As described in the previous chapter, during the last fifteen years DLs have been investigated thoroughly with respect to their expressive power and the complexity of the standard inference problems. In some applications it has turned out, however, that additional non-standard inferences are needed to support the construction and maintenance of large DL knowledge bases. Some systems, e.g., Classic, contain ad hoc implementations of such novel inferences, mostly without having defined them formally or having investigated their computational complexity. This situation corresponds to the early days of DLs where systems have been built without an exact understanding of the formal properties of the implemented reasoning services. In this book, we aim at taking non-standard inferences to a formal level by providing precise definitions, complete algorithms, and first complexity results.
KeywordsNormal Form Matching Problem Concept Description Concept Conjunction Standard Inference
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