A Family of Incomplete Relational Database Models

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 are introduced at the relation level, tuple level or attribute-value level. And, based on these relationships among tuples in different tables, we present a family of incomplete relational database models. tuples in the set of cubes (also called d-rectangles) are called candidate tuples for the tmknown tuple t, and exactly one of the points is the tmknown tuple. This approach allows database operations to be. transformed into operations in Computational Geometry, leading to efficient operator evaluations [OlaO 88a]. Following [ImiL 841 we use the terminology that a table in the incomplete database enviromnent represents a relation some tuples of which are unknown. Tables contain partial tupks (i.e., tuples with incomplete components) as well as total tuples (i.e., tuples whose components are all known). For each of the models, the query evaluation is sound (i.e., no incorrect results are derivable). None of the models is complete (i.e., all valid conclusions are derivable). 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 as a geometric database model. We are presently implementing a version of one of the models. We briefly summarize the geometric operations and the primitive update semantics being utilii in the implementation. Figure 1. Geometric View of Partial Tuples