Abstract
The current research works and the existing problems of terminological cycles in description logics are analyzed in this paper. Referring to the works of Baader F and Nebel B, we aim in a new direction. Firstly, description logic $$ v\mathcal{L} $$ is defined, and the description graphs GT and GJ are redefined. A syntax condition for the satisfiability of membership relation is given. By using this syntax condition, we prove the following: The subsumption reasoning in $$ v\mathcal{L} $$ with respect to gfp-model, lfp-model and descriptive model is polynomial.
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