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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 forces us to question established lines of research and to rethink the underlying approaches. We argue that reasoning for the Semantic Web should be understood as "shared inference," which is not necessarily based on deductive methods. Model-theoretic semantics (and sound and complete reasoning based on it) functions as a gold standard, but applications dealing with large-scale and noisy data usually cannot afford the required runtimes. Approximate methods, including deductive ones, but also approaches based on entirely different methods like machine learning or nature inspired computing need to be investigated, while quality assurance needs to be done in terms of precision and recall values (as in information retrieval) and not necessarily in terms of soundness and completeness of the underlying algorithms.


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