Aggregate queries over conditional tables

Conditional tables have been identified long ago as a way to capture unknown or incomplete information. However, queries over conditional tables have never been allowed to involve column functions such as aggregates. In this paper, the theory of conditional tables is extended in this direction, and it is shown that a strong representation system exists which has the closure property that the result of an aggregate query over a conditional table can be again represented by a conditional table. It turns out, however, that the number of tuples in a conditional table representing the result of an aggregate query may grow exponentially in the number of variables in the table. This phenomenon is analyzed in detail, and tight upper and lower bounds concerning the number of tuples contained in the result of an aggregate query are given. Finally, representation techniques are sketched that approximate aggregation results in tables of reasonable size.