## A crisp representation for fuzzy SHOIN with fuzzy nominals and general concept inclusions (2006)

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Venue: | IN PROC. OF THE 2ND INTERNATIONAL WORKSHOP ON UNCERTAINTY REASONING FOR THE SEMANTIC WEB (URSW 06 |

Citations: | 30 - 6 self |

### BibTeX

@INPROCEEDINGS{Bobillo06acrisp,

author = {Fernando Bobillo and Miguel Delgado and Juan Gómez-romero},

title = {A crisp representation for fuzzy SHOIN with fuzzy nominals and general concept inclusions},

booktitle = {IN PROC. OF THE 2ND INTERNATIONAL WORKSHOP ON UNCERTAINTY REASONING FOR THE SEMANTIC WEB (URSW 06},

year = {2006},

publisher = {}

}

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### Abstract

Fuzzy Description Logics are a family of logics which allow the representation of (and the reasoning within) structured knowledge affected by uncertainty and vagueness. They were born to overcome the limitations of classical Description Logics when dealing with such kind of knowledge, but they bring out some new challenges, requiring an appropriate fuzzy language to be agreed and needing practical and highly optimized implementations of the reasoning algorithms. In the current paper we face these problems by presenting a reasoning preserving procedure to obtain a crisp representation for a fuzzy extension of SHOIN, which makes possible to reuse a crisp representation language as well as currently available reasoners, which have demonstrated a very good performance in practice. As an additional contribution, we define the syntax and semantics of a novel fuzzy version of the nominal construct and allow to reason within fuzzy general concept inclusions.

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2633 | A translation approach to portable ontology specifications
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(Show Context)
Citation Context ...an additional contribution, we define the syntax and semantics of a novel fuzzy version of the nominal construct and allow to reason within fuzzy general concept inclusions. 1 Introduction Ontologies =-=[1]-=- are a core element in the layered architecture of the Semantic Web [2]. Description Logics (DLs for short) [3] are a family of logics for representing structured knowledge. The name of each logic is ... |

1899 | The semantic web - Berners-Lee - 2001 |

981 |
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(Show Context)
Citation Context ...in D I (a) = 1 or 1 − C I (a) ≥ 1 ⇒ C I (a) = 0. These problems point out the need of further investigation involving alternative fuzzy operators. For example, using a residuum based implication (see =-=[18]-=- for a refresh on fuzzy operators) it is always true that a → b = 1 if a ≤ b, which would fix the first problem; while using ̷Lukasiewicz implication (a → b = min{1, 1 − a + b}) would fix the second o... |

413 | RACER system description
- Haarslev, Möller
(Show Context)
Citation Context ...n the design of a decision procedure and the achievement of a practical implementation [9] (as a matter of fact, some of the OWL DL reasoners used in practice do not support full SHOIN (D) e.g. Racer =-=[10]-=- and FaCT [11]). Regarding fuzzy DLs, there does not exist any implemented reasoner for fSHOIN . A reasoner for fSHIF(D) has been recently developed (fuzzyDL 2 ), but its efficiency is still to be inv... |

268 |
Pellet: A practical OWL-DL reasoner
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(Show Context)
Citation Context ... fuzzy DLs to reasoning within crisp DLs. This way it would be possible to translate them automatically into a crisp ontology language (e.g. OWL) and to use currently available reasoners (e.g. Pellet =-=[12]-=-). Unfortunately, there does not exist a lot of work following this line and the logics investigated are still far from OWL DL: [13] shows a reasoning preserving procedure for fALCH, [14] considers fA... |

264 | Using an expressive description logic: FaCT or fiction
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(Show Context)
Citation Context ...f a decision procedure and the achievement of a practical implementation [9] (as a matter of fact, some of the OWL DL reasoners used in practice do not support full SHOIN (D) e.g. Racer [10] and FaCT =-=[11]-=-). Regarding fuzzy DLs, there does not exist any implemented reasoner for fSHOIN . A reasoner for fSHIF(D) has been recently developed (fuzzyDL 2 ), but its efficiency is still to be investigated. Mor... |

239 | The even more irresistible SROIQ
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- 2006
(Show Context)
Citation Context ...ed datatypes, it seems interesting to consider OWL Eu [20], a promising extension of OWL supporting them. Another interesting direction for future research is to consider the more expressive DL SROIQ =-=[21]-=- (providing some additional role constructs such as disjoint roles and negated role assertions) and which is the subjacent DL of OWL 1.1 4 , an extension of OWL which has been recently proposed. We th... |

209 | Reducing OWL entailment to description logic satisfiability
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(Show Context)
Citation Context ...L Web Ontology Language 1 , a language comprising three sublanguages of increasing expressive power: OWL Lite, OWL DL and OWL Full (being OWL DL the most used level and nearly equivalent to SHOIN (D) =-=[8]-=- but without customised datatypes). In order to deal with uncertain knowledge, OWL may be extended to a fuzzy DL-based language e.g. FuzzyOWL [6], with the drawback that the large number of resources ... |

165 | Reasoning within fuzzy description logics
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(Show Context)
Citation Context ...roles denote fuzzy binary relations between individuals. Our logic is similar to [5, 6], adding fuzzy nominals and fuzzy GCIs. In fuzzy DLs most reasoning services are reducible to fKB satisfiability =-=[16]-=-, so here in after we will only consider this task. Syntax. fSHOIN assumes three alphabets of symbols, for concepts, roles and individuals. The concepts of the language (denoted C or D) can be built i... |

156 | Terminological reasoning is inherently intractable
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(Show Context)
Citation Context ...iom into either an axiom or an assertion. This reduction in the size of the TBox (although it is still quadratic) is very interesting since reasoning with GCIs is a source of computational complexity =-=[19]-=-. Finally, an important theorem can be shown: Theorem 1. A fKDSHOIN fKB fK is satisfiable iff K(fK) is satisfiable. Unfortunately, we cannot show the proof due to space limitations. Firstly, it has to... |

147 | Description logics as ontology languages for the semantic web
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(Show Context)
Citation Context ...ogics for representing structured knowledge. The name of each logic is composed by some labels which identify the constructs of the logic. DLs have been proved to be very useful as ontology languages =-=[4]-=-. As it has been widely pointed out, classical ontologies and DLs are not appropriate to handle uncertain knowledge [5, 6] and since uncertainty is inherent to a lot of real-world application domains,... |

113 | Towards a fuzzy description logic for the semantic web
- Straccia
- 2004
(Show Context)
Citation Context ...ructs of the logic. DLs have been proved to be very useful as ontology languages [4]. As it has been widely pointed out, classical ontologies and DLs are not appropriate to handle uncertain knowledge =-=[5, 6]-=- and since uncertainty is inherent to a lot of real-world application domains, the Semantic Web will not be fully operative as long as it does not provide means to manage it. A well studied solution i... |

55 | A fuzzy description logic, in
- Straccia
- 1998
(Show Context)
Citation Context ...common to use the Kleene-Dienes implication in the semantics of universal quantification, so for the sake of coherence we have chosen to use it in the semantics of fuzzy GCIs as well. Similarly as in =-=[17]-=-, fKDSHOIN allows some sort of modus ponens over concepts and roles, even with the new semantics of fuzzy GCIs: Lemma 2. For α, β, γ ∈ [0, 1], ⊲⊳ = {≥, >} and α +⊲⊳ 1 − β (+≥ = >, +> = ≥), the followi... |

47 | Transforming fuzzy description logics into classical description logics, in
- Straccia
- 2004
(Show Context)
Citation Context ...ge (e.g. OWL) and to use currently available reasoners (e.g. Pellet [12]). Unfortunately, there does not exist a lot of work following this line and the logics investigated are still far from OWL DL: =-=[13]-=- shows a reasoning preserving procedure for fALCH, [14] considers fALC with truth values taken from an uncertainty lattice and [15], a restricted version of fALCQ (e.g. they do not allow to reason wit... |

41 | Fuzzy OWL: uncertainty and the semantic web
- Stoilos, Stamou, et al.
- 2005
(Show Context)
Citation Context ...ructs of the logic. DLs have been proved to be very useful as ontology languages [4]. As it has been widely pointed out, classical ontologies and DLs are not appropriate to handle uncertain knowledge =-=[5, 6]-=- and since uncertainty is inherent to a lot of real-world application domains, the Semantic Web will not be fully operative as long as it does not provide means to manage it. A well studied solution i... |

38 |
P.F.: The Description Logic Handbook: Theory, Implementation and Application
- Baader, Calvanese, et al.
- 2003
(Show Context)
Citation Context ...t and allow to reason within fuzzy general concept inclusions. 1 Introduction Ontologies [1] are a core element in the layered architecture of the Semantic Web [2]. Description Logics (DLs for short) =-=[3]-=- are a family of logics for representing structured knowledge. The name of each logic is composed by some labels which identify the constructs of the logic. DLs have been proved to be very useful as o... |

37 | OWL-Eu: Adding customised datatypes into OWL
- Pan, Horrocks
- 2006
(Show Context)
Citation Context ...eene-Dienes implication. We also plan to include a crisp representation for fuzzy datatypes. Since OWL does not currently allow to define customised datatypes, it seems interesting to consider OWL Eu =-=[20]-=-, a promising extension of OWL supporting them. Another interesting direction for future research is to consider the more expressive DL SROIQ [21] (providing some additional role constructs such as di... |

21 | From Wine to Water: Optimizing Description Logic Reasoning for Nominals
- Sirin, Grau, et al.
(Show Context)
Citation Context ...ery high worst-case complexity (e.g. NExpTime in SHOIN ) and, consequently, there exists a significant gap between the design of a decision procedure and the achievement of a practical implementation =-=[9]-=- (as a matter of fact, some of the OWL DL reasoners used in practice do not support full SHOIN (D) e.g. Racer [10] and FaCT [11]). Regarding fuzzy DLs, there does not exist any implemented reasoner fo... |

10 | Description logics over lattices - Straccia - 2006 |

7 |
Reasoning technique for extended fuzzy ALCQ, in
- Li, Xu, et al.
- 2006
(Show Context)
Citation Context ...ing this line and the logics investigated are still far from OWL DL: [13] shows a reasoning preserving procedure for fALCH, [14] considers fALC with truth values taken from an uncertainty lattice and =-=[15]-=-, a restricted version of fALCQ (e.g. they do not allow to reason within a TBox). On the other hand, current fuzzy DLs still present some limitations which we think that should be overcome. Some works... |