The RDF Schema reification method allows the introduction of meta-data about RDF(S) statements, but it is not possible to perform inference over reified data. As an alternative it was proposed to extend classical Semantic Web data with annotations. This extension possesses a formal semantics accompanied by a complete set of inference rules. Furthermore Semantic Web data with annotations is becoming available, where YAGO knowledge base is a prominent example. In our work we present an approach to perform the closure of large RDF Schema graphs with confidence annotations using standard relational database technology. We define a $\rho$df rule dependency graph, introduce inheritance rules as non-recursive and present implementations for both classical and annotated inference rules. We also focus on the implementation of different algorithms to perform the transitive closure. A comparative analysis and extensive benchmarking are also detailed.
