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Query answering in circumscribed OWL2 profiles


This paper partially bridges a gap in the literature on Circumscription in Description Logics by investigating the tractability of conjunctive query answering in OWL2’s profiles. It turns out that the data complexity of conjunctive query answering is coNP-hard in circumscribed \(\mathcal {E}{\mathscr{L}}\) and DL-lite, while in circumscribed OWL2-RL conjunctive queries retain their classical semantics. In an attempt to capture nonclassical inferences in OWL2-RL, we consider conjunctive queries with safe negation. They can detect some of the nonclassical consequences of circumscribed knowledge bases, but data complexity becomes coNP-hard. In circumscribed \(\mathcal {E}{\mathscr{L}}\), answering queries with safe negation is undecidable.


  1. 1.

    Ahmetaj, S., Ortiz, M., Simkus, M.: Polynomial rewritings from expressive description logics with closed predicates to variants of Datalog. Artif. Intell. 280, 103–220 (2020)

    MathSciNet  Article  Google Scholar 

  2. 2.

    Alviano, M., Morak, M., Pieris, A.: Stable model semantics for tuple-generating dependencies revisited. In: Sallinger, E., den Bussche, J.V., Geerts, F. (eds.) Proceedings of the 36th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS Chicago, IL, USA, May 14-19, 2017, pp 377–388. ACM (2017)

  3. 3.

    Alviano, M., Pieris, A.: Default negation for non-guarded existential rules. In: Milo, T., Calvanese, D. (eds.) Proceedings of the 34th ACM Symposium on Principles of Database Systems, PODS Melbourne, Victoria, Australia, May 31 - June 4, 2015, pp 79–90 (2015)

  4. 4.

    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, Cambridge (2003)

  5. 5.

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

    MathSciNet  Article  Google Scholar 

  6. 6.

    Baader, F., Hollunder, B.: Priorities on defaults with prerequisites, and their application in treating specificity in terminological default logic. J. Autom Reasoning 15(1), 41–68 (1995)

    MathSciNet  Article  Google Scholar 

  7. 7.

    Berger, R.: The Undecidability of the Domino Problem, volume 1/66 of Memoirs of the AMS American Mathematical Society (1966)

  8. 8.

    Bonatti, P.A., Faella, M., Lutz, C., Sauro, L., Wolter, F.: Decidability of circumscribed description logics revisited. In: Eiter, T., Strass, H., Truszczynski, M., Woltran, S. (eds.) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation - Essays Dedicated to Gerhard Brewka on the Occasion of His 60th Birthday, volume 9060 of Lecture Notes in Computer Science, pp 112–124. Springer (2015)

  9. 9.

    Bonatti, P. A., Faella, M., Petrova, I. M., Sauro, L.: A new semantics for overriding in description logics. Artif. Intell. 222, 1–48 (2015)

    MathSciNet  Article  Google Scholar 

  10. 10.

    Bonatti, P. A., Faella, M., Sauro, L.: Defeasible inclusions in low-complexity DLs. J. Artif Intell. Res. (JAIR) 42, 719–764 (2011)

    MathSciNet  MATH  Google Scholar 

  11. 11.

    Bonatti, P. A., Lutz, C., Wolter, F.: The complexity of circumscription in DLs. J. Artif. Intell. Res. (JAIR) 35, 717–773 (2009)

    Article  Google Scholar 

  12. 12.

    Calì, A., Gottlob, G., Lukasiewicz, T.: A general datalog-based framework for tractable query answering over ontologies. J. Web Semant. 14, 57–83 (2012)

    Article  Google Scholar 

  13. 13.

    Calvanese, D., Giacomo, G. D., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. Artif. Intell. 195, 335–360 (2013)

    MathSciNet  Article  Google Scholar 

  14. 14.

    Casini, G., Straccia, U.: Defeasible inheritance-based description logics. J. Artif. Intell. Res. (JAIR) 48, 415–473 (2013)

    MathSciNet  Article  Google Scholar 

  15. 15.

    Delivorias, S., Rudolph, S.: Revisiting grounded circumscription in description logics. In: Ortiz, M., Schlobach, S. (eds.) Web Reasoning and Rule Systems - 10th International Conference, RR 2016, Aberdeen, UK, September 9-11, 2016, Proceedings, volume 9898 of Lecture Notes in Computer Science. Springer (2016)

  16. 16.

    Donini, F. M., Nardi, D., Rosati, R.: Description logics of minimal knowledge and negation as failure. ACM Trans. Comput. Log. 3(2), 177–225 (2002)

    MathSciNet  Article  Google Scholar 

  17. 17.

    Franconi, E., Ibáñez-García, Y.A., Seylan, I.: Query answering with dboxes is hard. Electron. Notes Theor. Comput. Sci. 278, 71–84 (2011)

    MathSciNet  Article  Google Scholar 

  18. 18.

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

    MathSciNet  Article  Google Scholar 

  19. 19.

    Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Semantic characterization of rational closure From propositional logic to description logics. Artif. Intell. 226, 1–33 (2015)

    MathSciNet  Article  Google Scholar 

  20. 20.

    Gottlob, G., Hernich, A., Kupke, C., Lukasiewicz, T.: Applications to description logics. In: Hoffmann, J., Selman, B. (eds.) Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, July 22-26 Equality-friendly well-founded Toronto, Ontario, Canada, p 2012. AAAI Press (2012)

  21. 21.

    Gottlob, G., Hernich, A., Kupke, C., Lukasiewicz, T.: Stable model semantics for guarded existential rules and description logics. In: Baral, C., Giacomo, G. D., Eiter, T. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Fourteenth International Conference, KR 2014, Vienna, Austria, July 20-24, 2014. AAAI Press (2014)

  22. 22.

    Gutiérrez-Basulto, V., Ibáñez-García, Y. A., Kontchakov, R., Kostylev, E. V.: Queries with negation and inequalities over lightweight ontologies. J. Web Semant. 35, 184–202 (2015)

    Article  Google Scholar 

  23. 23.

    Krisnadhi, A.A., Sengupta, K., Hitzler, P.: Local closed world semantics: Grounded circumscription for description logics. In: Rudolph, S., Gutiérrez, C. (eds.) Web Reasoning and Rule Systems - 5th International Conference, RR 2011, Galway, Ireland, August 29-30, 2011. Proceedings, volume 6902 of Lecture Notes in Computer Science , pp 263–268. Springer (2011)

  24. 24.

    Krötzsch, M.: Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning, KR 2020, Rhodes, Greece, September 12-18, 2020. In: Calvanese, D., Erdem, E., Thielscher, M. (eds.) , pp 603–613 (2020)

  25. 25.

    Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Intell. 172(6-7), 852–883 (2008)

    MathSciNet  Article  Google Scholar 

  26. 26.

    Lutz, C., Toman, D., Wolter, F.: Conjunctive query answering in the description logic EL using a relational database system. In: IJCAI 2009, Proceedings of the 21st International Joint Conference on Artificial Intelligence, Pasadena, California, USA, July 11–17, 2009, pp 2070–2075 (2009)

  27. 27.

    Recto, A.L.: Defaults, context, and knowledge: Alternatives for OWL-indexed knowledge bases. In: Pacific Symposium on Biocomputing, pp 226–237. World Scientific (2004)

  28. 28.

    Rosati, R.: The limits of querying ontologies. In: Schwentick, T., Suciu, D. (eds.) Database Theory - ICDT 2007, 11th International Conference, Barcelona, Spain, January 10–12 Proceedings, volume 4353 of Lecture Notes in Computer Science, p 2007 (2007)

  29. 29.

    Stevens, R., Aranguren, M. E., Wolstencroft, K., Sattler, U., Drummond, N., Horridge, M., Rector, A. L.: Using OWL to model biological knowledge. International Journal of Man-Machine Studies 65(7), 583–594 (2007)

    Google Scholar 

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Correspondence to Piero A. Bonatti.

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Bonatti, P.A. Query answering in circumscribed OWL2 profiles. Ann Math Artif Intell (2021).

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  • Low-complexity nonmonotonic description logics
  • Circumscription
  • Query answering

Mathematics Subject Classification (2010)

  • 68T30
  • 68Q17