A Temporal Relational Algebra as Basis for Temporal Relational Completeness

We define a tenlporal algebra that is applicable to any temporal relational data model supporting discrete linear bounded time. This algebra has the five basic relational algebra operators extended to the temporal domain and an operator of linear recursion. We show that this algebra has the expressive power of a safe temporal calculus based on the predicate temporal logic with the until and since temporal operators. In [CrC189], a historical calculus was proposed as a basis for historical relational completeness. We propose the temporal algebra defined in this paper and the equivalent temporal calculus as an alternative basis for temporal relational completeness.