Abstract
Ontologies based on Description Logic (DL) represent general background knowledge in a terminology (TBox) and the actual data in an ABox. Both human-made and machine-learned data sets may contain errors, which are usually detected when the DL reasoner returns unintuitive or obviously incorrect answers to queries. To eliminate such errors, classical repair approaches offer as repairs maximal subsets of the ABox not having the unwanted answers w.r.t. the TBox. It is, however, not always clear which of these classical repairs to use as the new, corrected data set. Error-tolerant semantics instead takes all repairs into account: cautious reasoning returns the answers that follow from all classical repairs whereas brave reasoning returns the answers that follow from some classical repair. It is inspired by inconsistency-tolerant reasoning and has been investigated for the DL \(\mathcal{E}\mathcal{L} \), but in a setting where the TBox rather than the ABox is repaired. In a series of papers, we have developed a repair approach for ABoxes that improves on classical repairs in that it preserves a maximal set of consequences (i.e., answers to queries) rather than a maximal set of ABox assertions. The repairs obtained by this approach are called optimal repairs. In the present paper, we investigate error-tolerant reasoning in the DL \(\mathcal{E}\mathcal{L} \), but we repair the ABox and use optimal repairs rather than classical repairs as the underlying set of repairs. To be more precise, we consider a static \(\mathcal{E}\mathcal{L} \) TBox (which is assumed to be correct), represent the data by a quantified ABox (where some individuals may be anonymous), and use \(\mathcal{E}\mathcal{L} \) concepts as queries (instance queries). We show that brave entailment of instance queries can be decided in polynomial time. Cautious entailment can be decided by a coNP procedure, but is still in P if the TBox is empty.
Partially supported by the AI competence center ScaDS.AI Dresden/Leipzig and the German Research Foundation (DFG) in Project 430150274 and SFB/TRR 248.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
- 2.
- 3.
Since we are only interested in instance relationships, the appropriate entailment and equivalence relations between quantified ABoxes are IQ-entailment and IQ-equivalence [3].
- 4.
- 5.
A repair pre-type need only satisfy the first two conditions. If the TBox is empty, then this third condition is trivially true since one can take \(K' = K\).
References
Baader, F., Brandt, S., Lutz, C.: Pushing the \(\cal{EL} \) envelope. In: IJCAI-05, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence. Professional Book Center (2005). https://www.ijcai.org/Proceedings/05/Papers/0372.pdf
Baader, F., Horrocks, I., Lutz, C., Sattler, U.: An Introduction to Description Logic. Cambridge University Press, Cambridge (2017)
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
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, Germany (2021). https://doi.org/10.25368/2022.64
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
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, Germany (2022). https://doi.org/10.25368/2022.65
Baader, F., Kriegel, F., Nuradiansyah, A.: Privacy-preserving ontology publishing for \(\cal{EL} \) instance stores. In: Calimeri, F., Leone, N., Manna, M. (eds.) JELIA 2019. LNCS (LNAI), vol. 11468, pp. 323–338. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-19570-0_21
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
Baader, F., Suntisrivaraporn, B.: Debugging SNOMED CT using axiom pinpointing in the description logic \(\cal{EL} ^+\). In: Proceedings of the International Conference on Representing and Sharing Knowledge Using SNOMED (KR-MED 2008), Phoenix, Arizona (2008). http://ceur-ws.org/Vol-410/Paper01.pdf
Bienvenu, M., Rosati, R.: Tractable approximations of consistent query answering for robust ontology-based data access. In: IJCAI 2013, Proceedings of the 23rd International Joint Conference on Artificial Intelligence. IJCAI/AAAI (2013). https://www.ijcai.org/Proceedings/13/Papers/121.pdf
Calì, A., Lembo, D., Rosati, R.: On the decidability and complexity of query answering over inconsistent and incomplete databases. In: Proceedings of the Twenty-Second ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. ACM (2003). https://doi.org/10.1145/773153.773179
Cima, G., Lembo, D., Rosati, R., Savo, D.F.: Controlled query evaluation in description logics through instance indistinguishability. In: Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020. ijcai.org (2020). https://doi.org/10.24963/ijcai.2020/248
Kriegel, F.: Optimal fixed-premise repairs of \(\cal{EL} \) TBoxes. In: Bergmann, R., Malburg, L., Rodermund, S.C., Timm, I.J. (eds.) KI 2022. LNCS, vol. 13404, pp. 115–130. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-15791-2_11
Kriegel, F.: Optimal fixed-premise repairs of \(\cal{EL} \) TBoxes (extended version). LTCS-Report 22-04, Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany (2022). https://doi.org/10.25368/2022.321
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
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
Parsia, B., Sirin, E., Kalyanpur, A.: Debugging OWL ontologies. In: Proceedings of the 14th International Conference on World Wide Web (WWW 2005). ACM (2005). https://doi.org/10.1145/1060745.1060837
Peñaloza, R.: Error-tolerance and error management in lightweight description logics. Künstliche Intell. 34(4), 491–500 (2020). https://doi.org/10.1007/s13218-020-00684-5
Schlobach, S., Huang, Z., Cornet, R., Harmelen, F.: Debugging incoherent terminologies. J. Autom. Reason. 39(3), 317–349 (2007). https://doi.org/10.1007/s10817-007-9076-z
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Baader, F., Kriegel, F., Nuradiansyah, A. (2022). Error-Tolerant Reasoning in the Description Logic \(\mathcal{E}\mathcal{L}\) Based on Optimal Repairs. In: Governatori, G., Turhan, AY. (eds) Rules and Reasoning. RuleML+RR 2022. Lecture Notes in Computer Science, vol 13752. Springer, Cham. https://doi.org/10.1007/978-3-031-21541-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-031-21541-4_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-21540-7
Online ISBN: 978-3-031-21541-4
eBook Packages: Computer ScienceComputer Science (R0)