A four-valued semantics for terminological logics
Artificial Intelligence
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
Combining Horn rules and description logics in CARIN
Artificial Intelligence
{\cal A}{\cal L}-log: Integrating Datalog and Description Logics
Journal of Intelligent Information Systems
Description logic programs: combining logic programs with description logic
WWW '03 Proceedings of the 12th international conference on World Wide Web
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Algorithms for Paraconsistent Reasoning with OWL
ESWC '07 Proceedings of the 4th European conference on The Semantic Web: Research and Applications
A Coherent Well-founded Model for Hybrid MKNF Knowledge Bases
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Non-standard reasoning services for the debugging of description logic terminologies
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Nonmonotonic databases and epistemic queries
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Foundations of Semantic Web Technologies
Foundations of Semantic Web Technologies
Query Answering for OWL-DL with rules
Web Semantics: Science, Services and Agents on the World Wide Web
Reconciling description logics and rules
Journal of the ACM (JACM)
A better uncle for OWL: nominal schemas for integrating rules and ontologies
Proceedings of the 20th international conference on World wide web
Local closed world reasoning with description logics under the well-founded semantics
Artificial Intelligence
RW'11 Proceedings of the 7th international conference on Reasoning web: semantic technologies for the web of data
A framework for handling inconsistency in changing ontologies
ISWC'05 Proceedings of the 4th international conference on The Semantic Web
Effective integration of declarative rules with external evaluations for semantic-web reasoning
ESWC'06 Proceedings of the 3rd European conference on The Semantic Web: research and applications
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Hybrid MKNF knowledge bases, originally based on the stable model semantics, is a mature method of combining rules and Description Logics (DLs). The well-founded semantics for such knowledge bases has been proposed subsequently for better efficiency of reasoning. However, integration of rules and DLs may give rise to inconsistencies, even if they are respectively consistent. Accordingly, reasoning systems based on the previous two semantics will break down. In this paper, we employ the four-valued logic proposed by Belnap, and present a paraconsistent semantics for Hybrid MKNF knowledge bases, which can detect inconsistencies and handle it effectively. Besides, we transform our proposed semantics to the stable model semantics via a linear transformation operator, which indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide a fixpoint algorithm for computing paraconsistent MKNF models.