ISSN 1000-1239 CN 11-1777/TP

• 论文 •

### 基于最大不动点模型的描述逻辑系统FLε的有穷基

1. 1(中南大学信息科学与工程学院 长沙 410083) 2(广西师范大学计算机科学与信息工程学院 广西桂林 541004) 3(计算机科学国家重点实验室(中国科学院软件研究所) 北京 100190) (sqtang@mailbox.gxnu.edu.cn)
• 出版日期: 2010-09-15

### Finite Basis for gfp-Model of Description Logic FLε

Tang Suqin1,2, Cai Zixing1, Wang Ju2, and Jiang Yuncheng2,3

1. 1(School of Information Science and Engineering, Central South University, Changsha 410083) 2(School of Computer Science and Information Engineering, Guangxi Normal University, Guilin, Guangxi 541004) 3(State Key Laboratory of Computer Science (Institute of Software, Chinese Academy of Sciences), Beijing 100190)
• Online: 2010-09-15

Abstract: Description logics (DLs) are a class of knowledge representation formalisms in the tradition of semantic networks and frames, which can be used to represent the terminological knowledge of an application domain in a structured and formally well-understood way. The finite basis problems in DLs, especially the fundamentality and the current research progresses of the finite basis problems in DLs are analyzed in this paper. The attribute implication and the Duguenne-Guigues basis in the formal concept analysis (FCA) are studied. Based on the existence of the Duguenne-Guigues basis in FCA and the works of F Baader, a new context, namely description context and the implications of description logic formulas are defined. It is proved that there exists a unique greatest fixed-points(gfp) model in the terminological cycles of the description logic system FLε. Based on the gfp-model, the existence of the finite basis (a finite set of implications) in the terminological cycles in the description logic system FLε is proved. Moreover, the soundness and the completeness of the finite basis are proved, too. Such a finite basis provides the knowledge engineers with interesting information on the application domain described by the description context. The knowledge engineers can use these implications as starting point for building an ontology describing this application domain.