Growing certainty with null values

Non-availability of part of the data is a problem common to many database systems. We study here some aspects relating to incomplete information. Obviously, when the information in a database is not complete the answer to any query is only an approximation to the true result. The aim is to get a precise approximation. We regard databases as many-sorted algebras. Based on the concept of extended algebra we define what it means for an algebra to approximate another algebra. We then give the following simple principle for extending query languages to handle missing data: “Whenever information is added to an incomplete database subsequent answers to queries must not be contradictory or less informative than previously.” We then apply this principle to extend the functional query language Varqa. Finally, we compare the previously proposed many-valued logic systems with the system devised based on our principles.