支持模糊数据类型表示的模糊描述逻辑F-SHOIQ(G)

Fuzzy Description Logic F-SHOIQ(G) Supporting Representation of Fuzzy Data Types

分析了现有描述逻辑在模糊知识和数据类型表示方面存在的问题,提出了一种新的模糊描述逻辑F-SHOIQ(G).F-SHOIQ(G)不仅能够表示模糊知识,而且能够表示含有自定义模糊数据类型及自定义模糊数据类型谓词的模糊数据信息.首先,给出了模糊数据类型域的概念和模糊数据类型表示的一般形式,在此基础上,定义了F-SHOIQ(G)的语法、语义及相应的知识库,进而给出了基于模糊Tableaux的F-SHOIQ(G)概念的可满足性推理算法.其次,将经典描述逻辑中的推理结构(该结构将Tableaux扩展规则推理和数据类型推理相分离)用于F-SHOIQ(G)的推理问题,设计了相应的模糊数据类型推理机.最后,详细证明了F-SHOIQ(G)概念的可满足性推理问题是可判定的.在数据类型表示方面,F-SHOIQ(G)具备比FSHOIQ更强的表达能力和推理能力,为语义Web表示和推理模糊数据信息提供了理论基础.

The shortcomings of existing description logics in the representation of fuzzy knowledge and data types are analyzed and a kind of new fuzzy description logic named F-SHOIQ（G） is proposed in the paper. F-SHOIQ（G） can support not only the representation of fuzzy knowledge, but also the representation of fuzzy data information with customized fuzzy data types and cus- tomized fuzzy data type predicates. Firstly, the concept of fuzzy data type group and a general formalism of the representation of fuzzy data types are introduced. Then, based on the fuzzy data type group, the syntax, semantics of F-SHOIQ（G） and the components of its corresponding knowledge base are defined. Furthermore, the satisfiability reasoning algorithm of F-SHOIQ（G）- concept based on the fuzzy Tableaux is presented. Secondly, the traditional reasoning architecture in which the reasoning of Tableaux expansion rules and data type can be divided is adopted for the reasoning of F-SHOIQ（G）. The corresponding fuzzy data type reasoner is designed. Finally, the decidability of the satisfiability reasoning problem of F-SHOIQ（G）-concept is proved. The representation and reasoning capabilities of F-SHOIQ（G） go beyond the fuzzy description logic FSHOIQ in the representation of data information. F-SHOIQ（G） lays a theoretical foundation for the representation and reasoning of fuzzy data information in the Semantic Web.