The complexity of query evaluation in indefinite temporal constraint databases

In previous work we have developed the scheme of indefinite L-constraint databases where L, the parameter, is a first-order constraint language. This scheme extends the constraint database proposal of Kanellakis et al. (1990, 1995) to include indefinite (or uncertain) information in the style of Imielinski and Lipski (1984). In this paper we study the complexity of query evaluation in an important instance of this abstract scheme: indefinite temporal constraint databases. Our results indicate that the data/combined complexity of query evaluation does not change when we move from queries in relational calculus over relational databases, to queries in relational calculus with temporal constraints over temporal constraint databases. This fact remains true even when we consider query evaluation in relational databases with indefinite information vs. query evaluation in indefinite temporal constraint databases. In the course of our work, we provide precise bounds on the complexity of decision/quantifier elimination for a subtheory of Presburger arithmetic and a subtheory of real addition with order. The bounds for the latter theory are original and of independent interest.