Approximation in databases

Abstract

One source of partial information in databases is the need to combine information from several databases. Even if each database is complete for some “world”, the combined databases will not be, and answers to queries against such combined databases can only be approximated. In this paper we describe various situations in which a precise answer cannot be obtained for a query asked against multiple databases. Based on an analysis of these situations, we propose a classification of constructs that can be used to model approximations.

A major goal is to obtain universality properties for these models of approximations. Universality properties suggest syntax for languages with approximations based on the operations which are naturally associated with them. We prove universality properties for most of the approximation constructs. Then we use them to design languages built around datatypes given by the approximation constructs. A straightforward approach results in langauges that have a number of limitations. In an attempt to overcome those limitations, we explain how all the languages can be embedded into a language for conjunctive and disjunctive sets from [17], and demonstrate its usefulness in querying independent databases.

Acknowledgements. I would like to thank Peter Buneman, Tim Griffin, Carl Gunter, Elsa Gunter, Paris Kanellakis, Hermann Puhlmann, Anna Romanowska and especially Achim Jung for their help.