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中文摘要：
分析描述逻辑循环术语集的研究现状和存在的问题，在F．Baader和S．Brandt的基础上进一步研究带RVM的描述逻辑εL混合循环术语集的语义及推理问题．给出带RVM的εL混合循环术语集的语法和语义．针对带RVM的εL混合循环术语集包含推理的需要，提出TBox-完全的概念，并重新定义描述图，使用描述图之间的模拟关系和TBox-完全给出最大不动点语义和描述语义下带RVM的εL混合循环术语集的概念包含推理算法，证明推理算法的正确性，并证明推理算法是多项式时间复杂的．
英文摘要：
The current research progresses and problems of terminological cycles in description logics are analyzed in this paper. Based on the research of Baader F and Brandt S, the semantics and reasoning of hybrid terminological cycles in description logic eL with RVM is further studied. The syntax and semantics of hybrid terminological cycles in description logic eL with RVM are given. Aiming at the requirement of subsumption reasoning of hybrid terminological cycles in description logic eL with RVM, TBox-completion is presented and the description graph is redefined. The subsumption reasoning algorithms of hybrid terminological cycles in description logic eL with RVM w. r. t. greatest fixpoint semantics and descriptive semantics are presented using TBox-completion and description graph.The correctness of reasoning algorithms has been proved. And it is also proved that the subsumption reasoning w. r. t. greatest fixpoint semantics and descriptive semantics can be computed in polynomial time.
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