An overview of fuzzy Description Logics for the Semantic Web

2012 ◽  
Vol 28 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Z. M. Ma ◽  
Fu Zhang ◽  
Hailong Wang ◽  
Li Yan
Keyword(s):  
Fuzzy Logic ◽  
Semantic Web ◽  
Description Logics ◽  
Expressive Power ◽  
Future Research ◽  
Practical Applications ◽  
Fuzzy Description Logics ◽  
Knowledge Based ◽  
Fuzzy Logic Theory ◽  
Fuzzy Description

AbstractInformation imprecision and uncertainty exist in many real world applications, and such information would be retrieved, processed, shared, reused, and aligned in the maximum automatic way possible. As a popular family of formally well-founded and decidable knowledge representation languages, fuzzy Description Logics (fuzzy DLs), which extend DLs with fuzzy logic, are very well suited to cover for representing and reasoning with imprecision and uncertainty. Thus, a requirement naturally arises in many practical applications of knowledge-based systems, in particular the Semantic Web, because DLs are the logical foundation of the Semantic Web. Currently, there have been lots of fuzzy extensions of DLs with Zadeh's fuzzy logic theory papers published, to investigate fuzzy DLs and more importantly serve as identifying the direction of fuzzy DLs study. In this paper, we aim at providing a comprehensive literature overview of fuzzy DLs, and we focus our attention on fuzzy extensions of DLs based on fuzzy set theory. Other relevant formalisms that are based on approaches like probabilistic theory or non-monotonic logics are covered elsewhere. In detail, we first introduce the existing fuzzy DLs (including the syntax, semantics, knowledge base, and reasoning algorithm) from the origin, development (from weaker to stronger in expressive power), some special techniques, and so on. Then, the other important issues on fuzzy DLs, such as reasoning, querying, applications, and directions for future research, are also discussed in detail. Also, we make a comparison and analysis.

scholarly journals Reasoning with Very Expressive Fuzzy Description Logics

2007 ◽  
Vol 30 ◽  
pp. 273-320 ◽  
Author(s):  
G. Stoilos ◽  
G. Stamou ◽  
J. Z. Pan ◽  
V. Tzouvaras ◽  
I. Horrocks
Keyword(s):  
Knowledge Representation ◽  
Knowledge Base ◽  
High Performance ◽  
Description Logics ◽  
Decision Procedures ◽  
Satisfiability Problem ◽  
Fuzzy Description Logics ◽  
Knowledge Based ◽  
Fuzzy Description

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN.

A survey on fuzzy ontologies for the Semantic Web

2016 ◽  
Vol 31 (3) ◽  
pp. 278-321 ◽  
Author(s):  
Fu Zhang ◽  
Jingwei Cheng ◽  
Zongmin Ma
Keyword(s):  
Semantic Web ◽  
Real World ◽  
Semantic Representation ◽  
Future Research ◽  
Comprehensive Overview ◽  
Ongoing Research ◽  
Practical Applications ◽  
Knowledge Based ◽  
Formal Definitions ◽  
Main Ideas

AbstractOntology, as a standard (World Wide Web Consortium recommendation) for representing knowledge in the Semantic Web, has become a fundamental and critical component for developing applications in different real-world scenarios. However, it is widely pointed out that classical ontology model is not sufficient to deal with imprecise and vague knowledge strongly characterizing some real-world applications. Thus, a requirement of extending ontologies naturally arises in many practical applications of knowledge-based systems, in particular the Semantic Web. In order to provide the necessary means to handle such vague and imprecise information there are today many proposals for fuzzy extensions to ontologies, and until now the literature on fuzzy ontologies has been flourishing. To investigate fuzzy ontologies and more importantly serve as helping readers grasp the main ideas and results of fuzzy ontologies, and to highlight an ongoing research on fuzzy approaches for knowledge semantic representation based on ontologies, as well as their applications on various domains,in this paper,we provide a comprehensive overview of fuzzy ontologies. In detail, wefirstintroduce fuzzy ontologies from the most common aspects such asrepresentation(including categories, formal definitions, representation languages, and tools of fuzzy ontologies),reasoning(including reasoning techniques and reasoners), andapplications(the most relevant applications about fuzzy ontologies). Then,the other important issueson fuzzy ontologies, such asconstruction,mapping,integration,query,storage,evaluation,extension, anddirections for future research, are also discussed in detail. Also, we make somecomparisons and analysesin our whole review.

A Review of Fuzzy Models for the Semantic Web

2011 ◽  
pp. 63-77
Author(s):  
Hailong Wang ◽  
Zongmin Ma ◽  
Li Yan ◽  
Jingwei Cheng
Keyword(s):  
Computational Complexity ◽  
Semantic Web ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Description Logics ◽  
Expressive Power ◽  
Semantic Knowledge ◽  
Context Information ◽  
Semantic Knowledge Base

In the Semantic Web context, information would be retrieved, processed, shared, reused and aligned in the maximum automatic way possible. Our experience with such applications in the Semantic Web has shown that these are rarely a matter of true or false but rather procedures that require degrees of relatedness, similarity, or ranking. Apart from the wealth of applications that are inherently imprecise, information itself is many times imprecise or vague. In order to be able to represent and reason with such type of information in the Semantic Web, different general approaches for extending semantic web languages with the ability to represent imprecision and uncertainty has been explored. In this chapter, we focus our attention on fuzzy extension approaches which are based on fuzzy set theory. We review the existing proposals for extending the theoretical counterpart of the semantic web languages, description logics (DLs), and the languages themselves. The following statements will include the expressive power of the fuzzy DLs formalism and its syntax and semantic, knowledge base, the decidability of the tableaux algorithm and its computational complexity etc. Also the fuzzy extension to OWL is discussed in this chapter.

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