Modal logics, description logics and arithmetic reasoning
Artificial Intelligence
Introduction to Algorithms
Reasoning with Individuals for the Description Logic SHIQ
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Performance measurement and analysis of certain search algorithms.
Performance measurement and analysis of certain search algorithms.
The Description Logic Handbook
The Description Logic Handbook
Pellet: A practical OWL-DL reasoner
Web Semantics: Science, Services and Agents on the World Wide Web
A Tableau Decision Procedure for $\mathcal{SHOIQ}$
Journal of Automated Reasoning
Tableau-based reasoning for description logics with inverse roles and number restrictions
Tableau-based reasoning for description logics with inverse roles and number restrictions
A Hybrid Tableau Algorithm for ALCQ
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
How many legs do i have?: non-simple roles in number restrictions revisited
LPAR'07 Proceedings of the 14th 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
Automated reasoning in ALCQ via SMT
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Solving graded/probabilistic modal logic via linear inequalities (system description)
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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This article presents a hybrid Abox tableau calculus for 𝒮ℋ𝒬 which extends the basic description logic 𝒜ℒ𝒞 with role hierarchies, transitive roles, and qualified number restrictions. The prominent feature of our hybrid calculus is that it reduces reasoning about qualified number restrictions to integer linear programming. The calculus decides 𝒮ℋ𝒬 Abox consistency w.r.t. a Tbox containing general axioms. The presented approach ensures a more informed calculus which adequately handles the interaction between numerical and logical restrictions in 𝒮ℋ𝒬 concept and individual descriptions. A prototype reasoner for deciding 𝒜ℒ𝒞ℋ𝒬 concept satisfiability has been implemented. An empirical evaluation of our hybrid reasoner and its integrated optimization techniques for a set of synthesized benchmarks featuring qualified number restrictions clearly demonstrates the effectiveness of our hybrid calculus.