Paraconsistent Description Logics

Description logics (DLs) are a family of formal knowledge representation languageswhich is expressing structured knowledge and accessing and reasoning with it in a princi-pled way. They are of particular importance in providing a logical formalism for ontolo-gies in the semantic web. In an open, constantly changing and distributed collaborativeenvironment like the forthcoming semantic web, it is reasonable to expect that descriptionlogic-based knowledge bases will contain inconsistent information. However, classicalsemantics of description logics cannot handle inconsistency. Paraconsistent approach isusing a non-classical reasoning mechanism to tolerate inconsistency so that no all propo-sitions could be inferred from a theory with some inconsistencies, called paraconsistency.Paraconsistent DLs provide such a kind of reasoning mechanism with paraconsistency inDLs.This thesis aims to study paraconsistent DLs. The contribution of this thesis includesthe following points:1. This thesis presents quasi-classical DLs to ensure the resolution rule valid in para-consistent reasoning. Then this thesis develops quasi-classical tableau algorithmand transformation algorithm which is implemented as a new OWL DL paracon-sistent systems called PROSE. 2. This thesis introduces the minimal paradoxical semantics in DLs to satisfy theproperty of (classical) consistency-protected and the law of excluded middle whichare invalid in quasi-classical DLs. And this thesis develops a minimal sign-basedtableau algorithm for instance checking in ?????.3. This thesis proposes a description logic argumentation framework to analyze whichplays a primordial role among information causing inconsistency. However, neithermulti-valued approaches nor consistent subsets-based approaches can make thisanalysis. Then this thesis develops a graph-based algorithm to search arguments inDL-Lite knowledge bases.