SQL's Three-Valued Logic and Certain Answers.

The goal of the article is to bridge the difference between theoretical and practical approaches to answering queries over databases with nulls. Theoretical research has long ago identified the notion of correctness of query answering over incomplete data: one needs to find certain answers, which are true regardless of how incomplete information is interpreted. This serves as the notion of correctness of query answering, but carries a huge complexity tag. In practice, on the other hand, query answering must be very efficient, and to achieve this, SQL uses three-valued logic for evaluating queries on databases with nulls. Due to the complexity mismatch, the two approaches cannot coincide, but perhaps they are related in some way. For instance, does SQL always produce answers we can be certain about? This is not so: SQL’s and certain answers semantics could be totally unrelated. We show, however, that a slight modification of the three-valued semantics for relational calculus queries can provide the required certainty guarantees. The key point of the new scheme is to fully utilize the three-valued semantics, and classify answers not into certain or noncertain, as was done before, but rather into certainly true, certainly false, or unknown. This yields relatively small changes to the evaluation procedure, which we consider at the level of both declarative (relational calculus) and procedural (relational algebra) queries. These new evaluation procedures give us certainty guarantees even for queries returning tuples with null values.