Three-Valued Paraconsistent Reasoning for Semantic Web Agents

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Description logics [1] 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. One of widely applied description logics is \(\mathcal{SHIQ}\) [7,8]. 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 define three three-valued paraconsistent semantics for \(\mathcal{SHIQ}\), reflecting different meanings of concept inclusion of practical importance. We also provide a quite general syntactic condition of safeness guaranteeing satisfiability of a knowledge base w.r.t. three-valued semantics and define a faithful translation of our formalism into a suitable version of a two-valued description logic. Such a translation allows one to use existing tools and \(\mathcal{SHIQ}\) reasoners to deal with inconsistent knowledge.