A four-valued semantics for terminological logics
Artificial Intelligence
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SIGIR '96 Proceedings of the 19th annual international ACM SIGIR conference on Research and development in information retrieval
Artificial Intelligence
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
Paraconsistent reasoning and preferential entailments by signed quantified Boolean formulae
ACM Transactions on Computational Logic (TOCL)
Algorithms for Paraconsistent Reasoning with OWL
ESWC '07 Proceedings of the 4th European conference on The Semantic Web: Research and Applications
RaDON -- Repair and Diagnosis in Ontology Networks
ESWC 2009 Heraklion Proceedings of the 6th European Semantic Web Conference on The Semantic Web: Research and Applications
Paraconsistent Reasoning for OWL 2
RR '09 Proceedings of the 3rd International Conference on Web Reasoning and Rule Systems
Scalable OWL 2 reasoning for linked data
RW'11 Proceedings of the 7th international conference on Reasoning web: semantic technologies for the web of data
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The four-valued paraconsistent logic SROIQ4, originally presented by Ma and Hitzler, is extended to incorporate additional elements of SROIQ. It is shown that the modified logic is classically sound and that its embedding into classical SROIQ is consequence preserving. Furthermore, inserting special axioms into a SROIQ4 knowledge base allows additional nontrivial conclusions to be drawn, without affecting paraconsistency. It is also shown that the interaction of nominals and cardinality restrictions prevents some SROIQ4 knowledge bases from having models. For such knowledge bases, the logic remains explosive.