Automata-Theoretic techniques for modal logics of programs
Journal of Computer and System Sciences
Terminological reasoning is inherently intractable (research note)
Artificial Intelligence
Attributive concept descriptions with complements
Artificial Intelligence
The complexity of existential quantification in concept languages
Artificial Intelligence
The complexity of concept languages
Information and Computation
Artificial Intelligence
Information and Computation
Complexity of Terminological Reasoning Revisited
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A practical decision method for propositional dynamic logic (Preliminary Report)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
The description logic handbook
Proof-Theoretic Approach to Description-Logic
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
The complexity of propositional implication
Information Processing Letters
The Complexity of Satisfiability for Fragments of Hybrid Logic--Part I
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
DL-Lite: tractable description logics for ontologies
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
DL-lite in the light of first-order logic
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Terminological cycles in a description logic with existential restrictions
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
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The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and DL-Lite families, have an easier satisfiability problem; sometimes it is even tractable. We classify the complexity of the standard satisfiability problems for all possible Boolean and quantifier fragments of ALC in the presence of general axioms.