Attributive concept descriptions with complements
Artificial Intelligence
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
On the relative expressiveness of description logics and predicate logics
Artificial Intelligence
Cardinality restrictions on concepts
Artificial Intelligence
Reasoning in description logics
Principles of knowledge representation
On the decidability of query containment under constraints
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Complexity of Two-Variable Logic with Counting
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Two-variable logic with counting is decidable
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Source Integration in Data Warehousing
DEXA '98 Proceedings of the 9th International Workshop on Database and Expert Systems Applications
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Description Logics for Information Integration
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
The description logic handbook
Journal of Logic, Language and Information
A Tableau Decision Procedure for $\mathcal{SHOIQ}$
Journal of Automated Reasoning
Data Complexity of Query Answering in Expressive Description Logics via Tableaux
Journal of Automated Reasoning
Role Conjunctions in Expressive Description Logics
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Package-Based Description Logics
Modular Ontologies
Decidability of $\mathcal{SHI}$ with Transitive Closure of Roles
ESWC 2009 Heraklion Proceedings of the 6th European Semantic Web Conference on The Semantic Web: Research and Applications
Integrating description logics and action formalisms: first results
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Modular reuse of ontologies: theory and practice
Journal of Artificial Intelligence Research
Reasoning within expressive fuzzy rough description logics
Fuzzy Sets and Systems
The complexity of circumscription in description logic
Journal of Artificial Intelligence Research
Identification constraints and functional dependencies in description logics
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Ontology reasoning in the SHOQ(D) description logic
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
A tableaux decision procedure for SHOIQ
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Regular path queries in expressive description logics with nominals
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A Case Study in Integrating Multiple E-commerce Standards via Semantic Web Technology
ISWC '09 Proceedings of the 8th International Semantic Web Conference
Hypertableau reasoning for description logics
Journal of Artificial Intelligence Research
Journal of Ambient Intelligence and Smart Environments
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A description logic based situation calculus
Annals of Mathematics and Artificial Intelligence
Reasoning and explanation in EL and in expressive description logics
ReasoningWeb'10 Proceedings of the 6th international conference on Semantic technologies for software engineering
Description logic reasoning for semantic web ontologies
Proceedings of the International Conference on Web Intelligence, Mining and Semantics
ESWC'11 Proceedings of the 8th extended semantic web conference on The semantic web: research and applications - Volume Part I
Foundations of instance level updates in expressive description logics
Artificial Intelligence
Reasoning about actions using description logics with general TBoxes
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
Query answering in the horn fragments of the description logics SHOIQ and SROIQ
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
A Family of Dynamic Description Logics for Representing and Reasoning About Actions
Journal of Automated Reasoning
Journal of Ambient Intelligence and Smart Environments
Reasoning over ontologies with hidden content: the import-by-query approach
Journal of Artificial Intelligence Research
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We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C2, the two variable fragment of predicate logic with counting quantifiers, which yields decidability in NExpTime. We show that this approach leads to an optimal solution for ALCQI, as ALCQI with cardinality restrictions has the same complexity as C2 (NExpTime-complete). In contrast, we show that for ALCQ, the problem can be solved in ExpTime. This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals. Using the same reduction, we show that, for the extension of ALCQI with nominals, reasoning with general axioms is a NExpTime-complete problem. Finally, we sharpen this result and show that pure concept satisfiability for ALCQI with nominals is NExpTime-complete. Without nominals, this problem is known to be PSpace-complete.