Abstract: In computer science,ontologies are dynamic entities.To make them adapt to new and evolving applications,it is necessary to constantly perform modifications such as the extension with new axioms and merging with other ontologies.Based on the different requires and application domains,users choose the appropriate ontology to import another ontology and implement the extension of the existing ontology in many application domains of developing ontologies.We argued that it is very significant to know that the resulting ontology remains a conservative extension of the original one after performing such modifications.If this is not the case,there may be unexpected consequences when using the modified ontology in the place of the the existing one in applications.Lutz et al. studied the conservative extension problem of description logic and proved that conservative extension remaines ExpTime-completeness.The conservative extension in the description logic with cyclic terminolgies was analyzed based on Lutz’s work.On the one hand,the sufficient condition of conservative extensions with respect to greatest fixpoint semantics in the description logic with cyclic termino-logies has the same primitive concepts,and its complexity is proved to be polynomial.On the other hand,conservative extension ofterminological cycles with respect to the greatest fixpoint semantics is prestented and its complexity is proved to be exponential.

Key words: Ontologies,Description logic,Cyclic terminologies,Conservative extension