Skip to main content
SpringerLink
Log in

Inconsistency- and Error-Tolerant Reasoning w.r.t. Optimal Repairs of \(\mathcal{E}\mathcal{L}^\bot \) Ontologies

  • Conference paper
  • First Online:
Foundations of Information and Knowledge Systems (FoIKS 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14589))

  • 80 Accesses

Abstract

Errors in knowledge bases (KBs) written in a Description Logic (DL) are usually detected when reasoning derives an inconsistency or a consequence that does not hold in the application domain modelled by the KB. Whereas classical repair approaches produce maximal subsets of the KB not implying the inconsistency or unwanted consequence, optimal repairs maximize the consequence sets. In this paper, we extend previous results on how to compute optimal repairs from the DL \(\mathcal{E}\mathcal{L}\) to its extension \(\mathcal{E}\mathcal{L}^\bot \), which in contrast to \(\mathcal{E}\mathcal{L}\) can express inconsistency. The problem of how to deal with inconsistency in the context of optimal repairs was addressed previously, but in a setting where the (fixed) terminological part of the KB must satisfy a restriction on cyclic dependencies. Here, we consider a setting where this restriction is not required. We also show how the notion of optimal repairs obtained this way can be used in inconsistency- and error-tolerant reasoning.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Notes

  1. 1.

    https://www.w3.org/TR/owl2-overview/.

  2. 2.

    For example, the CI \( Human \sqsubseteq \exists { loves }.{ Human }\) destroys cycle-restrictedness, whereas the CI \(\exists { loves }.{ Human }\sqsubseteq Human \) does not.

  3. 3.

    In the CQ-case, using conjunctive instead of instance queries as repair requests may appear to be more appropriate, but this may destroy the covering property [9].

  4. 4.

    A homomorphism is a total and functional simulation.

References

  1. Baader, F., Brandt, S., Lutz, C.: Pushing the \(\cal{EL} \) envelope. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pp. 364–369. Professional Book Center (2005). http://ijcai.org/Proceedings/05/Papers/0372.pdf

  2. Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.) The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press (2003). https://doi.org/10.1017/cbo9780511711787

  3. Baader, F., Horrocks, I., Lutz, C., Sattler, U.: An Introduction to Description Logic. Cambridge University Press, Cambridge (2017). https://doi.org/10.1017/9781139025355

  4. Baader, F., Koopmann, P., Kriegel, F.: Optimal repairs in the description logic \(\cal{EL} \) revisited. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds.) JELIA 2023. LNCS, vol. 14281, pp. 11–34. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-43619-2_2

    Chapter  Google Scholar 

  5. Baader, F., Koopmann, P., Kriegel, F., Nuradiansyah, A.: Computing optimal repairs of quantified ABoxes w.r.t. static \(\cal{EL}\) TBoxes. In: Platzer, A., Sutcliffe, G. (eds.) CADE 2021. LNCS (LNAI), vol. 12699, pp. 309–326. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-79876-5_18

    Chapter  Google Scholar 

  6. Baader, F., Koopmann, P., Kriegel, F., Nuradiansyah, A.: Computing optimal repairs of quantified ABoxes w.r.t. static \(\cal{EL} \) TBoxes (extended version). LTCS-Report 21-01, Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden (2021). https://doi.org/10.25368/2022.64

  7. Baader, F., Koopmann, P., Kriegel, F., Nuradiansyah, A.: Optimal ABox repair w.r.t. static \(\cal{EL} \) TBoxes: From quantified ABoxes back to ABoxes. In: Groth, P., et al. (eds.) ESWC 2022. LNCS, vol. 13261, pp. 130–146. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-06981-9_8

    Chapter  Google Scholar 

  8. Baader, F., Koopmann, P., Kriegel, F., Nuradiansyah, A.: Optimal ABox repair w.r.t. static \(\cal{EL} \) TBoxes: from quantified ABoxes back to ABoxes (extended version). LTCS-Report 22-01, Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden (2022). https://doi.org/10.25368/2022.65

  9. Baader, F., Kriegel, F.: Pushing optimal ABox repair from \(\cal{EL} \) towards more expressive Horn-DLs. In: Proceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning (KR) (2022). https://doi.org/10.24963/kr.2022/3

  10. Baader, F., Kriegel, F., Nuradiansyah, A.: Error-tolerant reasoning in the description logic \(\cal{EL} \) based on optimal repairs. In: Governatori, G., Turhan, A.Y. (eds.) RuleML+RR 2022. LNCS, vol. 13752, pp. 227–243. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-21541-4_15

    Chapter  Google Scholar 

  11. Baader, F., Kriegel, F., Nuradiansyah, A.: Treating role assertions as first-class citizens in repair and error-tolerant reasoning. In: Proceedings of the 38th ACM/SIGAPP Symposium on Applied Computing (SAC), pp. 974–982. ACM (2023). https://doi.org/10.1145/3555776.3577630

  12. Baader, F., Kriegel, F., Nuradiansyah, A.: Inconsistency- and error-tolerant reasoning w.r.t. optimal repairs of \(\cal{EL} ^{\bot }\) ontologies (extended version). LTCS-Report 24-02, Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden (2024). https://doi.org/10.25368/2024.6

  13. Baader, F., Kriegel, F., Nuradiansyah, A., Peñaloza, R.: Making repairs in description logics more gentle. In: Proceedings of the 16th International Conference on Principles of Knowledge Representation and Reasoning (KR), pp. 319–328. AAAI Press (2018). https://cdn.aaai.org/ocs/18056/18056-78653-1-PB.pdf

  14. Baader, F., Kriegel, F., Nuradiansyah, A., Peñaloza, R.: Computing compliant anonymisations of quantified ABoxes w.r.t. \(\cal{EL} \) policies. In: Pan, J.Z., et al. (eds.) ISWC 2020. LNCS, vol. 12506, pp. 3–20. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-62419-4_1

    Chapter  Google Scholar 

  15. Baader, F., Suntisrivaraporn, B.: Debugging SNOMED CT using axiom pinpointing in the description logic \(\cal{EL}^+\). In: Proceedings of the 3rd International Conference on Knowledge Representation in Medicine (KR-MED). CEUR Workshop Proceedings, vol. 410. CEUR-WS.org (2008). https://ceur-ws.org/Vol-410/Paper01.pdf

  16. Bienvenu, M., Ortiz, M.: Ontology-mediated query answering with data-tractable description logics. In: Faber, W., Paschke, A. (eds.) Reasoning Web 2015. LNCS, vol. 9203, pp. 218–307. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21768-0_9

    Chapter  Google Scholar 

  17. Bienvenu, M., Rosati, R.: Tractable approximations of consistent query answering for robust ontology-based data access. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI), pp. 775–781. IJCAI/AAAI (2013). https://www.ijcai.org/Proceedings/13/Papers/121.pdf

  18. Calì, A., Lembo, D., Rosati, R.: On the decidability and complexity of query answering over inconsistent and incomplete databases. In: Proceedings of the 22nd ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS), pp. 260–271. ACM (2003). https://doi.org/10.1145/773153.773179

  19. Gottlob, G., Leone, N., Scarcello, F.: The complexity of acyclic conjunctive queries. J. ACM 48(3), 431–498 (2001). https://doi.org/10.1145/382780.382783

    Article  MathSciNet  Google Scholar 

  20. Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing simulations on finite and infinite graphs. In: Proceedings of the 36th Annual Symposium on Foundations of Computer Science (FOCS), pp. 453–462. IEEE Computer Society (1995). https://doi.org/10.1109/sfcs.1995.492576

  21. Hoehndorf, R., Schofield, P.N., Gkoutos, G.V.: The role of ontologies in biological and biomedical research: a functional perspective. Brief. Bioinform. 16(6), 1069–1080 (2015). https://doi.org/10.1093/bib/bbv011

    Article  Google Scholar 

  22. Lembo, D., Lenzerini, M., Rosati, R., Ruzzi, M., Savo, D.F.: Inconsistency-tolerant query answering in ontology-based data access. J. Web Semant. 33, 3–29 (2015). https://doi.org/10.1016/j.websem.2015.04.002

    Article  Google Scholar 

  23. Ludwig, M., Peñaloza, R.: Error-tolerant reasoning in the description logic \(\cal{E{}L}\). In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS (LNAI), vol. 8761, pp. 107–121. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11558-0_8

    Chapter  Google Scholar 

  24. Lutz, C., Wolter, F.: Deciding inseparability and conservative extensions in the description logic \(\cal{EL} \). J. Symb. Comput. 45(2), 194–228 (2010). https://doi.org/10.1016/j.jsc.2008.10.007

    Article  Google Scholar 

  25. Parsia, B., Sirin, E., Kalyanpur, A.: Debugging OWL ontologies. In: Proceedings of the 14th International Conference on World Wide Web (WWW), pp. 633–640. ACM (2005). https://doi.org/10.1145/1060745.1060837

  26. Peñaloza, R.: Error-tolerance and error management in lightweight description logics. Künstl. Intell. 34(4), 491–500 (2020). https://doi.org/10.1007/s13218-020-00684-5

    Article  Google Scholar 

  27. Schlobach, S., Huang, Z., Cornet, R., van Harmelen, F.: Debugging incoherent terminologies. J. Autom. Reason. 39(3), 317–349 (2007). https://doi.org/10.1007/s10817-007-9076-z

    Article  MathSciNet  Google Scholar 

  28. Xiao, G., et al.: Ontology-based data access: a survey. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI), pp. 5511–5519. ijcai.org (2018). https://doi.org/10.24963/ijcai.2018/777

Download references

Acknowledgements

This work has been supported by Deutsche Forschungsgemeinschaft (DFG) in projects 430150274 (Repairing Description Logic Ontologies) and 389792660 (TRR 248: Foundations of Perspicuous Software Systems).

Author information

Authors and Affiliations

  1. Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany

    Franz Baader, Francesco Kriegel & Adrian Nuradiansyah

  2. Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Leipzig, Germany

    Franz Baader & Francesco Kriegel

Authors
  1. Franz Baader
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesco Kriegel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adrian Nuradiansyah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Francesco Kriegel .

Editor information

Editors and Affiliations

  1. Leibniz University Hannover, Hanover, Germany

    Arne Meier

  2. TU Wien, Wien, Austria

    Magdalena Ortiz

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Baader, F., Kriegel, F., Nuradiansyah, A. (2024). Inconsistency- and Error-Tolerant Reasoning w.r.t. Optimal Repairs of \(\mathcal{E}\mathcal{L}^\bot \) Ontologies. In: Meier, A., Ortiz, M. (eds) Foundations of Information and Knowledge Systems. FoIKS 2024. Lecture Notes in Computer Science, vol 14589. Springer, Cham. https://doi.org/10.1007/978-3-031-56940-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-56940-1_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-56939-5

  • Online ISBN: 978-3-031-56940-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation