: Proceedings of ICTCS 2016, CEUR-WS, Lecce, 7–9 September, vol. 1720, pp. 23–35 (2016)Google Scholar
  8. 8.
    Cantone, D., Nicolosi-Asmundo, M., Santamaria, D.F.: A set-theoretic approach to ABox reasoning services. CoRR, 1702.03096 (2017). Extended versionGoogle Scholar
  9. 9.
    Cantone, D., Nicolosi-Asmundo, M., Santamaria, D.F., Trapani, F.: Ontoceramic: an OWL ontology for ceramics classification. In Proceedings of CILC 2015, CEUR-WS, vol. 1459, pp. 122–127, Genova, 1–3 July 2015Google Scholar
  10. 10.
    D’Agostino, M.: Tableau methods for classical propositional logic. In: D’Agostino, M., Gabbay, D.M., Hähnle, R., Posegga, J. (eds.) Handbook of Tableau Methods, pp. 45–123. Springer (1999)Google Scholar
  11. 11.
    Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\cal{SROIQ}\). In: Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, pp. 57–67. AAAI Press (2006)Google Scholar
  12. 12.
    Motik, B., Horrocks, I.: OWL datatypes: design and implementation. In: Sheth, A., Staab, S., Dean, M., Paolucci, M., Maynard, D., Finin, T., Thirunarayan, K. (eds.) ISWC 2008. LNCS, vol. 5318, pp. 307–322. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-88564-1_20 CrossRefGoogle Scholar
  13. 13.
    Ortiz, M., Sebastian, R., Šimkus, M.: Query answering in the Horn fragments of the description logics \(\cal{SHOIQ}\) and \(\cal{SROIQ}\). In: Proceedings of the 22th International Joint Conference on Artificial Intelligence, IJCAI 2011, vol. 2, pp. 1039–1044. AAAI Press (2011)Google Scholar
  14. 14.
    Smullyan, R.M.: First-Order Logic. Springer, Heidelberg (1968)CrossRefzbMATHGoogle Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of CataniaCataniaItaly

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