This paper contributes a coherent approach extending relational and deductive database technology towards an integration of expert system applications, which require sound and efficient capabilities to deal with uncertainty. Extending logic programming we define the semantics of quantitative deductive databases, where fixpoint theory plays a central role. Our calculus gives the rule programmer a great deal of flexibility to tailor the aggregation of certainties according to the application expertise at hand. Extending relational algebra we also introduce a quantitative relational algebra as a suitable target language for rule compilation. Importantly, well-known sophisticated optimization methods for logic data languages carry over to our system. Therefore we believe that our approach makes rule-based expert systems, requiring uncertainty reasoning on large and complex data, feasible for a variety of practical application areas.
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