Incomplete information arises naturally in numerous data management applications. Recently, several researchers have studied query processing in the context of incomplete information. Most work has combined the syntax of a traditional query language like relational algebra with a nonstandard semantics such as certain or ranked possible answers. There are now also languages with special features to deal with uncertainty. However, to the standards of the data management community, to date no language proposal has been made that can be considered a natural analog to SQL or relational algebra for the case of incomplete information. In this paper we propose such a language, World-set Algebra, which satisfies the robustness criteria and analogies to relational algebra that we expect. The language supports the contemplation on alternatives and can thus map from a complete database to an incomplete one comprising several possible worlds. We show that World-set Algebra is conservative over rel...