A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Resolution decision procedures
Handbook of automated reasoning
Combining superposition, sorts and splitting
Handbook of automated reasoning
Deciding Regular Grammar Logics with Converse Through First-Order Logic
Journal of Logic, Language and Information
The foundational model of anatomy in OWL: Experience and perspectives
Web Semantics: Science, Services and Agents on the World Wide Web
Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family
Journal of Automated Reasoning
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Web Semantics: Science, Services and Agents on the World Wide Web
Complexity boundaries for horn description logics
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Data complexity of reasoning in very expressive description logics
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Consequence-driven reasoning for horn SHIQ ontologies
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
The DL-lite family and relations
Journal of Artificial Intelligence Research
Hypertableau reasoning for description logics
Journal of Artificial Intelligence Research
Concurrent classification of EL ontologies
ISWC'11 Proceedings of the 10th international conference on The semantic web - Volume Part I
A comparison of reasoning techniques for querying large description logic ABoxes
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
FaCT++ description logic reasoner: system description
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
A novel approach to ontology classification
Web Semantics: Science, Services and Agents on the World Wide Web
Consequence-based reasoning beyond horn ontologies
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Performance heterogeneity and approximate reasoning in description logic ontologies
ISWC'12 Proceedings of the 11th international conference on The Semantic Web - Volume Part I
ExpTime Tableaux for Using Sound Global Caching
Journal of Automated Reasoning
Parameterized Complexity
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In this paper we investigate the consequence-based algorithms that are nowadays commonly used for subsumption reasoning with description logic ontologies, presenting the following novel results. First, we present a very general consequence-based reasoning algorithm that can be instantiated so as to capture the essential features of the known algorithms. Second, we use this algorithm to develop a novel framework for a quantitative and parametric analysis of the complexity of subsumption reasoning in description logic ontologies. Our approach is based on the notion of a decomposition-a graph-like structure that, roughly speaking, summarizes the models relevant during ontology reasoning. We identify width and length as decomposition parameters that determine the ''level'' of combinatorial reasoning. We prove that, when parameterized by a decomposition, our consequence-based algorithm runs in time that is fixed-parameter tractable in width and length. Third, we briefly discuss how length and width characterize the behavior of tableau algorithms. Fourth, we show that the width and length of existing ontologies are reasonably small, which, we believe, explains the good performance of consequence-based algorithms in practice. We thus obtain a sound foundation for a practical implementation of ontology reasoners, as well as a way to analyze the reasoners' performance.