The VLDB Journal

, Volume 25, Issue 3, pp 381–397 | Cite as

Mapping-equivalence and oid-equivalence of single-function object-creating conjunctive queries

  • Angela Bonifati
  • Werner Nutt
  • Riccardo Torlone
  • Jan Van den Bussche
Regular Paper


Conjunctive database queries have been extended with a mechanism for object creation to capture important applications such as data exchange, data integration, and ontology-based data access. Object creation generates new object identifiers in the result that do not belong to the set of constants in the source database. The new object identifiers can be also seen as Skolem terms. Hence, object-creating conjunctive queries can also be regarded as restricted second-order tuple-generating dependencies (SO-tgds), considered in the data exchange literature. In this paper, we focus on the class of single-function object-creating conjunctive queries, or sifo CQs for short. The single-function symbol can be used only once in the head of the query. We give a new characterization for oid-equivalence of sifo CQs that is simpler than the one given by Hull and Yoshikawa and places the problem in the complexity class NP. Our characterization is based on Cohen’s equivalence notions for conjunctive queries with multiplicities. We also solve the logical entailment problem for sifo CQs, showing that also this problem belongs to NP. Results by Pichler et al. have shown that logical equivalence for more general classes of SO-tgds is either undecidable or decidable with as yet unknown complexity upper bounds.


Conjunctive query Object creation Oid Equivalence Logical entailment SO-tgd Sifo CQ Nested tgd Schema mapping 



We thank the anonymous referees for their careful comments which helped improve the presentation of the paper. The work by Angela Bonifati has been partially supported by the ANR through the grant Datacert: Coq deep specification of security aware data integration (ANR-15-CE39-0009). The work by Werner Nutt has been partially supported by the grant CANDy of the Free University of Bozen-Bolzano.


  1. 1.
    Abiteboul, S., Buneman, P., Suciu, D.: Data on the Web: From Relations to Semistructured Data and XML. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2000)Google Scholar
  2. 2.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)zbMATHGoogle Scholar
  3. 3.
    Abiteboul, S., Kanellakis, P.: Object identity as a query language primitive. J. ACM 45(5), 798–842 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Abiteboul, S., Vianu, V.: Procedural languages for database queries and updates. J. Comput. Syst. Sci. 41(2), 181–229 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Abiteboul, S., Vianu, V.: Datalog extensions for database queries and updates. J. Comput. Syst. Sci. 43(1), 62–124 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Alexe, B., Tan, W.C., Velegrakis, Y.: STBenchmark: towards a benchmark for mapping systems. Proc. VLDB Endow. 1(1), 230–244 (2008)CrossRefGoogle Scholar
  7. 7.
    Arenas, M., Pérez, J., Reutter, J., Riveros, C.: The language of plain SO-TGDS: composition, inversion and structural properties. J. Comput. Syst. Sci. 79(6), 737–1002 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Arocena, P., Glavic, B., Miller, R.: Value invention in data exchange. In: Proceedings of the SIGMOD Conference, pp. 157–168. ACM (2013)Google Scholar
  9. 9.
    Arocena, P.C., Ciucanu, R., Glavic, B., Miller, R.J.: Gain control over your integration evaluations. Proc. VLDB Endow. 8(12), 1960–1971 (2015)Google Scholar
  10. 10.
    Van den Bussche, J., Paredaens, J.: The expressive power of complex values in object-based data models. Inf. Comput. 120, 220–236 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Van den Bussche, J., Van Gucht, D., Andries, M., Gyssens, M.: On the completeness of object-creating database transformation languages. J. ACM 44(2), 272–319 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    ten Cate, B., Kolaitis, P.: Structural characterizations of schema-mapping languages. Commun. ACM 53(1), 101–110 (2010)CrossRefGoogle Scholar
  13. 13.
    Chandra, A., Merlin, P.: Optimal implementation of conjunctive queries in relational data bases. In: Proceedings of the 9th ACM Symposium on the Theory of Computing, pp. 77–90. ACM (1977)Google Scholar
  14. 14.
    Cohen, S.: Equivalence of queries that are sensitive to multiplicities. VLDB J. 18, 765–785 (2009)CrossRefGoogle Scholar
  15. 15.
    Cohen, S., Nutt, W., Sagiv, Y.: Containment of aggregate queries. In: Calvanese, D., Lenzerini, M., Motwani, R. (eds.) Database Theory—ICDT 2003. Lecture Notes in Computer Science, vol. 2572, pp. 111–125. Springer, Berlin (2003)Google Scholar
  16. 16.
    Fagin, R., Haas, L., M. Hernández, R.M., Popa, L., Velegrakis, Y.: Clio: schema mapping creation and data exchange. In: Borgida, A., Chaudhuri, V., Giorgini, P., Yu, E. (eds.) Conceptual Modeling: Foundations and Applications. Lecture Notes in Computer Science, vol. 5600, pp. 198–236. Springer, Berlin (2009)Google Scholar
  17. 17.
    Fagin, R., Kolaitis, P., Nash, A., Popa, L.: Towards a theory of schema-mapping optimization. In: Proceedings of the 27th ACM Symposium on Principles of Database Systems, pp. 33–42 (2008)Google Scholar
  18. 18.
    Fagin, R., Kolaitis, P., Popa, L.: Composing schema mappings: second-order dependencies to the rescue. ACM Trans. Database Syst. 30(4), 994–1055 (2005)CrossRefGoogle Scholar
  19. 19.
    Feinerer, I., Pichler, R., Sallinger, E., Savenkov, V.: On the undecidability of the equivalence of second-order tuple generating dependencies. Inf. Syst. 48, 113–129 (2015)CrossRefGoogle Scholar
  20. 20.
    Friedman, M., Levy, A.Y., Millstein, T.D.: Navigational plans for data integration. In: AAAI/IAAI, pp. 67–73 (1999)Google Scholar
  21. 21.
    Garcia-Molina, H., Papakonstantinou, Y., Quass, D., Rajaraman, A., Sagiv, Y., Ullman, J., Vassalos, V., Widom, J.: The TSIMMIS approach to mediation: data models and languages. J. Intell. Inf. Syst. 8(2), 117–132 (1997)CrossRefGoogle Scholar
  22. 22.
    Hull, R., Yoshikawa, M.: ILOG: declarative creation and manipulation of object identifiers. In: McLeod, D., Sacks-Davis, R., Schek, H. (eds.) Proceedings of the 16th International Conference on Very Large Data Bases, pp.455–468. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1990)Google Scholar
  23. 23.
    Hull, R., Yoshikawa, M.: On the equivalence of database restructurings involving object identifiers. In: Proceedings of the 10th ACM Symposium on Principles of Database Systems, pp. 328–340. ACM Press, New York (1991)Google Scholar
  24. 24.
    Kifer, M., Wu, J.: A logic for programming with complex objects. J. Comput. Syst. Sci. 47(1), 77–120 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Klug, A., Price, R.: Determining view dependencies using tableaux. ACM Trans. Database Syst. 7, 361–380 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Kolaitis, P., Pichler, R., Sallinger, E., Savenkov, V.: Nested dependencies: structure and reasoning. In: Proceedings of the 33rd ACM Symposium on Principles of Database Systems (2014)Google Scholar
  27. 27.
    Lenzerini, M.: Data integration: A theoretical perspective. In: Proceedings 21st ACM Symposium on Principles of Database Systems, pp. 233–246 (2002)Google Scholar
  28. 28.
    Levy, A.Y., Rajaraman, A., Ordille, J.J.: Querying heterogeneous information sources using source descriptions. In: Vijayaraman, T., Buchmann, A., Mohan, C., Sarda, N. (eds.) Proceedings of the 22nd International Conference on Very Large Data Bases, pp. 251–262. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1996)Google Scholar
  29. 29.
    Maier, D.: A logic for objects. In: Workshop on Foundations of Deductive Databases and Logic Programming, pp. 6–26 (1986)Google Scholar
  30. 30.
    Papakonstantinou, Y., Garcia-Molina, H., Widom, J.: Object exchange across heterogeneous information sources. In: ICDE, pp. 251–260 (1995)Google Scholar
  31. 31.
    Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Semant. 10, 133–173 (2008)zbMATHGoogle Scholar
  32. 32.
    Sequeda, J.F., Arenas, M., Miranker, D.P.: On directly mapping relational databases to RDF and OWL. In: International Conference on World Wide Web (WWW), pp. 649–658 (2012). doi: 10.1145/2187836.2187924
  33. 33.
    Ullman, J.D.: Information integration using logical views. Theor. Comput. Sci. 239(2), 189–210 (2000)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Angela Bonifati
    • 1
  • Werner Nutt
    • 2
  • Riccardo Torlone
    • 3
  • Jan Van den Bussche
    • 4
  1. 1.LIRISUniversity of Lyon 1LyonFrance
  2. 2.Free University of Bozen-BolzanoBolzanoItaly
  3. 3.Università Roma TreRomeItaly
  4. 4.Hasselt University and Transnational University of LimburgHasseltBelgium

Personalised recommendations