On Representing Incomplete Information in a Relational Data Base

Precise conditions are formulated which should be satisfied in a semantically meaningful extension of the usual relational operators of projection, selection, union and join, from operators on relations to operators on tables with "null values" of various kinds allowed. These conditions require that our system be safe in the sense that no incorrect conclusion is derivable by using a specified subset Omega of the relational operators; and that it be complete in the sense that all valid conclusions expressible by relational expressions using operators in Omega are in fact derivable in our system. Examples of three such systems are studied in more detail. The effect of dependencies of various kinds is briefly discussed.