Contents of Definition

Definition

Informally, two tuples on the same (temporal) relation schema are value equivalent if they have identical non-timestamp attribute values.

To formally define the concept, let temporal relation schema R have n time dimensions, D_i, i = 1,…, n, and let τⁱ, i = 1,…, n be corresponding timeslice operators, e.g., the valid timeslice and transaction timeslice operators. Then tuples x and y are value equivalent if

∃t₁∈D₁…∃t_n∈D_n(τⁿ_{t_n}(…(τ¹_t₁(x))…)≠∅)	∧	∃s₁∈D₁,…, s_n∈D_n(τⁿ_{s_n}(…(τ¹_s₁(y))…)≠∅)
⇒ $\displaystyle \bigcup_{{\forall t_1 \in D_1,\ldots, t_n \in D_n}}^{}$ *-.8cmτⁿ_{t_n}(…(τ¹_t₁(x))…)	=	$\displaystyle \bigcup_{{\forall s_1 \in D_1,\ldots, s_n \in D_n}}^{}$ *-.8cmτⁿ_{s_n}(…(τ¹_s₁(y))…) .

Thus the set of tuples in snapshots of x and the set of tuples in snapshots of y are required to be identical. This is required only when each tuple has some non-empty snapshot.