Cardinality restrictions on concepts
Artificial Intelligence
The complexity of concept languages
Information and Computation
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
On evaluating decision procedures for modal logic
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Comparative study of variable precision rough set model and graded rough set model
International Journal of Approximate Reasoning
From Tableaux to Automata for Description Logics
Fundamenta Informaticae - The 1st International Workshop on Knowledge Representation and Approximate Reasoning (KR&AR)
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We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(KR)--a natural extension of propositional modal logic KR by counting expressions--which plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the first known algorithm which meets the lower bound for the complexity of the problem. Thus, we exactly fix the complexity of the problem and refute a EXPTIME-hardness conjecture. This establishes a kind of "theoretical benchmark" that all algorithmic approaches can be measured with.