INCOMPLETE RELATIONAL DATABASE MODELS BASED ON INTERVALS

In this paper, we utilize intervals for unknown values in incomplete relational databases. We use tables to represent unknown relations. First, we define three partial tuple types in a table to specify incompleteness relationships among tuples of the same table. For tuples of different tables, we distinguish between the cases where incompleteness is introduced at the relation level, tuple level, or attribute value level. Also, based on these relationships among tuples in different tables, we present a family of incomplete relational database models. For each of the models, we show that query evaluation is sound (i.e., no incorrect results are derivable) in the Imielinski-Lipski sense. None of the models is complete (i.e., all valid conclusions are derivable) in the Imielinski-Lipski sense. We briefly compare two of the models in the family with other approaches. Considering each table tuple as a set of d-dimensional cubes, each model in the family of models presented in this paper can be considered and implemented as a geometric database model. We briefly summarize the geometric operations and the primitive update semantics that need to be utilized in such an implementation.