Skip to main content
SpringerLink
Log in
Book cover

Description Logic, Theory Combination, and All That pp 135–146Cite as

Strong Explanations for Nonmonotonic Reasoning

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11560))

Abstract

The ability to generate explanations for inferences drawn from a knowledge base is of utmost importance for intelligent systems. A central notion in this context are minimal subsets of the knowledge base entailing a certain formula. Such subsets are often referred to as justifications, and their identification is called axiom pinpointing.As observed by Franz Baader, this concept of explanations is useful for monotonic logics in which additional information can never invalidate former conclusions. However, for nonmonotonic logics the concept simply makes no sense. In this paper, we introduce a different notion, called strong explanation. Strong explanations coincide with the standard notion for monotonic logics, but also handle the nonmonotonic case adequately.

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

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

Learn about institutional subscriptions

Notes

  1. 1.

    See www.darpa.mil/program/explainable-artificial-intelligence.

  2. 2.

    We will use both terms interchangeably in this paper.

  3. 3.

    See https://protege.stanford.edu/.

  4. 4.

    Since Tbox and ABox elements differ syntactically, we do not explicitly distinguish these to sets.

References

  1. Baader, F., Hollunder, B.: Embedding defaults into terminological knowledge representation formalisms. J. Autom. Reason. 14(1), 149–180 (1995)

    Article  MathSciNet  Google Scholar 

  2. Baader, F., Horrocks, I., Lutz, C., Sattler, U.: An Introduction to Description Logic. Cambridge University Press, Cambridge (2017)

    Book  Google Scholar 

  3. Baader, F., Peñaloza, R.: Axiom pinpointing in general tableaux. J. Log. Comput. 20(1), 5–34 (2010)

    Article  MathSciNet  Google Scholar 

  4. Bonatti, P.A., Lutz, C., Wolter, F.: Description logics with circumscription. In: Proceedings of Tenth International Conference on Principles of Knowledge Representation and Reasoning, Lake District of the United Kingdom, 2–5 June 2006, pp. 400–410 (2006)

    Google Scholar 

  5. Brewka, G., Eiter, T.: Equilibria in heterogeneous nonmonotonic multi-context systems. In: Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence, Vancouver, British Columbia, Canada, 22–26 July 2007, pp. 385–390 (2007)

    Google Scholar 

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

    Article  Google Scholar 

  7. Brewka, G., Thimm, M., Ulbricht, M.: Strong inconsistency. Artif. Intell. 267, 78–117 (2019)

    Article  MathSciNet  Google Scholar 

  8. Casini, G., Meyer, T., Moodley, K., Varzinczak, I.J.: Towards practical defeasible reasoning for description logics. In: Informal Proceedings of the 26th International Workshop on Description Logics, Ulm, Germany, 23–26 July 2013, pp. 587–599 (2013)

    Google Scholar 

  9. Casini, G., Meyer, T., Varzinczak, I.J., Moodley, K.: Nonmonotonic reasoning in description logics: rational closure for the ABox. In: Informal Proceedings of the 26th International Workshop on Description Logics, Ulm, Germany, 23–26 July 2013, pp. 600–615 (2013)

    Google Scholar 

  10. Casini, G., Meyer, T., Moodley, K., Sattler, U., Varzinczak, I.: Introducing defeasibility into OWL ontologies. In: Arenas, M., et al. (eds.) ISWC 2015. LNCS, vol. 9367, pp. 409–426. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25010-6_27

    Chapter  Google Scholar 

  11. Casini, G., Straccia, U.: Rational closure for defeasible description logics. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 77–90. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15675-5_9

    Chapter  MATH  Google Scholar 

  12. Donini, F.M., Nardi, D., Rosati, R.: Autoepistemic description logics. In: Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence, IJCAI 1997, Nagoya, Japan, 23–29 August 1997, vol. 2, pp. 136–141 (1997)

    Google Scholar 

  13. Gelfond, M., Leone, N.: Logic programming and knowledge representation - the a-Prolog perspective. Artif. Intell. 138(1–2), 3–38 (2002)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  15. Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: A non-monotonic description logic for reasoning about typicality. Artif. Intell. 195, 165–202 (2013)

    Article  MathSciNet  Google Scholar 

  16. Horridge, M., Bail, S., Parsia, B., Sattler, U.: Toward cognitive support for OWL justifications. Knowl.-Based Syst. 53, 66–79 (2013)

    Article  Google Scholar 

  17. Horridge, M., Parsia, B., Sattler, U.: Laconic and precise justifications in OWL. In: Sheth, A., et al. (eds.) ISWC 2008. LNCS, vol. 5318, pp. 323–338. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88564-1_21

    Chapter  Google Scholar 

  18. Kalyanpur, A., Parsia, B., Sirin, E., Grau, B.C., Hendler, J.A.: Swoop: a web ontology editing browser. J. Web Semant. 4(2), 144–153 (2006)

    Article  Google Scholar 

  19. Kalyanpur, A., Parsia, B., Sirin, E., Hendler, J.A.: Debugging unsatisfiable classes in OWL ontologies. J. Web Semant. 3(4), 268–293 (2005)

    Article  Google Scholar 

  20. Kraus, S., Lehmann, D.J., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1–2), 167–207 (1990)

    Article  MathSciNet  Google Scholar 

  21. Lehmann, D.J., Magidor, M.: What does a conditional knowledge base entail? Artif. Intell. 55(1), 1–60 (1992)

    Article  MathSciNet  Google Scholar 

  22. Manthey, N., Peñaloza, R., Rudolph, S.: Efficient axiom pinpointing in \(\cal{EL}\) using SAT technology. In: Proceedings of the 29th International Workshop on Description Logics, Cape Town, South Africa, 22–25 April 2016 (2016). http://ceur-ws.org/Vol-1577/paper_33.pdf

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

    Article  MathSciNet  Google Scholar 

  24. Pensel, M., Turhan, A.: Reasoning in the defeasible description logic \(\cal{EL_{\bot }}\) - computing standard inferences under rational and relevant semantics. Int. J. Approx. Reason. 103, 28–70 (2018). https://doi.org/10.1016/j.ijar.2018.08.005

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  26. Schlobach, S.: Diagnosing terminologies. In: Proceedings of the Twentieth National Conference on Artificial Intelligence and the Seventeenth Innovative Applications of Artificial Intelligence Conference, Pittsburgh, Pennsylvania, USA, 9–13 July 2005, pp. 670–675 (2005)

    Google Scholar 

  27. Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, IJCAI 2003, Acapulco, Mexico, 9–15 August 2003, pp. 355–362 (2003)

    Google Scholar 

  28. Schlobach, S., Huang, Z., Cornet, R., van Harmelen, F.: Debugging incoherent terminologies. J. Autom. Reason. 39(3), 317–349 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We thank the reviewers for their comments which helped to significantly improve this paper. The work presented in this paper was supported by QuantLA, the joint Dresden/Leipzig doctoral school on Quantitative Logics and Automata (DFG Research Training Group 1763) which was initiated and run by Franz Baader. The second author was a PhD student in QuantLA from 2015–2018. There was additional support from the DFG Research Unit Hybris (Hybrid Reasoning in Intelligent Systems, FOR 1513) in which the first author had the great pleasure to cooperate with Franz Baader for 6 years. The first author is deeply indebted to Franz for more than three decades of challenge, inspiration, and insight.

Author information

Authors and Affiliations

  1. Department of Informatics, Leipzig University, Augustusplatz 10, 04109, Leipzig, Germany

    Gerhard Brewka & Markus Ulbricht

Authors
  1. Gerhard Brewka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Markus Ulbricht
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gerhard Brewka .

Editor information

Editors and Affiliations

  1. University of Bremen, Bremen, Germany

    Carsten Lutz

  2. University of Manchester, Manchester, UK

    Uli Sattler

  3. University of Iowa, Iowa City, IA, USA

    Cesare Tinelli

  4. TU Dresden, Dresden, Germany

    Anni-Yasmin Turhan

  5. University of Liverpool, Liverpool, UK

    Frank Wolter

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Brewka, G., Ulbricht, M. (2019). Strong Explanations for Nonmonotonic Reasoning. In: Lutz, C., Sattler, U., Tinelli, C., Turhan, AY., Wolter, F. (eds) Description Logic, Theory Combination, and All That. Lecture Notes in Computer Science(), vol 11560. Springer, Cham. https://doi.org/10.1007/978-3-030-22102-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-22102-7_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22101-0

  • Online ISBN: 978-3-030-22102-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation