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中文摘要：
循环术语集是描述逻辑长期以来的研究难点，其最基本的问题即语义及推理问题没有得到合理的解决．分析了描述逻辑循环术语集的研究现状和存在的问题，将Baader的工作扩展到新的方向．针对更大的描述逻辑系统研究了循环术语集的语义及推理机制，即在描述逻辑εL的基础上添加数量约束构造算子，提出了描述逻辑εLN，给出了εLN的语义（包括不动点语义和描述语义）．针对εLN的需要，重新定义了描述图（包括语法描述图和语义描述图）．使用描述图之间的模拟关系给出了不动点语义下εLN循环术语集的可满足性和包含关系推理算法，并证明了推理算法是多项式时间复杂的．
英文摘要：
Terminological cycles have been a very hard problem in description logics for a long time, and their essential problems, i.e. semantics and reasoning problems, have not been solved reasonably. Current research progress and the existing problems of terminological cycles in description logics are analyzed in this paper. Based on the work of Baader, a new direction in terminological cycles is put forward. Aiming at more expressive description logic, the semantics and reasoning mechanism of terminological cycles are studied. The number restrictions are added to description logic eL, and the descripion logic εLN is presented. The semantics （fixpoint semantics and descriptive semantics） of εLN are given. To meet the requirement of εLN, the description graphs （syntax description graph and semantics description graph） are redefined. The satisfiability and subsumption reasoning algorithms of terminological cycles in description logic εLN w.r.t, fixpoint semantics are presented with simulation between description graphs. It is proved that the satisfiability and subsumption reasoning algorithms of terminological cycles in εLN are polynomial.
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