2 the Solution : a Semi - Formal Outline 3

Based on F-logic, we specify an advanced data model with object-oriented and logic-oriented features that substantially extend the relational approach. For this model we exhibit and study the counterpart to the well-known decomposition of a relation scheme according to a nontrivial nonkey functional dependency. For decomposing a class of a database schema the transformation of pivoting is used. Pivoting separates apart some attributes of the class into a newly generated class. This new class is declared to be a subclass of the result class of the so-called pivot attribute. Moreover the pivot attribute provides the link between the original class and the new subclass. We identify the conditions for the result of pivoting being equivalent with its input: the expressive power of path functional dependencies, the validity of the path functional dependency between the pivot attribute and the transplanted attributes, and the validity of the onto-constraint guaranteeing that values for the transplanted attributes can be referenced from the remaining part of the original class. 1 The problem: an introduction into decomposition The theory of database schema design (see any suitable database textbook or MR92, Bis95b, Bis95a, Bis98] aims at formally characterizing \good" schemas and at inventing algorithms to test and to improve the quality of a given schema. Semantic constraints play a key role for both tasks. On the one side, semantic constraints are purely syntactic items, and as such they can be algorithmically examined and manipulated by the schema administrator at design time. On the other side, they represent the collection of all potential instances of the schema, and as such they essentially determine the performance of the database application during its future lifetime. As a general heuristic, a schema is considered to be \good" if it consists of mostly atomic and mostly independent components where atomicity and independence are expressed relative to the features of the data model, in particular, of the available semantic constraints. Accordingly, the semantic constraints of a schema can indicate whether there are still compound components and how to decompose them into simpler ones.