Efficient TBox Reasoning with Value Restrictions—Introducing the \(\mathcal {F\!L}_{o}{} \textit{wer}\) Reasoner

  • Friedrich Michel
  • Anni-Yasmin TurhanEmail author
  • Benjamin Zarrieß
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11784)


The Description Logic (DL) \({\mathcal {F\!L}_0}\) uses universal quantification, whereas its well-known counter-part \(\mathcal {E\!L}\) uses the existential one. While for \(\mathcal {E\!L}\) deciding subsumption in the presence of general TBoxes is tractable, this is no the case for \({\mathcal {F\!L}_0}\). We present a novel algorithm for solving the ExpTime-hard subsumption problem in \({\mathcal {F\!L}_0}\) w.r.t. general TBoxes, which is based on the computation of so-called least functional models. To build a such a model our algorithm treats TBox axioms as rules that are applied to objects of the interpretation domain. This algorithm is implemented in the \(\mathcal {F\!L}_{o}{} \textit{wer}\) reasoner, which uses a variant of the Rete pattern matching algorithm to find applicable rules. We present an evaluation of \(\mathcal {F\!L}_{o}{} \textit{wer}\) on a large set of TBoxes generated from real world ontologies. The experimental results indicate that our prototype implementation of the specialised technique for \({\mathcal {F\!L}_0}\) leads in most cases to a huge performance gain in comparison to the highly-optimised tableau reasoners.


  1. 1.
    Baader, F., Brandt, S., Lutz, C.: Pushing the \(\cal{EL}\) envelope. In: IJCAI-05, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, 2005, pp. 364–369.
  2. 2.
    Baader, F., Fernández Gil, O., Pensel, M.: Standard and Non-Standard Inferences in the Description Logic \(\cal{FL}_0\) using Tree Automata. LTCS-Report 18–04, Chair for Automata Theory, Institute for Theoretical Computer Science, TU Dresden, Dresden, Germany (2018).
  3. 3.
    Baader, F., Fernández Gil, O., Marantidis, P.: Matching in the description logic \(\cal{FL}_0\) with respect to general TBoxes. In: LPAR-22, 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, 2018, EPiC Series in Computing, EasyChair, vol. 57, pp. 76–94 (2018).
  4. 4.
    Baader, F., Fernández Gil, O., Pensel, M.: Standard and non-standard inferences in the description logic \(\cal{FL}_0\) using tree automata. In: GCAI-2018, 4th Global Conference on Artificial Intelligence, 2018, EPiC Series in Computing, EasyChair, vol. 55, pp. 1–14 (2018).
  5. 5.
    Baader, F., Marantidis, P., Okhotin, A.: Approximate unification in the description logic \(\cal{FL}_0\). In: Michael, L., Kakas, A. (eds.) JELIA 2016. LNCS (LNAI), vol. 10021, pp. 49–63. Springer, Cham (2016). Scholar
  6. 6.
    Baader, F., Marantidis, P., Pensel, M.: The data complexity of answering instance queries in \(\cal{FL}_0\). In: Companion of the The Web Conference 2018, WWW 2018, ACM, pp. 1603–1607 (2018).
  7. 7.
    Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69(1), 5–40 (2001). Scholar
  8. 8.
    Brachman, R.J., Levesque, H.J.: The tractability of subsumption in frame-based description languages. In: Proceedings of the National Conference on Artificial Intelligence, 1984, AAAI Press, pp. 34–37 (1984).
  9. 9.
    Forgy, C.: Rete: a fast algorithm for the many patterns/many objects match problem. Artif. Intell. 19(1), 17–37 (1982). Scholar
  10. 10.
    Cuenca Grau, B., Horrocks, I., Motik, B., Parsia, B., Patel-Schneider, P.F., Sattler, U.: OWL 2: the next step for OWL. J. Web Semant. 6(4), 309–322 (2008)CrossRefGoogle Scholar
  11. 11.
    Horridge, M., Bechhofer, S.: The OWL API: a java API for OWL ontologies. Seman. Web 2(1), 11–21 (2011)Google Scholar
  12. 12.
    Kazakov, Y., de Nivelle, H.: Subsumption of concepts in \(\cal{FL}_0\) for (cyclic) terminologies with respect to descriptive semantics is PSPACE-complete. In: Proceedings of the 2003 International Workshop on Description Logics (DL 2003), 2003, CEUR Workshop Proceedings.
  13. 13.
    Krötzsch, M., Rudolph, S., Hitzler, P.: Complexity boundaries for Horn description logics. In: Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence, AAAI Press, pp. 452–457 (2007).
  14. 14.
    Michel, F.: Entwurf und Implementierung eines Systems zur Entscheidung von Subsumption in der Beschreibungslogik \(\cal{FL}_0\). Bachelor’s thesis, TU Dresden (2017). (in German)Google Scholar
  15. 15.
    Nebel, B.: Terminological reasoning is inherently intractable. Artif. Intell. 43(2), 235–249 (1990). Scholar
  16. 16.
    Parsia, B., Matentzoglu, N., Gonçalves, R.S., Glimm, B., Steigmiller, A.: The OWL reasoner evaluation (ORE) 2015 competition report. J. Autom. Reason. 59(4), 455–482 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Armas Romero, A., Cuenca Grau, B., Horrocks, I.: MORe: modular combination of OWL reasoners for ontology classification. In: Cudré-Mauroux, P., et al. (eds.) ISWC 2012. LNCS, vol. 7649, pp. 1–16. Springer, Heidelberg (2012). Scholar
  18. 18.
    Simancik, F., Kazakov, Y., Horrocks, I.: Consequence-based reasoning beyond Horn ontologies. In: IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, 2011, IJCAI/AAAI, pp. 1093–1098 (2011).

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Friedrich Michel
    • 1
  • Anni-Yasmin Turhan
    • 1
    Email author
  • Benjamin Zarrieß
    • 1
  1. 1.Institute for Theoretical Computer ScienceTechnische Universität DresdenDresdenGermany

Personalised recommendations