A recursive temporal algebra and temporal completeness

This paper introduces a recursive temporal algebra based on temporal semantics for querying time-varying data. The algebra, called ℜ*, is based on a temporal relational data model in which a temporal database is modeled as a collection of time-varying relations. Each time-varying relation is a collection of ordinary relations indexed by moments in time. In ℜ*, recursive queries (such as the transitive closure of a given relation) can be formulated through equations. It is shown that other forms of recursion, such as linear recursion, can also be expressed using iteration through time. Temporal completeness of ℜ* is established, with respect to two other temporal algebras based on temporal semantics which offer linear recursive operators