A Tableau-based Reasoning Method for Four-valued Description Logic $ALC$

Paraconsistent logic is an attractive approach when dealing with a huge amount of knowledge in an open, dynamic and collaborative environment. It allows users to draw useful conclusions in the presence of inconsistencies. In this sense, introducing paraconsistent reasoning into standard reasoning system not only economizes resources used for fixing contradictions but also maintains proper functioning. In this paper, a four-valued semantics for the description logic ALC with a corresponding tableau-based reasoning method is presented. The results demonstrate that this proposed logic collaborating with the tableau-based method has the ability to derive reasonable conclusions from inconsistent knowledge bases.