Advertisement

Assertional Removed Sets Merging of DL-Lite Knowledge Bases

  • Salem Benferhat
  • Zied Bouraoui
  • Odile Papini
  • Eric WürbelEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11940)

Abstract

DL-Lite is a tractable family of Description Logics that underlies the OWL-QL profile of the ontology web language, which is specifically tailored for query answering. In this paper, we consider the setting where the queried data are provided by several and potentially conflicting sources. We propose a merging approach, called “Assertional Removed Sets Fusion” (ARSF) for merging \(DL\)-\(Lite\) assertional bases. This approach stems from the inconsistency minimization principle and consists in determining the minimal subsets of assertions, called assertional removed sets, that need to be dropped from the original assertional bases in order to resolve conflicts between them. We give several merging strategies based on different definitions of minimality criteria, and we characterize the behaviour of these strategies with respect to rational properties. The last part of the paper shows how to use the notion of hitting sets for computing the assertional removed sets, and the merging outcome.

Notes

Acknowledgements

This work is partially supported by the European project H2020-MSCA-RISE: AniAge (High Dimensional Heterogeneous Data based Animation Techniques for Southeast Asian Intangible Cultural Heritage). Zied Bouraoui was supported by CNRS PEPS INS2I MODERN.

References

  1. 1.
    Alchourrón, C., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Log. 50(2), 510–530 (1985)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Arenas, M., Bertossi, L.E., Chomicki, J.: Consistent query answers in inconsistent databases. In: Proceedings of the Eighteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Philadelphia, Pennsylvania, USA, pp. 68–79 (1999)Google Scholar
  3. 3.
    Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-Lite family and relations. J. Artif. Intell. Res. (JAIR) 36, 1–69 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Baget, J.F., et al.: A general modifier-based framework for inconsistency-tolerant query answering. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, Cape Town, South Africa, 25–29 April 2016, pp. 513–516 (2016)Google Scholar
  5. 5.
    Baget, J.F., et al.: Inconsistency-tolerant query answering: rationality properties and computational complexity analysis. In: Michael, L., Kakas, A. (eds.) JELIA 2016. LNCS (LNAI), vol. 10021, pp. 64–80. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-48758-8_5CrossRefGoogle Scholar
  6. 6.
    Baral, C., Kraus, S., Minker, J., Subrahmanian, V.S.: Combining knowledge bases consisting of first order theories. Comp. Intell. 8(1), 45–71 (1992)CrossRefGoogle Scholar
  7. 7.
    Benferhat, S., Bouraoui, Z., Papini, O., Würbel, E.: Assertional-based removed sets revision of DL-Lite\(_{R}\) knowledge bases. In: ISAIM (2014)Google Scholar
  8. 8.
    Benferhat, S., Dubois, D., Kaci, S., Prade, H.: Possibilistic merging and distance-based fusion of propositional information. Stud. Logica. 58(1), 17–45 (1997)CrossRefGoogle Scholar
  9. 9.
    Bienvenu, M.: On the complexity of consistent query answering in the presence of simple ontologies. In: Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence (2012)Google Scholar
  10. 10.
    Bloch, I., Hunter, A., et al.: Fusion: general concepts and characteristics. Int. J. Intell. Syst. 16(10), 1107–1134 (2001) CrossRefGoogle Scholar
  11. 11.
    Bloch, I., Lang, J.: Towards mathematical morpho-logics. In: Bouchon-Meunier, B., Gutiérrez-Ríos, J., Magdalena, L., Yager, R.R. (eds.) Technologies for Constructing Intelligent Systems 2. STUDFUZZ, vol. 90, pp. 367–380. Physica, Heidelberg (2002).  https://doi.org/10.1007/978-3-7908-1796-6_29CrossRefGoogle Scholar
  12. 12.
    Calvanese, D., Giacomo, G.D., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: the DL-Lite family. J. Autom. Reasoning 39(3), 385–429 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Calvanese, D., Kharlamov, E., Nutt, W., Zheleznyakov, D.: Evolution of DL - Lite knowledge bases. In: Patel-Schneider, P.F., et al. (eds.) ISWC 2010. LNCS, vol. 6496, pp. 112–128. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-17746-0_8CrossRefGoogle Scholar
  14. 14.
    Falappa, M.A., Kern-Isberner, G., Reis, M.D.L., Simari, G.R.: Prioritized and non-prioritized multiple change on belief bases. J. Philos. Log. 41, 77–113 (2012)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Falappa, M.A., Kern-Isberner, G., Simari, G.R.: Explanations, belief revision and defeasible reasoning. Artif. Intell. 141(1/2), 1–28 (2002)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Fuhrmann, A.: An Essay on Contraction. CSLI Publications, Stanford (1997)Google Scholar
  17. 17.
    Hue, J., Papini, O., Würbel, E.: Syntactic propositional belief bases fusion with removed sets. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 66–77. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-75256-1_9CrossRefzbMATHGoogle Scholar
  18. 18.
    Hué, J., Würbel, E., Papini, O.: Removed sets fusion: performing off the shelf. In: Proceedings of ECAI 2008 (FIAI 178), pp. 94–98 (2008)Google Scholar
  19. 19.
    Konieczny, S.: On the difference between merging knowledge bases and combining them. In: Proceedings of KR 2000, pp. 135–144 (2000)Google Scholar
  20. 20.
    Konieczny, S., Lang, J., Marquis, P.: DA2 merging operators. Artif. Intell. 157, 49–79 (2004)CrossRefGoogle Scholar
  21. 21.
    Konieczny, S., Pérez, R.P.: Merging information under constraints. J. Log. Comput. 12(5), 773–808 (2002)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Lembo, D., Lenzerini, M., Rosati, R., Ruzzi, M., Savo, D.F.: Inconsistency-tolerant query answering in ontology-based data access. J. Web Sem. 33, 3–29 (2015)CrossRefGoogle Scholar
  23. 23.
    Lin, J., Mendelzon, A.: Knowledge base merging by majority. In: Pareschi, R., Fronhoefer, B. (eds.) In Dynamic Worlds: From the Frame Problem to Knowledge Management. Kluwer, Dordrecht (1999)Google Scholar
  24. 24.
    Meyer, T., Ghose, A., Chopra, S.: Syntactic representations of semantic merging operations. In: Ishizuka, M., Sattar, A. (eds.) PRICAI 2002. LNCS (LNAI), vol. 2417, p. 620. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-45683-X_88CrossRefGoogle Scholar
  25. 25.
    Revesz, P.Z.: On the semantics of theory change: arbitration between old and new information. In: 12th ACM SIGACT-SGMIT-SIGART Symposium on Principes of Databases, pp. 71–92 (1993)Google Scholar
  26. 26.
    Revesz, P.Z.: On the semantics of arbitration. J. Algebra Comput. 7, 133–160 (1997)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Wang, Z., Wang, K., Jin, Y., Qi, G.: Ontomerge a system for merging DL-Lite ontologies. In: CEUR Workshop Proceedings, vol. 969, pp. 16–27 (2014)Google Scholar
  28. 28.
    Wilkerson, R.W., Greiner, R., Smith, B.A.: A correction to the algorithm in Reiter’s theory of diagnosis. Artif. Intell. 41, 79–88 (1989)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Salem Benferhat
    • 1
  • Zied Bouraoui
    • 1
  • Odile Papini
    • 2
  • Eric Würbel
    • 2
    Email author
  1. 1.CRIL-CNRS UMR 8188, Univ ArtoisArrasFrance
  2. 2.LIS-CNRS UMR 7020, Aix Marseille Univ, Université de ToulonMarseilleFrance

Personalised recommendations