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Top1. Introduction
As an extension of the World Wide Web (WWW), the Semantic Web (Berners-Lee et al., 2001) becomes more constantly changing and highly collaborative. Ontologies considered one of the pillars of the Semantic Web will rarely be perfect due to many reasons, such as modeling errors, migration from other formalisms, merging ontologies, and ontology evolution (Flouris et al., 2006; Pan et al., 2014; Zhang et al., 2016). As a fragment of predicate logic, description logic (DL), which is the logical foundation of the Web Ontology Language (McGuinness et al., 2009; Compton., 2015) (e.g., sublanguages OWL Lite and OWL DL correspond to 
and 
respectively), is unable to tolerate inconsistencies occurring in ontologies (Bertossi et al., 2005). Thus, the topic of inconsistency handling in OWL and DL has received extensive interests in the community in recent years (Maier et al., 2013; Lecue et al., 2015).
There are several approaches to handling inconsistencies in DLs. All of them can be functionally roughly classified into two different types. One type is based on the assumption that inconsistencies indicate erroneous data which are to be removed in order to obtain a consistent ontology (Huang et al., 2005; Qi et al., 2006; Qi et al., 2009). In these approaches, researchers hold a common view that ontologies should be completely free of inconsistencies, and thus try to eliminate inconsistencies from them to recovery consistency immediately by any means possible. However, there are some different opinions about the first type of treating inconsistency. And (Bertossi et al., 2005) argues that inconsistencies in knowledge are the norm in the real world, and so should be formalized and used, rather than always rejected. The other, called inconsistency-tolerant (or paraconsistent) approaches, is not to simply avoid inconsistencies but to apply non-standard reasoning methods (e.g., non-standard inference or non-classical semantics) to obtain meaningful answers (Odintsov et al., 2008; Alejandro et al., 2010; Zhang et al., 2010; Kamide et al., 2010; Nguyen et al., 2010; Maier et al., 2013; Zhang et al., 2013; Du J et al., 2013). In the second type of approaches, inconsistency treated as a natural phenomenon in realistic data, should be tolerated in reasoning. So far, the main idea of existing paraconsistent methods for handling inconsistency is introducing either non-standard inference or non-classical semantics to draw meaningful conclusions from inconsistent KBs (Flouris et al., 2006). Those paraconsistent approaches with non-standard inference presented by (Zhang et al., 2013; Alejandro et al., 2010) are employing argument principles where consistent subsets are selected from an inconsistent KB as substitutes in reasoning. Those approach with preferred semantics by (Du J et al., 2013) are introducing some preference between interpretations and collecting minimal interpretations as candidate models. In this sense, this approach is employing a non-monotone strategy to handle inconsistency. Those paraconsistent approaches are based on multi-valued semantics (a popular kind of non-classical semantics) such as four-valued DL studied by (Odintsov et al.,2008; Maier et al.,2013) based on Belnap’s four-valued semantics (Belnap., 1977; Lang et al., 2006), paradoxical DL presented by (Zhang et al.,2010) based on Priest’s paradoxical semantics, three-valued DL discussed by (Nguyen et al.,2010) based on Kleene’s three-valued semantics, and (Kamide et al., 2010) based on a dual interpretation semantics.