A Study on Information-Preserving Schema Transformations

The problem of determining the relative information capacity between two knowledge bases or schemas, of the same or different models, is inherent when implementing schema transformations. When restructuring one schema into another, one expects that the schema transformation supports the complete and correct mapping of all the information contents from the source schema to the target schema. Such a characteristic is commonly referred to as information capacity preservation or schema dominance. This paper presents a formal and constructive approach to measure the relative information capacity, in the restricted case of first-order schemas related by first-order mappings. It complements the existing definitions of information capacity preservation from the perspective of model theory, showing the exact relationships among the constraints of the involved schemas, the mappings between the components of these schemas, and the database states which the schemas admit. Since satisfying some sort of schema equivalence property is essential in areas such as database conceptual design and database reverse engineering, our approach allows us to characterize the notion of normalization in database design. We review the current literature concerning database normal forms and decompositions. We also review the process of reverse engineering a database schema. In addition, we provide deeper insight into database reverse engineering methodologies, suggesting horizontal decompositions as a useful tool for facilitating the discovery of more specific objects and relationships in the conceptualization phase of the process. With the aid of simple examples, we show the essence behind our reasoning. We discuss the need for an unambiguous means through which objects in the output schema can be identified. Ultimately, the knowledge this paper ensues will be beneficial to database engineers in performing a correct schema transformation.