ISSN 1000-1239 CN 11-1777/TP

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基于最大不动点模型的描述逻辑系统FLε的有穷基

唐素勤1,2 蔡自兴1 王驹2 蒋运承2,3   

  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

摘要: 研究了描述逻辑的有穷基问题,分析了有穷基在描述逻辑中的重要意义及其研究现状,并研究了形式概念分析中的属性蕴含和Duguenne-Guigues基问题.利用形式概念分析中Duguenne-Guigues基存在的证明结果,在F.Baader工作基础上设置了描述逻辑的描述背景,重新定义了描述背景下的属性蕴含,证明了带循环术语的描述逻辑系统FLε存在最大不动点语义(greatest fixed-points,gfp)模型,给出了带循环术语的描述逻辑系统FLε在最大不动点模型下的有穷基的存在性定理,并证明有穷基的可靠性和完备性.描述逻辑有穷基可以帮助知识工程师构建一个更适用于推理的描述逻辑知识库.

关键词: 描述逻辑, 有穷基, 形式概念分析, 蕴含, 最大不动点

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.

Key words: description logics, finite basis, formal concept analysis, implication, greatest fixed-point