A relevance terminological logic for information retrieval
SIGIR '96 Proceedings of the 19th annual international ACM SIGIR conference on Research and development in information retrieval
Handbook of defeasible reasoning and uncertainty management systems
Consensus system for solving conflicts in distributed systems
Information Sciences—Informatics and Computer Science: An International Journal
Quasi-classical Logic: Non-trivializable classical reasoning from incosistent information
ECSQARU '95 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
A Sequent Calculus for Reasoning in Four-Valued Description Logics
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Knowledge Representation Techniques (Studies in Fuzziness and Soft Computing)
Knowledge Representation Techniques (Studies in Fuzziness and Soft Computing)
Using Distance Functions to Solve Representation Choice Problems
Fundamenta Informaticae
A paraconsistent logic programming approach for querying inconsistent databases
International Journal of Approximate Reasoning
INCONSISTENCY OF KNOWLEDGE AND COLLECTIVE INTELLIGENCE
Cybernetics and Systems
Paraconsistent Logic Programs with Four-Valued Rough Sets
RSCTC '08 Proceedings of the 6th International Conference on Rough Sets and Current Trends in Computing
Paraconsistent Reasoning for OWL 2
RR '09 Proceedings of the 3rd International Conference on Web Reasoning and Rule Systems
Modeling and Reasoning with Paraconsistent Rough Sets
Fundamenta Informaticae
Paraconsistent and approximate semantics for the OWL 2 web ontology language
RSCTC'10 Proceedings of the 7th international conference on Rough sets and current trends in computing
Three-valued paraconsistent reasoning for semantic web agents
KES-AMSTA'10 Proceedings of the 4th KES international conference on Agent and multi-agent systems: technologies and applications, Part I
A consensus-based method for fuzzy ontology integration
ICCCI'10 Proceedings of the Second international conference on Computational collective intelligence: technologies and applications - Volume Part II
Argumentation-Based reasoning with inconsistent knowledge bases
AI'10 Proceedings of the 23rd Canadian conference on Advances in Artificial Intelligence
Towards a paradoxical description logic for the semantic web
FoIKS'10 Proceedings of the 6th international conference on Foundations of Information and Knowledge Systems
Living with inconsistency and taming nonmonotonicity
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
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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 $\mathcal{SROIQ}$, 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 $\mathcal{SROIQ}$, 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 $\mathcal{SROIQ}$ 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.