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中文摘要：
分析了描述逻辑循环术语集的研究现状和存在的问题，在F.Baader工作的基础上进一步研究了描述逻辑εL混合循环术语集的LCS（least common subsumer）和MSC（most specific concept）推理问题．给出了εL混合循环术语集的语法和语义．针对εL混合循环术语集LCS和MSC推理的需要，提出了TBox-完全的概念，并重新定义了描述图．使用描述图和TBox-完全给出了最大不动点语义下εL混合循环术语集LCS和MSC的推理算法，证明了推理算法的正确性，并证明了推理算法是多项式时间复杂的．该推理算法为εL混合循环术语集的LCS和MSC推理提供了理论基础．
英文摘要：
Current research progresses and the existing problems of terminological cycles in description logics are analyzed in this paper. Based on the works ofF. Baader, the LCS （least common subsumer） and MSC （most specific concept） reasoning of hybrid terminological cycles in description logic εL is further studied. The syntax and semantics of hybrid terminological cycles in description logic εL are given. Under the requirement of the LCS and MSC reasoning of hybrid terminological cycles in description logic εL, TBox-completion is presented, and the description graph is redefined. The LCS and MSC reasoning algorithms of hybrid terminological cycles in description logic eL w.r.t, greatest fixpoint semantics are presented by using TBox-completion and description graph The correctness of reasoning algorithms is proved, and it is also proved that the LCS and MSC reasoning w.r.t. greatest fixpoint semantics can be computed in the polynomial time. Theoretical foundation for the LCS and MSC reasoning for hybrid terminological cycles in description logic eL is provided through the reasoning algorithms.
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