Abstract. The realization of Semantic Web reasoning is central to substantiating the Semantic Web vision. However, current mainstream research on this topic faces serious challenges, which force us to question established lines of research and to rethink the underlying approaches. 1 What is Semantic Web Reasoning? The ability to combine data, mediated by metadata, in order to derive knowledge which is only implicitly present, is central to the Semantic Web idea. This process of accessing implicit knowledge is commonly called reasoning, and formal modeltheoretic semantics tells us exactly what knowledge is implicit in the data. 1 Let us attempt to define reasoning in rather general terms: Reasoning is about arriving at the exact answer(s) to a given query. Formulated in this generality, this encompasses many situations which would classically not be considered reasoning – but it will suffice for our purposes. Note that the definition implicitly assumes that there is an exact answer. In a reasoning context, such an exact answer would normally be defined by a model-theoretic semantics.