Skip to main content

Justifications for Description Logic Knowledge Bases Under the Fixed-Domain Semantics

  • Conference paper
  • First Online:
Rules and Reasoning (RuleML+RR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11092))

Included in the following conference series:

Abstract

The fixed-domain semantics for OWL and description logic has been introduced to open up the OWL modeling and reasoning tool landscape for use cases resembling constraint satisfaction problems. While standard reasoning under this new semantics is by now rather well-understood theoretically and supported practically, more elaborate tasks like computation of justifications have not been considered so far, although being highly important in the modeling phase. In this paper, we compare three approaches to this problem: one using standard OWL technology employing an axiomatization of the fixed-domain semantics, one using our dedicated fixed-domain reasoner Wolpertinger in combination with standard justification computation technology, and one where the problem is encoded entirely into answer-set programming.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://github.com/wolpertinger-reasoner.

  2. 2.

    Subsequently just called explanation workbench.

  3. 3.

    We do not provide details on the normalization part, an refer instead to our previous work [6].

  4. 4.

    http://mat.gsia.cmu.edu/COLOR/instances.html.

References

  1. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook: Theory, Implementation, and Applications, 2nd edn., Cambridge University Press (2007)

    Google Scholar 

  2. Baader, F., Peñaloza, R., Suntisrivaraporn, B.: Pinpointing in the description logic \(\cal{EL}^+\). In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS (LNAI), vol. 4667, pp. 52–67. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74565-5_7

    Chapter  Google Scholar 

  3. Brewka, G., Delgrande, J.P., Romero, J., Schaub, T.: asprin: Customizing answer set preferences without a headache. In: AAAI, pp. 1467–1474. AAAI Press (2015)

    Google Scholar 

  4. Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)

    Article  Google Scholar 

  5. Calvanese, D.: Finite model reasoning in description logics. In: Proceedings of the 5th International Conference on the Principles of Knowledge Representation and Reasoning (KR 1996), pp. 292–303. Morgan Kaufmann (1996)

    Google Scholar 

  6. Gaggl, S.A., Rudolph, S., Schweizer, L.: Fixed-domain reasoning for description logics. In: Kaminka, G.A., et al. (eds.) Proceedings of the 22nd European Conference on Artificial Intelligence (ECAI 2016), Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 819–827. IOS Press, September 2016

    Google Scholar 

  7. Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T.: Answer set solving in practice. Synth. Lect. Artif. Intell. Mach. Learn. 6, 1–238 (2012)

    Article  Google Scholar 

  8. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9(3/4), 365–386 (1991)

    Article  Google Scholar 

  9. Hitzler, P., Gangemi, A., Janowicz, K., Krisnadhi, A., Presutti, V. (eds.): Ontology Engineering with Ontology Design Patterns - Foundations and Applications, Studies on the Semantic Web, vol. 25. IOS Press (2016)

    Google Scholar 

  10. Hitzler, P., Krötzsch, M., Parsia, B., Patel-Schneider, P.F., Rudolph, S. (eds.): OWL 2 Web Ontology Language: Primer. W3C Recommendation

    Google Scholar 

  11. Horridge, M.: Justification based explanation in ontologies. Ph.D. thesis, University of Manchester (2011)

    Google Scholar 

  12. Horridge, M., Parsia, B., Sattler, U.: Explanation of OWL entailments in Protege 4. In: Bizer, C., Joshi, A. (eds.) Proceedings of the Poster and Demonstration Session at the 7th International Semantic Web Conference (ISWC 2008), 28 October 2008, CEUR Workshop Proceedings, vol. 401. CEUR-WS.org (2008)

    Google Scholar 

  13. Horridge, M., Parsia, B., Sattler, U.: Explaining inconsistencies in OWL ontologies. In: Godo, L., Pugliese, A. (eds.) SUM 2009. LNCS (LNAI), vol. 5785, pp. 124–137. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04388-8_11

    Chapter  Google Scholar 

  14. Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\cal{SROIQ}\). In: Doherty, P., Mylopoulos, J., Welty, C.A. (eds.) Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, KR 2006, pp. 57–67. AAAI Press (2006)

    Google Scholar 

  15. Kalyanpur, A., Parsia, B., Horridge, M., Sirin, E.: Finding all justifications of OWL DL entailments. In: Aberer, K., et al. (eds.) ASWC/ISWC -2007. LNCS, vol. 4825, pp. 267–280. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76298-0_20

  16. Kazakov, Y.: \(\cal{RIQ}\) and \(\cal{SROIQ}\) are harder than \(\cal{SHOIQ}\). In: Brewka, G., Lang, J. (eds.) Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), pp. 274–284. AAAI Press (2008)

    Google Scholar 

  17. Lifschitz, V., Turner, H.: Splitting a logic program. In: ICLP, vol. 94, pp. 23–37 (1994)

    Google Scholar 

  18. Lutz, C., Sattler, U., Tendera, L.: The complexity of finite model reasoning in description logics. Inf. Comput. 199(1–2), 132–171 (2005)

    Article  MathSciNet  Google Scholar 

  19. Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Ann. Math. Artif. Intell. 25(3–4), 241–273 (1999)

    Article  MathSciNet  Google Scholar 

  20. Oetsch, J., Pührer, J., Tompits, H.: Stepwise debugging of answer-set programs. TPLP 18(1), 30–80 (2018)

    MathSciNet  MATH  Google Scholar 

  21. Papadimitriou, C.H., Wolfe, D.: The complexity of facets resolved. J. Comput. Syst. Sci. 37(1), 2–13 (1988)

    Article  MathSciNet  Google Scholar 

  22. Peñaloza, R., Sertkaya, B.: Understanding the complexity of axiom pinpointing in lightweight description logics. Artif. Intell. 250, 80–104 (2017)

    Article  MathSciNet  Google Scholar 

  23. Pontelli, E., Son, T.C., El-Khatib, O.: Justifications for logic programs under answer set semantics. TPLP 9(1), 1–56 (2009)

    MathSciNet  MATH  Google Scholar 

  24. Reiter, R.: A theory of diagnosis from first principles. Artif. Intell. 32(1), 57–95 (1987)

    Article  MathSciNet  Google Scholar 

  25. Rosati, R.: Finite model reasoning in DL-Lite. In: Bechhofer, S., Hauswirth, M., Hoffmann, J., Koubarakis, M. (eds.) ESWC 2008. LNCS, vol. 5021, pp. 215–229. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68234-9_18

    Chapter  Google Scholar 

  26. Rudolph, S.: Foundations of description logics. In: Polleres, A., et al. (eds.) Reasoning Web 2011. LNCS, vol. 6848, pp. 76–136. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23032-5_2

  27. Rudolph, S., Schweizer, L.: Not too big, not too small... complexities of fixed-domain reasoning in first-order and description logics. In: Oliveira, E., Gama, J., Vale, Z., Lopes Cardoso, H. (eds.) EPIA 2017. LNCS (LNAI), vol. 10423, pp. 695–708. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65340-2_57

    Chapter  Google Scholar 

  28. Rudolph, S., Schweizer, L., Tirtarasa, S.: Wolpertinger: a fixed-domain reasoner. In: Nikitina, N., Song, D., Fokoue, A., Haase, P. (eds.) Proceedings of the ISWC 2017 Posters and Demonstrations and Industry Tracks Co-located with 16th International Semantic Web Conference (ISWC 2017), 23–25 October 2017, CEUR Workshop Proceedings, vol. 1963. CEUR-WS.org (2017)

    Google Scholar 

Download references

Acknowledgements

We are grateful for the valuable feedback from the anonymous reviewers, which helped greatly to improve this work. This work is supported by DFG in the Research Training Group QuantLA (GRK 1763) and in the Research Training Group RoSI (GRK 1907).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lukas Schweizer .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rudolph, S., Schweizer, L., Tirtarasa, S. (2018). Justifications for Description Logic Knowledge Bases Under the Fixed-Domain Semantics. In: Benzmüller, C., Ricca, F., Parent, X., Roman, D. (eds) Rules and Reasoning. RuleML+RR 2018. Lecture Notes in Computer Science(), vol 11092. Springer, Cham. https://doi.org/10.1007/978-3-319-99906-7_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99906-7_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99905-0

  • Online ISBN: 978-3-319-99906-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics