Soft stratification for transformation-based approaches to deductive databases

The efficient evaluation of recursive views is a crucial issue in the research field of deductive databases. Results in this area are especially relevant for systems which will implement the new SQL:1999 standard, and hence will allow the definition of stratifiable recursive views. In particular, transformation-based solutions to query evaluation seem to be well-suited for extending existing relational databases as they are easy to implement and independent of other optimization methods such as index structures or algebraic manipulation techniques. The application of transformation-based approaches, however, may lead to unstratifiable recursion which requires an elaborate, and consequently very expensive evaluation of these kinds of views in general. In this thesis, we present a solution to this problem by identifying the new class of so-called softly stratifiable views which allow for a more efficient evaluation than arbitrary unstratifiable views. This subclass of unstratifiable views is especially relevant as it covers views resulting from the rewriting of an originally stratifiable schema. We will show that the concept soft stratification can be used in various database services such as query evaluation and update propagation. Additionally, it can be employed as a basic evaluation technique for the efficient computation of the general wellfounded semantics of unstratifiable schemata. With respect to transformation-based approaches, we focus on the Magic Sets rewriting of (function-free) stratifiable databases as this method has evolved into a kind of standard in the field of query evaluation. The language Datalog is used as a syntactical basis because of its simplicity which makes it particularly well-suited for presenting transformation-based techniques. We will show that Kerisit’s weak stratification approach for evaluating Magic Sets rewritten schemata may lead to a set of answers which is neither sound nor complete with respect to the wellfounded model. This problem is cured by introducing the new soft consequence operator in combination with the concept soft stratification, instead. Afterwards, it will be shown that this approach is suited for solving the problem of existential query evaluation, too. To this end, we develop the so-called Existential Magic Sets rewriting which extends the Magic Sets transformation in such a way that the computation of alternative answers with respect to (derived) existential queries is avoided. In case of update propagation, a novel deductive rule rewriting technique is developed incorporating the task of update propagation as well as Magic Sets optimizations into deductive propagation rules. To this end, Griefahn’s structured update propagation approach is extended such that the resulting rule sets becomes less complicated and softly stratifiable. The results from both services, i.e., query evaluation and update propagation, are then combined for developing the new soft alternating fixpoint computation approach to determining the well-founded model of unstratifiable databases. The algorithms and concepts presented in this thesis are developed by means of the abstract database language Datalog. The results can be almost directly transferred into the SQL context although additional language concepts of SQL such as Null values, multisets and aggregate functions have not been considered yet. However, it is our belief that the concept of soft stratification may already provide a realistic framework for extending the expressive power of relational database systems.