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... in more detail for DLs and compared with our approaches presented in this paper. A number of researchers have extended description logics with paraconsistent semantics and adequate reasoning methods =-=[19, 28, 27, 15, 14, 31, 30, 22, 21]-=-. The work [27] studies a constructive version of the basic description logic ALC, but it is not clear how to extend the semantics provided in this work to other description logics. Papers [19, 28, 15...

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...for developing robust intelligent systems, and fails to use the benefits of inconsistent knowledge in intelligent activities, or to acknowledge the fact that living with inconsistencies seems to be unavoidable”. And [4] 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 to not simply avoid inconsistencies but apply non-standard reasoning methods (e.g., non-standard inference or non-classical semantics) to obtain meaningful answers [38, 23, 30, 12, 45, 20, 29, 24, 43]. 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 meaning conclusions from inconsistent KBs [38]. Those paraconsistent approaches with non-standard inference presented by [43, 12] are employing argument principles where consistent subsets are selected from an inconsistent KB as substitutes in reasoning. Those paraconsistent ∗corresponding author Ema...

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...ent reasoning services, typically based on some many-valued logic, offer an alternative by being able to draw meaningful conclusions in the presence of contradictions. Paraconsistent reasoning has been extensively studied in both base formalisms of hybrid KBs. For DLs, most work [31, 39, 27, 41, 28] focuses on four-valued semantics varying which classical rules of inferences they satisfy. Among them, [27, 28] is most general as it covers SROIQ, the DL behind OWL 2, considers tractable subclasses and truth value removals, and permits re-using classical reasoners. Three-valued semantics for DLs [40] and measuring the degree of inconsistency in DL-Lite [42] have also been considered. For LPs, the comprehensive survey [8] discusses e.g. a four-valued semantics without default negation [6], a four-, six-, and nine-valued semantics [34] for answer sets [16], and a seven- [33] and nine-valued [3] well-founded semantics [15]. More recently, a very general framework for arbitrary bilattices of truth values [2] and paraconsistent Datalog [4] have been considered. At the same time, paraconsistent reasoning is still a rather unexplored field in the context of hybrid KBs. Notable exceptions are [20...

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...rticularly important research topic in the Semantic Web. There are some existing work for reasoning with inconsistent ontologies, which include the reasoning method based on paraconsistent approaches =-=[29,30,37]-=-, the reasoning method based on selection functions [23,24], the reasoning method based on possibility [33,34], the reasoning method based on Defeasible Logic Programs [19], and so on. All these metho...

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...Related Work There are many existing work for reasoning with inconsistent ontologies for its importance. One major work of reasoning with inconsistent ontologies is based on paraconsistent approaches =-=[25, 24, 37]-=-. The main idea is to extend the existing ontology languages to four-valued logics, which uses two additional truth values which stand for underde ned (i.e neither true nor false) and overde ned (or c...

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...r 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 =-=[36,18,25,9,41,15,23,19,39,43,44]-=-. 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 hand...

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... X. Zhang, Z. Lin, and K. Wang Belnap’s four-valued logic [8,9], Besnard and Hunter’s quasi-classical logic [10], Elvang-Gøransson and Hunter’s argumentative logic [11] and Priest’s paradoxical logic =-=[12]-=-. While these paraconsistent semantics can handle inconsistencies in DLs in a way, they share the same shortcoming: their reasoning ability is too weak to infer useful information in some cases. For i...