Reasoning about The Past with Two-Way Automata
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
The Complexity of Conjunctive Query Answering in Expressive Description Logics
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Query Answering in the Description Logic Horn-$\mathcal{SHIQ}$
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Complexity boundaries for horn description logics
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Journal of Artificial Intelligence Research
Data complexity of reasoning in very expressive description logics
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Query answering in description logics with transitive roles
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Nominals, inverses, counting, and conjunctive queries or: why infinity is your friend!
Journal of Artificial Intelligence Research
Complexities of Horn Description Logics
ACM Transactions on Computational Logic (TOCL)
Flag & check: data access with monadically defined queries
Proceedings of the 32nd symposium on Principles of database systems
HornDL: an expressive horn description logic with PTime data complexity
RR'13 Proceedings of the 7th international conference on Web Reasoning and Rule Systems
Ontology-based data access with databases: a short course
RW'13 Proceedings of the 9th international conference on Reasoning Web: semantic technologies for intelligent data access
Conjunctive regular path queries in lightweight description logics
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Computing datalog rewritings beyond horn ontologies
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Acyclicity notions for existential rules and their application to query answering in ontologies
Journal of Artificial Intelligence Research
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The high computational complexity of the expressive Description Logics (DLs) that underlie the OWL standard has motivated the study of their Horn fragments, which are usually tractable in data complexity and can also have lower combined complexity, particularly for query answering. In this paper we provide algorithms for answering conjunctive 2-way regular path queries (2CRPQs), a non-trivial generalization of plain conjunctive queries, in the Horn fragments of the DLs SHOIQ and SROIQ underlying OWL 1 and OWL 2. We show that the combined complexity of the problem is ExpTime-complete for Horn-SHOIQ and 2ExpTime- complete for the more expressive Horn-SROIQ, but is PTime-complete in data complexity for both. In contrast, even decidability of plain conjunctive queries is still open for full SHOIQ and SROIQ. These are the first completeness results for query answering in DLs with inverses, nominals, and counting, and show that for the considered logics the problem is not more expensive than standard reasoning.