Studies Of Fuzzy Description Logics Supporting Representation Of Fuzzy Data Types

The Semantic Web is an extension of the current web in which the web information can be given well-defined semantic meaning, and thus enabling better cooperation between computers and people. In order to recognize and reason the web resources by computers in an intelligent and automatic way, we should set up ontology and thus use ontology description languages to represent the abstract knowledge and data information in web. Over the past few years, several ontology description languages for the Semantic Web have emerged, including OIL, DAML+OIL and OWL. In order to make the Semantic Web have the inferable nature, all the above ontology languages adopt description logics serving as their theoretical counterparts.Classical description logics and OWL have limitations when dealing with fuzzy knowledge and data information that play an important role in many web applications, so they are necessary to be extended with fuzzy theory. According to the current research progresses in fuzzy description logics、description logic reasoners and fuzzy OWL, it is found that the current fuzzy extensions to description logics and OWL can’t support the representation and reasoning of fuzzy data information with customized fuzzy data types and customized fuzzy data type predicates, while such complex fuzzy data type information are very useful in practical applications. As a result, in-depth studies on the fuzzy description logics、the corresponding reasoner and fuzzy OWL which can support the representation and reasoning of fuzzy data information with customized fuzzy data types and predicates are presented in this paper. Our main contributions include:(i) Firstly, the limitations of OWL and description logics in the representation of fuzzy data types are pointed out by compared to the driven data type mechanism of XML Schema and its fuzzy extensions. Secondly, the definition of fuzzy data type group and the syntax and semantics of fuzzy data type expressions are given; then, the concepts of fuzzy data type queries and their satisfiability are defined; furthermore, how to constrain the expressive ability of the fuzzy data type group to ensure its decidability is investigated. Finally, the decidability of the fuzzy data type expression queries which are based on the conforming fuzzy data type group is discussed.(ii) A kind of new fuzzy description logic named F-ALC(G) is proposed by adding fuzzy data type group G into fuzzy description logic F-ALC. Firstly, the syntax, semantics of F-ALC(G) and the components of its corresponding knowledge base system are given. Secondly, the fuzzy Tableaux for F-ALC(G) ABox is defined and the ABox consistence checking algorithm of F-ALC(G) based on the fuzzy Tableaux is given; then, 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-ALC(G) and the corresponding fuzzy data type reasoner is designed; furthermore, how to translate the other reasoning problems to the F-ALC(G) ABox consistence checking problem is discussed here. Finally, the termination of the F-ALC(G) ABox consistence checking algorithm is discussed; then, the soundness and completeness of the checking algorithm are proved and its computational complexity is analyzed; furthermore, an optimal algorithm running in PsPACE is prompted.(iii) Based on the fuzzy description logic F-ALC(G), a description logic reasoner, named FRESG1.0, which can support the representation and reasoning of customized fuzzy data types and customized fuzzy data type predicates is designed and implemented. In this paper, the reasoning services provided by FRESG1.0 and the program language of it are briefly introduced. The overall architecture of FRESG1.0 and the design and implementation of its main components are also described, where the features of the reasoner as well as the algorithms and technologies adopted in the process of implementations are paid more attention to. Finally, the expressive ability and performance of FRESG1.0 are analyzed according to the given testing cases.(iv) A new kind of fuzzy description logic named F-SHOIN(G) is proposed because the representation ability of F-ALC(G) is not expressive enough to serve as the theoretical counterpart of the fuzzy extensions to OWL. Firstly, the syntax, semantics of F-SHOIN(G) and the components of its corresponding knowledge base system are given; then, the satisfiability reasoning algorithm of F-SHOIN(G)-concept based on the fuzzy Tableaux is presented; furthermore, the termination of the reasoning algorithm as well as its soundness and completeness are proved. During the discussions, compared to the fuzzy description logic F-ALC(G), the changes in the reasoning of fuzzy data types are paid more attention to because some new fuzzy constructors (such as transitive role S, inverse role I etc.) are introduced. Finally, the definition of G-combined fuzzy description logic is given by analyzing the two kinds of representative fuzzy description logics F-ALC(G) and F-SHOIN(G); furthermore, the components of the reasoning algorithm as well as the reasoning architecture for G-combined fuzzy description logics in a general sense are investigated.(v) OWL is extended to f-OWL by recoding the OWL DL class descriptions、OWL DL axioms and facts, based on the fuzzy description logic F-SHOIN(G) and the syntax specifications of RDF/XML. Then, the mapping rules from OWL to f-OWL are presents, which can unify the representation of crisp and fuzzy knowledge in fuzzy ontology. Finally, the conversion method from f-OWL ontology to description logic F-SHOIN(G) is given, which eventually transforms the f-OWL reasoning problems to the concept satisfiability reasoning problems of F-SHOIN(G) to be solved.