## The fuzzy description logic f-SHIN (2005)

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Venue: | Proc. of the International Workshop on Uncertainty Reasoning for the Semantic Web |

Citations: | 37 - 10 self |

### BibTeX

@INPROCEEDINGS{Stoilos05thefuzzy,

author = {Giorgos Stoilos and Giorgos Stamou and Vassilis Tzouvaras and Jeff Z. Pan and Ian Horrocks},

title = {The fuzzy description logic f-SHIN},

booktitle = {Proc. of the International Workshop on Uncertainty Reasoning for the Semantic Web},

year = {2005}

}

### Years of Citing Articles

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### Abstract

Abstract. In the Semantic Web information would be retrieved, processed, combined, shared and reused in the maximum automatic way possible. Obviously, such procedures involve a high degree of uncertainty and imprecision. For example ontology alignment or information retrieval are rarely true or false procedures but usually involve confidence degrees or provide rankings. Furthermore, it is often the case that information itself is imprecise and vague like the concept of a “tall ” person, a “hot” place and many more. In order to be able to represent and reason with such type of information in the Semantic Web (SW), as well as, enhance SW applications we present an extension of the Description Logic SHIN with fuzzy set theory. We present the semantics as well as detailed reasoning algorithms for the extended language. 1

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Citation Context ...al with such type of information, resulting in the improvement of their effectiveness. Applications like robotics [1], computer vision [2] and many more have embraced frameworks like fuzzy set theory =-=[3]-=- in order to improve their performance. On the other hand, in the Semantic Web context, little work has been carried out towards this direction. Apart from the fact that uncertainty is many times a fe... |

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328 | Practical reasoning for expressive description logics - Horrocks, Tobies |

161 | Reasoning within fuzzy description logics
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(Show Context)
Citation Context ...f f-SHIN and present a detailed procedure to reason with the extended language. 2 Syntax and Semantics of f-SHIN In this section we introduce the DL f-SHIN . As pointed out in the fuzzy DL literature =-=[9,14]-=-, fuzzy extensions of DLs involve only the assertion of individuals to concepts and the semantics of the new language. Hence, as usual we have an alphabet of distinct concept names (C), role names (R)... |

147 | Ontology reasoning in the SHOQ(D) description logic - Horrocks, Sattler |

141 | Reasoning with individuals for the description logic SHIQ
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(Show Context)
Citation Context ...theory. In the current paper we extend the results obtained in [9] for fuzzy SI (f-SI) to the language SHIN , thus creating f-SHIN . SHIN extends SI [12] with number restrictions and role hierarchies =-=[13]-=-. Number restrictions give us the ability to restrict the number of objects that a certain object is related to by a specific relation. For example we can state that a car has exactly four wheels, wri... |

124 | A description logic with transitive and inverse roles and role hierarchies
- Horrocks, Sattler
- 1999
(Show Context)
Citation Context ...nformation. One such important theory is fuzzy set theory. In the current paper we extend the results obtained in [9] for fuzzy SI (f-SI) to the language SHIN , thus creating f-SHIN . SHIN extends SI =-=[12]-=- with number restrictions and role hierarchies [13]. Number restrictions give us the ability to restrict the number of objects that a certain object is related to by a specific relation. For example w... |

112 | A fuzzy description logic for the semantic web
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(Show Context)
Citation Context ...b)=max(a,b)) and the Kleen-Dienes fuzzy implication (J (a,b)=max(1-a,b)) are used for performing the fuzzy set theoretic operations. The semantics of fuzzy number restrictions were first presented in =-=[17]-=-. We chose to follow these semantics because, as pointed out in [17], they are derived by the First-Order formulae of classical number restrictions [17]. In [9] the naming fKD-SI was used due to the u... |

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Citation Context ...appear within an ABox is denoted by sub(A). Since the De’Morgan laws are satisfied by the operations we use in the current paper [3] all concepts are assumed to be in their negation normal form (NNF) =-=[18]-=-. In the following we use the symbols ⊲ and ⊳ as a placeholder for the inequalities ≥, > and ≤, < and the symbol ⊲⊳ as a placeholder for all types of inequations. Furthermore we use the symbols ⊲⊳ − ,... |

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Citation Context ... algorithm was provided in order to perform reasoning. The DL language used was a sub-language of the basic DL ALC. Reasoning in fuzzy ALC was latter presented in [14], as well as in other approaches =-=[20, 21]-=-, where an additional concept constructor, called membership manipulator was included in the extended language. In all these approaches tableaux decision procedures were presented for performing reaso... |

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Citation Context ...e and clash-free completion forest. 4 Related Work Much work has been carried out towards combining fuzzy logic and description logics during the last decade. The initial idea was presented by Yen in =-=[19]-=-, where a structural subsumption algorithm was provided in order to perform reasoning. The DL language used was a sub-language of the basic DL ALC. Reasoning in fuzzy ALC was latter presented in [14],... |

25 | A Fuzzy Description Logic for Multimedia Knowledge Representation
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(Show Context)
Citation Context ...nformation we have to extend them with a theory capable of representing this kind of information. One such important theory is fuzzy set theory. In the current paper we extend the results obtained in =-=[9]-=- for fuzzy SI (f-SI) to the language SHIN , thus creating f-SHIN . SHIN extends SI [12] with number restrictions and role hierarchies [13]. Number restrictions give us the ability to restrict the numb... |

25 | Generalizing quantification in fuzzy description logics
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Citation Context ...nfimum and sup for the supremum of a set. Note that apart from thefuzzy number restrictions, the interpretation of fuzzy concepts and concept constructors is the usual one found in the DL literature =-=[9,14,16]-=-, where the Gödel conjunction (t(a,b)=min(a,b)), the Gödel disjunction (u(a,b)=max(a,b)) and the Kleen-Dienes fuzzy implication (J (a,b)=max(1-a,b)) are used for performing the fuzzy set theoretic ope... |

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(Show Context)
Citation Context ... algorithm was provided in order to perform reasoning. The DL language used was a sub-language of the basic DL ALC. Reasoning in fuzzy ALC was latter presented in [14], as well as in other approaches =-=[20, 21]-=-, where an additional concept constructor, called membership manipulator was included in the extended language. In all these approaches tableaux decision procedures were presented for performing reaso... |

22 | An enhanced model for searching in semantic portals - Zhang, Yu, et al. - 2005 |

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Citation Context ...ons and domains have incorporated mathematical frameworks that deal with such type of information, resulting in the improvement of their effectiveness. Applications like robotics [1], computer vision =-=[2]-=- and many more have embraced frameworks like fuzzy set theory [3] in order to improve their performance. On the other hand, in the Semantic Web context, little work has been carried out towards this d... |

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Citation Context ...s end, many applications and domains have incorporated mathematical frameworks that deal with such type of information, resulting in the improvement of their effectiveness. Applications like robotics =-=[1]-=-, computer vision [2] and many more have embraced frameworks like fuzzy set theory [3] in order to improve their performance. On the other hand, in the Semantic Web context, little work has been carri... |

3 | I.: A fuzzy extension of swrl - Stamou, Tzouvaras, et al. - 2005 |