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Using Ontologies to Query Probabilistic Numerical Data

  • Franz Baader
  • Patrick Koopmann
  • Anni-Yasmin Turhan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10483)

Abstract

We consider ontology-based query answering in a setting where some of the data are numerical and of a probabilistic nature, such as data obtained from uncertain sensor readings. The uncertainty for such numerical values can be more precisely represented by continuous probability distributions than by discrete probabilities for numerical facts concerning exact values. For this reason, we extend existing approaches using discrete probability distributions over facts by continuous probability distributions over numerical values. We determine the exact (data and combined) complexity of query answering in extensions of the well-known description logics \(\mathcal {EL}\) and \(\mathcal {ALC}\) with numerical comparison operators in this probabilistic setting.

References

  1. 1.
    Adams, M.R., Guillemin, V.: Measure Theory and Probability. Springer, Boston (1996)CrossRefMATHGoogle Scholar
  2. 2.
    Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-Lite family and relations. J. Artif. Intell. Res. 36, 1–69 (2009)MathSciNetMATHGoogle Scholar
  3. 3.
    Artale, A., Ryzhikov, V., Kontchakov, R.: DL-Lite with attributes and datatypes. In: Proceedings ECAI 2012, pp. 61–66. IOS Press (2012)Google Scholar
  4. 4.
    Baader, F., Borgwardt, S., Lippmann, M.: Query rewriting for DL-Lite with \(n\)-ary concrete domains. In: Proceedings IJCAI 2017 (2017, to appear)Google Scholar
  5. 5.
    Baader, F., Brandt, S., Lutz, C.: Pushing the \(\cal{EL}\) envelope. In: Proceedings of IJCAI 2005, pp. 364–369. Professional Book Center (2005)Google Scholar
  6. 6.
    Baader, F., Hanschke, P.: A scheme for integrating concrete domains into concept languages. In: Proceedings of IJCAI 1991, pp. 452–457 (1991)Google Scholar
  7. 7.
    Baader, F., Koopmann, P., Turhan, A.Y.: Using ontologies to query probabilistic numerical data (extended version). LTCS-Report 17–05, Chair for Automata Theory, Technische Universität Dresden, Germany (2017). https://lat.inf.tu-dresden.de/research/reports.html
  8. 8.
    Belle, V., Van den Broeck, G., Passerini, A.: Hashing-based approximate probabilistic inference in hybrid domains: an abridged report. In: Proceedings of IJCAI 2016, pp. 4115–4119 (2016)Google Scholar
  9. 9.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: the DL-Lite family. J. Autom. Reas. 39(3), 385–429 (2007)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    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)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Dalvi, N., Suciu, D.: Management of probabilistic data: foundations and challenges. In: Proceedings of SIGMOD 2007, pp. 1–12. ACM (2007)Google Scholar
  12. 12.
    Dargie, W.: The role of probabilistic schemes in multisensor context-awareness. In: Proceedings of PerCom 2007, pp. 27–32. IEEE (2007)Google Scholar
  13. 13.
    Durand, A., Hermann, M., Kolaitis, P.G.: Subtractive reductions and complete problems for counting complexity classes. Theoret. Comput. Sci. 340(3), 496–513 (2005)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Elkin, P.L., Brown, S.H., Husser, C.S., Bauer, B.A., Wahner-Roedler, D., Rosenbloom, S.T., Speroff, T.: Evaluation of the content coverage of SNOMED CT: ability of SNOMED clinical terms to represent clinical problem lists. Mayo Clin. Proc. 81(6), 741–748 (2006)CrossRefGoogle Scholar
  15. 15.
    Glimm, B., Lutz, C., Horrocks, I., Sattler, U.: Conjunctive query answering for the description logic \(\cal{SHIQ}\). J. Artif. Intell. Res. (JAIR) 31, 157–204 (2008)MathSciNetMATHGoogle Scholar
  16. 16.
    Hemaspaandra, L.A., Vollmer, H.: The satanic notations: counting classes beyond \(\# {P}\) and other definitional adventures. ACM SIGACT News 26(1), 2–13 (1995)CrossRefGoogle Scholar
  17. 17.
    Hernich, A., Lemos, J., Wolter, F.: Query answering in DL-Lite with datatypes: a non-uniform approach. In: Proceedings of AAAI 2017 (2017)Google Scholar
  18. 18.
    Hoover, H.J.: Feasible real functions and arithmetic circuits. SIAM J. Comput. 19(1), 182–204 (1990)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Jung, J.C., Lutz, C.: Ontology-based access to probabilistic data with OWL QL. In: Cudré-Mauroux, P., et al. (eds.) ISWC 2012. LNCS, vol. 7649, pp. 182–197. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-35176-1_12 CrossRefGoogle Scholar
  20. 20.
    Ko, K.I.: Complexity Theory of Real Functions. Birkhäuser, Boston (1991)CrossRefMATHGoogle Scholar
  21. 21.
    Kumar, N., Khunger, M., Gupta, A., Garg, N.: A content analysis of smartphone-based applications for hypertension management. J. Am. Soc. Hypertens. 9(2), 130–136 (2015)CrossRefGoogle Scholar
  22. 22.
    Lutz, C.: Adding numbers to the \(\cal{SHIQ}\) description logic–first results. In: Proceedings KR 2001, pp. 191–202. Citeseer (2001)Google Scholar
  23. 23.
    Lutz, C.: The complexity of description logics with concrete domains. Ph.D. thesis, RWTH Aachen (2002)Google Scholar
  24. 24.
    Lutz, C.: Description logics with concrete domains–a survey. In: Advances in Modal Logic 4, pp. 265–296. King’s College Publications (2002)Google Scholar
  25. 25.
    Lutz, C.: NExpTime-complete description logics with concrete domains. ACM Trans. Comput. Logic (TOCL) 5(4), 669–705 (2004)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Lutz, C.: The complexity of conjunctive query answering in expressive description logics. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 179–193. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-71070-7_16 CrossRefGoogle Scholar
  27. 27.
    Lutz, C., Schröder, L.: Probabilistic description logics for subjective uncertainty. In: Proceedings of KR 2010, pp. 393–403. AAAI Press (2010)Google Scholar
  28. 28.
    Lutz, C., Toman, D., Wolter, F.: Conjunctive query answering in the description logic \(\cal{EL}\) using a relational database system. In: Proceedings of IJCAI 2009, pp. 2070–2075. IJCAI/AAAI (2009)Google Scholar
  29. 29.
    Rector, A., Gangemi, A., Galeazzi, E., Glowinski, A., Rossi-Mori, A.: The GALEN CORE model schemata for anatomy: towards a re-usable application-independent model of medical concepts. In: Proceedings of MIE 1994, pp. 229–233 (1994)Google Scholar
  30. 30.
    Rosati, R.: On conjunctive query answering in \(\cal{EL}\). In: Proceedings of DL 2007, pp. 451–458. CEUR-WS.org (2007)Google Scholar
  31. 31.
    Savković, O., Calvanese, D.: Introducing datatypes in DL-Lite. In: Proceedings of ECAI 2012, pp. 720–725 (2012)Google Scholar
  32. 32.
    Schild, K.: A correspondence theory for terminological logics: preliminary report. In: Mylopoulos, J., Reiter, R. (eds.) Proceedings of IJCAI 1991, pp. 466–471. Morgan Kaufmann (1991)Google Scholar
  33. 33.
    Singh, S., Mayfield, C., Mittal, S., Prabhakar, S., Hambrusch, S., Shah, R.: Orion 2.0: native support for uncertain data. In: Proceedings of SIGMOD 2008, pp. 1239–1242. ACM (2008)Google Scholar
  34. 34.
    Thrun, S., Burgard, W., Fox, D.: A probabilistic approach to concurrent mapping and localization for mobile robots. Auton. Robots 5(3–4), 253–271 (1998)CrossRefMATHGoogle Scholar
  35. 35.
    Yilmaz, A., Javed, O., Shah, M.: Object tracking: a survey. ACM Comput. Surv. (CSUR) 38(4), 13 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Theoretical Computer ScienceTechnische Universität DresdenDresdenGermany

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