Terminological Reasoning is Inherently Intractable

Computational tractability has been a major concern in the area of termi-nological knowledge representation and reasoning. However, all analyses of the computational complexity of terminological reasoning are based on the hidden assumption that subsumption in terminologies reduces to subsumption of concept descriptions without a signiicant increase in computational complexity. In this paper it will be shown that this assumption, which seems to work in the \normal case," is nevertheless wrong. Subsumption in terminologies turns out to be co-NP-complete for a minimal terminolo-gical representation language that is a subset of every useful terminological language.