Combining Deduction by Certainty with the Power of Magic

After about two decades since the origin of relational database technology its benefits and shortcomings are well recognized in academics and in the market place. Many efforts have been focused during the past five years on extending current relational database technology towards deductive databases which offer a more powerful reasoning capability based on Horn clause logic; i.e. perform exact reasoning. Due to the ubiquity of uncertain knowledge in real-life applications, the integration of uncertainty in deductive databases is highly desirable, too, and led to so-called quantitative deductive databases very recently. As this integration can be achieved in a natural way preserving the foundations of fixpoint semantics and relational algebra, established query optimization techniques can be taken over directly. This paper focuses on how to integrate the popular magic methods for optimizing recursion in the quantitative deductive database framework. We describe two refined methods, the QMagic Set method and the Supplementary QMagic Set method. Our performance results for a series of benchmarks demonstrate their increased efficiency compared to the standard magic methods. As a specialty we show how to efficiently implement certainty-guided deduction by Yo-Yo iteration.