What Is Approximate Reasoning?

Approximate reasoning for the Semantic Web is based on the idea of sacrificing soundness or completeness for a significant speed-up of reasoning. This is to be done in such a way that the number of introduced mistakes is at least outweighed by the obtained speed-up. When pursuing such approximate reasoning approaches, however, it is important to be critical not only about appropriate application domains, but also about the quality of the resulting approximate reasoning procedures. With different approximate reasoning algorithms discussed and developed in the literature, it needs to be clarified how these approaches can be compared, i.e. what it means that one approximate reasoning approach is better than some other. In this paper, we will formally define such a foundation for approximate reasoning research. We will clarify --- by means of notions from statistics --- how different approximate algorithms can be compared, and ground the most fundamental notions in the field formally. We will also exemplify what a corresponding statistical comparison of algorithms would look like.

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