Encyclopedia of Database Systems

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

Naive Tables

  • Gösta GrahneEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1252


Extended relations; Relations with marked nulls


The simplest way to incorporate unknown values into the relational model, is to allow variables, in addition to constants, as entries in the columns of relations. Such constructs are called tables, instead of relations. A table is an incomplete database, and represents a set of complete databases, each obtained by substituting all variables with constants. Different occurrences of the same variable (marked null) are substituted with the same constant. The substitution is thus a function from the variables and constants, to the constants, such that the function is identity on the constants. A table T then represents the set of relations, denoted rep(T), defined as {v(T) : v is a valuation}. Then the certain answer to a query q on a table T, denoted sure(q, T) is the set of tuples that occur in every answer obtained by applying the query to every database in rep(T). In other words, the certain answer to q on T is sure(q,...

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Recommended Reading

  1. 1.
    Grahne G, Kiricenko V. Towards an algebraic theory of information integration. Inf Comput. 2004;194(2):79–100.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Imielinski T, Lipski Jr W. Incomplete information in relational databases. J ACM. 1984;31(4):761–91.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Lipski W Jr. On relational algebra with marked nulls. In: Proceedings of the 4th ACM SIGACT-SIGMOD Symposium on Principles of Database systems: 1985. p. 201–3.Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Concordia UniversityMontrealCanada

Section editors and affiliations

  • Leonid Libkin
    • 1
  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK