Conditional Tables
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-39940-9_1253
Synonyms
C-tables; Extended relations
Definition
A conditional table [4] generalizes relations in two ways. First, in the entries in the columns, variables, representing unknown values, are allowed in addition to the usual constants. The second generalization is that each tuple is associated with a condition, which is a Boolean combination of atoms of the form x = y, x = a, a = b, for x, y null values (variables), and a, b constants. A conditional table essentially represents an existentially quantified function free first order theory.
Formally, let
con be a countably infinite set of constants, and
var be a countably infinite set of variables, disjoint from
con. Let
U be a finite set of attributes, and
R ⊆
U a relational schema. A tuple in a c-table over
R is a mapping from
R, and a special attribute, denoted
φ, to
con ∪
var ∪
β, where
β is the set of all Boolean combinations of equality atoms, as above. Every attribute in
R maps to a variable or a constant, and
φ maps to
β. In a...
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Recommended Reading
- 1.Abiteboul S., Duschka O.M. Complexity of Answering Queries Using Materialized Views. In Proc. 17th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, 1998, pp. 254–263.Google Scholar
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- 4.Imielinski T., Lipski W. Jr. Incomplete Information in Relational Databases. J. ACM, 31(4):761–791, 1984.Google Scholar
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