Conditional Tables

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...