Advertisement

Effective Query Answering with Ontologies and DBoxes

  • Enrico FranconiEmail author
  • Volha Kerhet
Chapter
  • 376 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11560)

Abstract

The goal of this chapter is to survey the formalisation of a precise and uniform integration between first-order ontologies, first-order queries, and classical relational databases (DBoxes) We include here non-standard variants of first-order logic, such as the one with active domain semantics and standard name assumption, used typically in database theory. We present a general framework for the rewriting of a domain independent first-order query in presence of an arbitrary domain independent first-order logic ontology over a signature extending a database signature with additional predicates. The framework supports deciding the existence of a logically equivalent and – given the ontology – safe-range first-order reformulation (called exact reformulation) of a domain independent first-order query in terms of the database signature, and if such a reformulation exists, it provides an effective approach to construct the reformulation based on interpolation using standard theorem proving techniques (i.e., tableau). Since the reformulation is a safe-range formula, it is effectively executable as an SQL query. We finally present an application of the framework with the very expressive \(\mathcal {ALCHOI}\) and \(\mathcal {SHOQ}\) description logics ontologies, by providing effective means to compute safe-range first-order exact reformulations of queries.

References

  1. 1.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Boston (1995)zbMATHGoogle Scholar
  2. 2.
    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
  3. 3.
    Avron, A.: Constructibility and decidability versus domain independence and absoluteness. Theor. Comput. Sci. 394, 144–158 (2008).  https://doi.org/10.1016/j.tcs.2007.12.008. http://dl.acm.org/citation.cfm?id=1351194.1351447MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bárány, V., ten Cate, B., Otto, M.: Queries with guarded negation. PVLDB 5(11), 1328–1339 (2012)Google Scholar
  5. 5.
    Bárány, V., ten Cate, B., Segoufin, L.: Guarded negation. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6756, pp. 356–367. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22012-8_28CrossRefGoogle Scholar
  6. 6.
    Bárány, V., Gottlob, G., Otto, M.: Querying the guarded fragment. In: Proceedings of the 25th Annual IEEE Symposium on Logic in Computer Science (LICS 2010), pp. 1–10 (2010)Google Scholar
  7. 7.
    Beth, E.: On Padoa’s method in the theory of definition. Indagationes Math. 15, 330–339 (1953)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Calvanese, D., Franconi, E.: First-order ontology mediated database querying via query reformulation. In: Flesca, S., Greco, S., Masciari, E., Saccà, D. (eds.) A Comprehensive Guide Through the Italian Database Research Over the Last 25 Years. SBD, vol. 31, pp. 169–185. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-61893-7_10CrossRefGoogle Scholar
  9. 9.
    ten Cate, B., Franconi, E., Seylan, İ.: Beth definability in expressive description logics. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 1099–1106 (2011)Google Scholar
  10. 10.
    ten Cate, B., Franconi, E., Seylan, I.: Beth definability in expressive description logics. J. Artif. Intell. Res. (JAIR) 48, 347–414 (2013).  https://doi.org/10.1613/jair.4057MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Craig, W.: Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory. J. Symb. Log. 22(3), 269–285 (1957)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Etzioni, O., Golden, K., Weld, D.S.: Sound and efficient closed-world reasoning for planning. Artif. Intell. 89, 113–148 (1997).  https://doi.org/10.1016/S0004-3702(96)00026-4. http://dl.acm.org/citation.cfm?id=249678.249685MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Fan, W., Geerts, F., Zheng, L.: View determinacy for preserving selected information in data transformations. Inf. Syst. 37, 1–12 (2012).  https://doi.org/10.1016/j.is.2011.09.001CrossRefGoogle Scholar
  14. 14.
    Feinerer, I., Franconi, E., Guagliardo, P.: Lossless selection views under conditional domain constraints. IEEE Trans. Knowl. Data Eng. 27(2), 504–517 (2015).  https://doi.org/10.1109/TKDE.2014.2334327CrossRefGoogle Scholar
  15. 15.
    Fitting, M.: First-Order Logic and Automated Theorem Proving, 2nd edn. Springer, New York (1996).  https://doi.org/10.1007/978-1-4612-2360-3CrossRefzbMATHGoogle Scholar
  16. 16.
    Franconi, E., Ibanez-Garcia, Y.A., Seylan, İ.: Query answering with DBoxes is hard. Electron. Notes Theor. Comput. Sci. 278, 71–84 (2011)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Franconi, E., Kerhet, V., Ngo, N.: Exact query reformulation with first-order ontologies and databases. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS (LNAI), vol. 7519, pp. 202–214. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-33353-8_16CrossRefGoogle Scholar
  18. 18.
    Franconi, E., Kerhet, V., Ngo, N.: Exact query reformulation over databases with first-order and description logics ontologies. J. Artif. Intell. Res. (JAIR) 48, 885–922 (2013).  https://doi.org/10.1613/jair.4058MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Franconi, E., Ngo, N., Sherkhonov, E.: The definability abduction problem for data exchange. In: Krötzsch, M., Straccia, U. (eds.) RR 2012. LNCS, vol. 7497, pp. 217–220. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-33203-6_18CrossRefGoogle Scholar
  20. 20.
    Gurevich, Y.: Toward logic tailored for computational complexity. In: Börger, E., Oberschelp, W., Richter, M.M., Schinzel, B., Thomas, W. (eds.) Computation and Proof Theory. LNM, vol. 1104, pp. 175–216. Springer, Heidelberg (1984).  https://doi.org/10.1007/BFb0099486CrossRefGoogle Scholar
  21. 21.
    Halevy, A.Y.: Answering queries using views: a survey. VLDB J. 10, 270–294 (2001).  https://doi.org/10.1007/s007780100054CrossRefzbMATHGoogle Scholar
  22. 22.
    Horrocks, I., Sattler, U.: Ontology reasoning in the SHOQ(D) description logic. In: Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI 2001), pp. 199–204 (2001)Google Scholar
  23. 23.
    Kleene, S.C.: Mathematical Logic. Dover, New York (2002)zbMATHGoogle Scholar
  24. 24.
    Lutz, C., Seylan, I., Wolter, F.: Ontology-mediated queries with closed predicates. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, 25–31 July 2015, pp. 3120–3126 (2015). http://ijcai.org/Abstract/15/440
  25. 25.
    Marx, M.: Queries determined by views: pack your views. In: Proceedings of the 26th ACM symposium on Principles of Database Systems, PODS 2007, pp. 23–30 (2007).  https://doi.org/10.1145/1265530.1265534
  26. 26.
    Nash, A., Segoufin, L., Vianu, V.: Views and queries: determinacy and rewriting. ACM Trans. Database Syst. 35, 211–2141 (2010).  https://doi.org/10.1145/1806907.1806913CrossRefGoogle Scholar
  27. 27.
    Ngo, N., Franconi, E.: Unique solutions in data exchange under STS mappings. In: Proceedings of the 10th Alberto Mendelzon International Workshop on Foundations of Data Management (AMW-2016) (2016). http://ceur-ws.org/Vol-1644/paper5.pdf
  28. 28.
    Ngo, N., Ortiz, M., Simkus, M.: Closed predicates in description logics: results on combined complexity. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, Cape Town, South Africa, 25–29 April 2016, pp. 237–246 (2016). http://www.aaai.org/ocs/index.php/KR/KR16/paper/view/12906
  29. 29.
    Patel-Schneider, P.F., Franconi, E.: Ontology constraints in incomplete and complete data. In: Cudré-Mauroux, P., et al. (eds.) ISWC 2012. LNCS, vol. 7649, pp. 444–459. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-35176-1_28CrossRefGoogle Scholar
  30. 30.
    Rosati, R.: On the finite controllability of conjunctive query answering in databases under open-world assumption. J. Comput. Syst. Sci. 77(3), 572–594 (2011)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Seylan, İ., Franconi, E., de Bruijn, J.: Effective query rewriting with ontologies over DBoxes. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI 2009), pp. 923–925 (2009)Google Scholar
  32. 32.
    Toman, D., Weddell, G.E.: Fundamentals of physical design and query compilation. Synth. Lect. Data Manag. 3, 1–124 (2011).  https://doi.org/10.2200/S00363ED1V01Y201105DTM018CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.KRDB Research Centre for Knowledge and DataFree University of Bozen-BolzanoBolzanoItaly

Personalised recommendations