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Zusammenfassung: Four-valued extensions of description logics (DLs) enable paraconsistent reasoning with DL knowledge bases. We present a four-valued DL which features three kinds of class inclusions corresponding to three types of implications with different important logical properties. This extension provides a novel way to reason with inconsistent DL knowledge bases without causing additional computational complexity for the standard reasoning services of DLs. Currently, tableaux based and resolution based reasoners are the two main approaches to proof theory for DLs. However, only a sequence calculus based proof theory did exist for a four-valued extension of the description logic ALC. Here we present a paraconsistent resolution, together with its refined form, the ordered-resolution, which can service as a sound and complete decision procedure for our four-valued extension of ALC.
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