How to Define Certain Answers

Abstract

The standard way of answering queries over incomplete databases is to compute certain answers, defined as the intersection of query answers on all complete databases that the incomplete database represents. But is this universally accepted definition correct? We argue that this ``one-size-fits-all'' definition can often lead to counterintuitive or just plain wrong results, and propose an alternative framework for defining certain answers. We combine three previously used approaches, based on the semantics and representation systems, on ordering incomplete databases in terms of their informativeness, and on viewing databases as knowledge expressed in a logical language, to come up with a well justified and principled notion of certain answers. Using it, we show that for queries satisfying some natural conditions (like not losing information if a more informative input is given), computing certain answers is surprisingly easy, and avoids the complexity issues that have been associated with the classical definition.