Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Implication of Constraints

  • Wenfei FanEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1238


Logical implication or entailment


The implication problem is to decide whether or not a given set of constraints logically implies another constraint. With any constraint (dependency) language \({\mathcal {L}}\)

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Abiteboul S, Hull R, Vianu V. Foundations of databases. Reading: Addison-Wesley; 1995.zbMATHGoogle Scholar
  2. 2.
    Abiteboul S, Vianu V. Regular path queries with constraints. J Comput Syst Sci. 1999;58(3): 428–52.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Aho AV, Beeri C, Ullman JD. The theory of joins in relational databases. ACM Trans Database Syst. 1979;4(3):297–314.CrossRefGoogle Scholar
  4. 4.
    Arenas M, Fan W, Libkin L. Consistency of XML specifications. In: Inconsistency tolerance. Berlin: Springer; 2005. p. 15–41.CrossRefGoogle Scholar
  5. 5.
    Armstrong WW. Dependency structures of data base relationships. In: Proceedings of the IFIP Congress, Information Processing 74; 1974. p. 580–3.Google Scholar
  6. 6.
    Beeri C, Bernstein PA. Computational problems related to the design of normal form relational schemas. ACM Trans Database Syst. 1979;4(1):30–59.CrossRefGoogle Scholar
  7. 7.
    Beeri C, Vardi MY. The implication problem for data dependencies. In: Proceedings of the 8th International Colloquium on Automata, Languages, and Programming. 1981. p. 73–85.CrossRefGoogle Scholar
  8. 8.
    Bernstein PA. Synthesizing third normal form relations from functional dependencies. ACM Trans Database Syst. 1976;1(4):277–98.CrossRefGoogle Scholar
  9. 9.
    Casanova MA, Fagin R, Papadimitriou CH. Inclusion dependencies and their interaction with functional dependencies. In: Proceedings of the 1st ACM SIGACT-SIGMOD Symposium on Principles of Database Systems; 1982. p. 171–6.Google Scholar
  10. 10.
    Chandra AK, Lewis HR, Makowsky JA. Embedded implicational dependencies and their inference problem. In: Proceedings of the 13th Annual ACM Symposium on Theory of Computing; 1981. p. 342–54.Google Scholar
  11. 11.
    Chandra AK, Vardi MY. The implication problem for functional and inclusion dependencies is undecidable. SIAM J Comput. 1985;14(3):671–7.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Fagin R, Vardi MY. The theory of data dependencies – an overview. In: Proceedings of the 11th International Colloquium on Automata, Languages, and Programming; 1984. p. 1–22.Google Scholar
  13. 13.
    Fan W, Libkin L. On XML integrity constraints in the presence of DTDs. J ACM. 2002;49(3):368–406.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Klug AC. Calculating constraints on relational expressions. ACM Trans Database Syst. 1980;5(3):260–90.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Maier D, Mendelzon AO, Sagiv Y. Testing implications of data dependencies. ACM Trans Database Syst. 1979;4(4):455–69.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of EdinburghEdinburghUK
  2. 2.Beihang UniversityBeijingChina