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, Di, 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…∃tn∈Dn(τntn(…(τ1t1(x))…)≠∅)  ∧ 


∃s1∈D1…∃sn∈Dn(τnsn(…(τ1s1(y))…)≠∅) 


⇒ 


$\bigcup_{{\forall t_1 \in D_1 \ldots \forall t_n \in D_n}}^{}$τntn(…(τ1t1(x))…)   = 


$\bigcup_{{\forall s_1 \in D_1 \ldots \forall s_n \in D_n}}^{}$τnsn(…(τ1s1(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.