Description logics refer to a family of formalisms concentrated around concepts, roles and individuals. They are used in many multiagent and Semantic Web applications as a foundation for specifying knowledge bases and reasoning about them. Among them, one of the most important logics is SROIQ, providing the logical foundation for the OWL 2 Web Ontology Language recommended by W3C in October 2009. In the current paper we address the problem of inconsistent knowledge. Inconsistencies may naturally appear in the considered application domains, for example as a result of fusing knowledge from distributed sources. We introduce a number of paraconsistent semantics for SROIQ, including three-valued and four-valued semantics. The four-valued semantics reflects the well-known approach introduced in [5,4] and is considered here for comparison reasons only. We also study the relationship between the semantics and paraconsistent reasoning in SROIQ through a translation into the traditional two-valued semantics. Such a translation allows one to use existing tools and reasoners to deal with inconsistent knowledge.