The Semantic Web contributes to the elicitation of knowl- edge from data, and leverages implicit knowledge through reasoning al- gorithms. The dynamic aspect of the Web pushes actual batch reasoning solutions, providing the best scalability so far, to upgrade towards incre- mental reasoning. This paradigm enables reasoners to handle new data as they arrive. In this paper we introduce Slider-p, an efficient incre- mental reasoner. It is designed to handle streaming expanding data with a growing background knowledge base. Directed reasoning implemented in Slider-p allows to influence the order of inferred triples. This feature, novel in the state of the art at the best of our knowledge, enables the adaptation of Slider-p’s behavior to answer at best queries as the rea- soning process is not over. It natively supports ρdf and RDFS, and its architecture allows to extend it to more complex fragments with a min- imal effort. Our experimentations show that it is able to influence the order of the inferred triples, prioritizing the inference of selected kinds of triples.