Reasoning with Very Expressive Fuzzy Description Logics

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.

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Completeness Knowledge Representation in Fuzzy Description Logics

Communications in Computer and Information Science - Knowledge Technology ◽

10.1007/978-3-642-32826-8_17 ◽

2012 ◽

pp. 164-173 ◽

Cited By ~ 2

Author(s):

Kamaluddeen Usman Danyaro ◽

Jafreezal Jaafar ◽

Mohd Shahir Liew

Keyword(s):

Knowledge Representation ◽

Description Logics ◽

Fuzzy Description Logics ◽

Fuzzy Description

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Knowledge Representation and Reasoning in Norm-Parameterized Fuzzy Description Logics

Canadian Semantic Web ◽

10.1007/978-1-4419-7335-1_2 ◽

2010 ◽

pp. 27-53 ◽

Cited By ~ 5

Author(s):

Jidi Zhao ◽

Harold Boley

Keyword(s):

Knowledge Representation ◽

Description Logics ◽

Knowledge Representation And Reasoning ◽

Fuzzy Description Logics ◽

Fuzzy Description

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An overview of fuzzy Description Logics for the Semantic Web

The Knowledge Engineering Review ◽

10.1017/s0269888912000306 ◽

2012 ◽

Vol 28 (1) ◽

pp. 1-34 ◽

Cited By ~ 9

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.

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CRISP REPRESENTATIONS AND REASONING FOR FUZZY ONTOLOGIES

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488509006121 ◽

2009 ◽

Vol 17 (04) ◽

pp. 501-530 ◽

Cited By ~ 33

Author(s):

FERNANDO BOBILLO ◽

MIGUEL DELGADO ◽

JUAN GÓMEZ-ROMERO

Keyword(s):

Knowledge Base ◽

Description Logics ◽

Membership Functions ◽

Logic Formula ◽

Fuzzy Concept ◽

Fuzzy Description Logics ◽

Fuzzy Language ◽

Representation Language ◽

Fuzzy Description ◽

Available Resources

Classical ontologies are not suitable to represent imprecise nor uncertain pieces of information. Fuzzy Description Logics were born to represent the former type of knowledge, but they require an appropriate fuzzy language to be agreed on and an important number of available resources to be adapted. This paper faces these problems by presenting a reasoning preserving procedure to obtain a crisp representation for a fuzzy extension of the logic [Formula: see text] which includes fuzzy nominals and trapezoidal membership functions, and uses Gödel implication in the semantics of fuzzy concept and role subsumption. This reduction makes it possible to reuse a crisp representation language as well as currently available reasoners. Our procedure is optimized with respect to related work, reducing the size of the resulting knowledge base. Finally, we also suggest some further optimizations before applying crisp reasoning.

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