Value Equivalence

Definition

In temporal databases, the scheme of a temporal relation S has the form S(E, I) where E and I represent two disjoint sets of attributes, termed by some authors explicit and implicit, respectively. Explicit are the attributes in which ordinary data are recorded, such as Employee_Id, Name, Salary, etc. Implicit are the attributes in which either valid time (one or more) or transaction time is recorded. Given two tuples (e₁, i₁) and (e₂, i₂) with the scheme of S, it is said that there is a value equivalence between them if and only if e₁ = e₂. Equivalently, it is said that (e₁, i₁) and (e₂, i₂) are value equivalent.

Example

Consider one tuple, (Alex, 100, d400, d799), with scheme SALARY (Name, Amount, ValidTime), indicating that Alex’s salary was 100 on each of the dates d400, d401,…,d799. Let also another tuple of the same scheme be (Alex, 100, d500, d899). For the given scheme, E = {Name, Amount} and I= {ValidTime}. Given that both tuples have the same value for Name and...