Relative information capacity of simple relational database schemata

Fundamental notions of relative information capacity between database structures are studied in the context of the relational model. Four progressively less restrictive formal definitions of "dominance" between pairs of relational database schemata are given. Each of these is shown to capture intuitively appealing, semantically meaningful properties which are natural for measures of relative information capacity between schemata. Relational schemata, both with and without key dependencies, are studied using these notions. A significant intuitive conclusion concerns the informal notion of relative information capacity often suggested in the conceptual database literature, which is based on accessability of data via queries. Results here indicate that this notion is too general to accurately measure whether an underlying semantic connection exists between database schemata. Another important result of the paper shows that under any natural notion of information capacity equivalence, two relational schemata (with no dependencies) are equivalent if and only if they are identical (up to re-ordering of the attributes and relations). The approach and definitions used here can form part of the foundation for a rigorous investigation of a variety of important database problems involving data relativism, including those of schema integration and schema translation.