Computational complexity of terminological reasoning in BACK
Artificial Intelligence
Terminological reasoning is inherently intractable (research note)
Artificial Intelligence
Reasoning and revision in hybrid representation systems
Reasoning and revision in hybrid representation systems
Subsumption in KL-ONE is undecidable
Proceedings of the first international conference on Principles of knowledge representation and reasoning
Attributive concept descriptions with complements
Artificial Intelligence
The complexity of existential quantification in concept languages
Artificial Intelligence
ISMIS '93 Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems
A Terminological Knowledge Representation System with Complete Inference Algorithms
PDK '91 Proceedings of the International Workshop on Processing Declarative Knowledge
Decidable reasoning in terminological knowledge representation systems
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Augmenting concept languages by transitive closure of roles: an alternative to terminological cycles
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
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It is believed by the scientific community that PL1 and PL2 are the largest concept languages for which there exists a polynomial algorithm that solves the subsumption problem. This is due to Donini, Lenzerini, Nardi, and Nutt, who have presented two tractable algorithms that are intended to solve the subsumption problem in those languages. In contrast, this paper proves that the algorithm for checking subsumption of concepts expressed in the language PL2 is not complete. As a direct consequence, it still remains an open problem to which computational complexity class this subsumption problem belongs.