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On Horn Knowledge Bases in Regular Description Logic with Inverse

  • Linh Anh Nguyen
  • Thi-Bich-Loc Nguyen
  • Andrzej Szałas
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 244)

Abstract

We study a Horn fragment called Horn-\(\mathcal{R}eg^I\) of the regular description logic with inverse \(\mathcal{R}eg^I\), which extends the description logic \(\mathcal{ALC}\) with inverse roles and regular role inclusion axioms characterized by finite automata. In contrast to the well-known Horn fragments \(\mathcal{EL}\), DL-Lite, DLP, Horn-\(\mathcal{SHIQ}\) and Horn-\(\mathcal{SROIQ}\) of description logics, Horn-\(\mathcal{R}eg^I\) allows a form of the concept constructor “universal restriction” to appear at the left hand side of terminological inclusion axioms, while still has PTime data complexity. Namely, a universal restriction can be used in such places in conjunction with the corresponding existential restriction. We provide an algorithm with PTime data complexity for checking satisfiability of Horn-\(\mathcal{R}eg^I\) knowledge bases.

Keywords

Knowledge Base Description Logic Edge Base Concept Constructor Universal Restriction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Baader, F., Brandt, S., Lutz, C.: Pushing the EL envelope. In: Kaelbling, L.P., Saffiotti, A. (eds.) Proceedings of IJCAI 2005, pp. 364–369. Morgan-Kaufmann Publishers (2005)Google Scholar
  2. 2.
    Baader, F., Brandt, S., Lutz, C.: Pushing the EL envelope further. In: Proceedings of the OWLED 2008 DC Workshop on OWL: Experiences and Directions (2008)Google Scholar
  3. 3.
    Brandt, S.: Polynomial time reasoning in a description logic with existential restrictions, GCI axioms, and - what else? In: de Mántaras, R.L., Saitta, L. (eds.) Proceedings of ECAI 2004, pp. 298–302. IOS Press (2004)Google Scholar
  4. 4.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. Autom. Reasoning 39(3), 385–429 (2007)CrossRefzbMATHGoogle Scholar
  5. 5.
    Demri, S., de Nivelle, H.: Deciding regular grammar logics with converse through first-order logic. Journal of Logic, Language and Information 14(3), 289–329 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Grosof, B.N., Horrocks, I., Volz, R., Decker, S.: Description logic programs: combining logic programs with description logic. In: Proceedings of WWW 2003, pp. 48–57 (2003)Google Scholar
  7. 7.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press (2000)Google Scholar
  8. 8.
    Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible SROIQ. In: Doherty, P., Mylopoulos, J., Welty, C.A. (eds.) Proceedings of KR 2006, pp. 57–67. AAAI Press (2006)Google Scholar
  9. 9.
    Hustadt, U., Motik, B., Sattler, U.: Reasoning in description logics by a reduction to disjunctive Datalog. J. Autom. Reasoning 39(3), 351–384 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Nguyen, L.A.: A bottom-up method for the deterministic horn fragment of the description logic \(\mathcal{ALC}\). In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 346–358. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Nguyen, L.A.: Horn knowledge bases in regular description logics with PTime data complexity. Fundamenta Informaticae 104(4), 349–384 (2010)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Nguyen, L.A., Nguyen, T.-B.-L., Szałas, A.: A long version of the current paper, http://www.mimuw.edu.pl/~nguyen/HornRegI-long.pdf
  13. 13.
    Nguyen, L.A., Nguyen, T.-B.-L., Szałas, A.: A long version of the paper [14], http://www.mimuw.edu.pl/~nguyen/horn_dl_long.pdf
  14. 14.
    Nguyen, L.A., Nguyen, T.-B.-L., Szałas, A.: HornDL: An expressive horn description logic with pTime data complexity. In: Faber, W., Lembo, D. (eds.) RR 2013. LNCS, vol. 7994, pp. 259–264. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  15. 15.
    Nguyen, L.A., Szałas, A.: ExpTime tableau decision procedures for regular grammar logics with converse. Studia Logica 98(3), 387–428 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Nguyen, L.A., Szałas, A.: On the Horn fragments of serial regular grammar logics with converse. In: Proceedings of KES-AMSTA 2013. Frontiers of Artificial Intelligence and Applications, vol. 252, pp. 225–234. IOS Press (2013)Google Scholar
  17. 17.
    Ortiz, M., Rudolph, S., Simkus, M.: Query answering in the Horn fragments of the description logics SHOIQ and SROIQ. In: Walsh, T. (ed.) Proceedings of IJCAI 2011, pp. 1039–1044 (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Linh Anh Nguyen
    • 1
    • 2
  • Thi-Bich-Loc Nguyen
    • 3
  • Andrzej Szałas
    • 1
    • 4
  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland
  2. 2.Faculty of Information TechnologyVNU University of Engineering and TechnologyHanoiVietnam
  3. 3.Department of Information TechnologyHue University of SciencesHue CityVietnam
  4. 4.Dept. of Computer and Information ScienceLinköping UniversityLinköpingSweden

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