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Encyclopedia of Database Systems pp 1808–1814Cite as

Implication of Constraints

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Synonyms

Logical implication or entailment

Definition

The implication problem is to decide whether or not a given set of constraints logically implies another constraint. With any constraint (dependency) language \({\mathcal {L}}\) there are two implication problems associated, which do not coincide in general.

In the traditional logic framework, an instance of a schema R is a logical structure that is either finite or infinite, referred to as an unrestricted instance of R. A set Σ of constraints over R implies without restriction a constraint ϕ, denoted by Σ⊧unrϕ, if for each unrestricted instance I of R that satisfies Σ, I also satisfies ϕ. The unrestricted implication problem for \({\mathcal {L}}\) is to determine, given a set Σ of constraints in \({\mathcal {L}}\) and another constraint ϕ in \({\mathcal {L}}\), whether or not Σ⊧unrϕ.

In the context of databases, only finite instances are considered, and implication analysis lies within finite model theory. A set Σ of constraints...

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Recommended Reading

  1. Abiteboul S, Hull R, Vianu V. Foundations of databases. Reading: Addison-Wesley; 1995.

    MATH  Google Scholar 

  2. Abiteboul S, Vianu V. Regular path queries with constraints. J Comput Syst Sci. 1999;58(3): 428–52.

    Article  MathSciNet  MATH  Google Scholar 

  3. Aho AV, Beeri C, Ullman JD. The theory of joins in relational databases. ACM Trans Database Syst. 1979;4(3):297–314.

    Article  Google Scholar 

  4. Arenas M, Fan W, Libkin L. Consistency of XML specifications. In: Inconsistency tolerance. Berlin: Springer; 2005. p. 15–41.

    Chapter  Google Scholar 

  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. Beeri C, Bernstein PA. Computational problems related to the design of normal form relational schemas. ACM Trans Database Syst. 1979;4(1):30–59.

    Article  Google Scholar 

  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.

    Chapter  Google Scholar 

  8. Bernstein PA. Synthesizing third normal form relations from functional dependencies. ACM Trans Database Syst. 1976;1(4):277–98.

    Article  Google Scholar 

  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. 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. Chandra AK, Vardi MY. The implication problem for functional and inclusion dependencies is undecidable. SIAM J Comput. 1985;14(3):671–7.

    Article  MathSciNet  MATH  Google Scholar 

  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. Fan W, Libkin L. On XML integrity constraints in the presence of DTDs. J ACM. 2002;49(3):368–406.

    Article  MathSciNet  MATH  Google Scholar 

  14. Klug AC. Calculating constraints on relational expressions. ACM Trans Database Syst. 1980;5(3):260–90.

    Article  MathSciNet  MATH  Google Scholar 

  15. Maier D, Mendelzon AO, Sagiv Y. Testing implications of data dependencies. ACM Trans Database Syst. 1979;4(4):455–69.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Edinburgh, Edinburgh, UK

    Wenfei Fan

  2. Beihang University, Beijing, China

    Wenfei Fan

Authors
  1. Wenfei Fan
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Corresponding author

Correspondence to Wenfei Fan .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology College of Computing, Atlanta, GA, USA

    Ling Liu

  2. University of Waterloo School of Computer Science, Waterloo, ON, Canada

    M. Tamer Özsu

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Fan, W. (2018). Implication of Constraints. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_1238

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