## A Generic Framework For Description Logics With Uncertainty (2005)

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Venue: | In Proceedings of the 2005 Workshop on Uncertainty Reasoning for the Semantic Web at the 4th International Semantic Web Conference |

Citations: | 6 - 4 self |

### BibTeX

@INPROCEEDINGS{Haarslev05ageneric,

author = {Volker Haarslev and Hsueh-ieng Pai and Nematollaah Shiri},

title = {A Generic Framework For Description Logics With Uncertainty},

booktitle = {In Proceedings of the 2005 Workshop on Uncertainty Reasoning for the Semantic Web at the 4th International Semantic Web Conference},

year = {2005},

pages = {77--86}

}

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### Abstract

Abstract. We propose an extension to Description Logics (DLs) with uncertainty which unifies and/or generalizes a number of existing frameworks for DLs with uncertainty. To this end, we first give a classification of these frameworks and identify the essential features as well as properties of the various combination functions allowed in the underlying uncertainty formalisms they model. This also allows us express the semantics of the DL elements in a flexible manner. We illustrate how various DLs with uncertainty can be expressed in our generic framework. 1

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Citation Context ... uncertainty modeled, we can classify existing proposals of DLs with uncertainty into three approaches: fuzzy, probabilistic, and possibilistic approach. The fuzzy approach, based on fuzzy set theory =-=[19]-=-, deals with the vagueness in the knowledge, where a proposition is true to only some degree. For example, the statement “Jason is obese with degree 0.4” indicates Jason is slightly obese. Here, the v... |

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Citation Context ...xample, one could state that: “The probability that Jason would have heart disease given that he is obese lies in the range [0.8, 1].” Finally, the possibilistic approach, based on possibility theory =-=[20]-=-, allows both certainty (necessity measure) and possibility (possibility measure) be handled in the same formalism. For example, by knowing that “Jason’s weight is above 80 Kg”, the proposition “Jason... |

165 | Reasoning within fuzzy description logics
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Citation Context ...certainty lattice as L = 〈V, ≤〉, where V = C[0, 1] is the set of closed intervals [α, β] in [0, 1] such that α � β. The negation operator in this case is defined as ∼([a1, a2]) = [1 − a2, 1 − a1]. In =-=[5, 13, 15, 16, 18]-=-, the meet operator is inf (infimum) and the join operator is sup (supremum). On the other hand, [17] uses min as the meet operator, and max as the join. The conjunction function used in all these pro... |

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Citation Context ...− a2, 1 − a1]. Note that this allows us to express both interval probability (such as [0.4, 0.8]) and exact probability (e.g., [0.8, 0.8]). Currently existing probabilistic extensions to DLs, such as =-=[3, 4, 7, 8]-=-, support mainly conditional constraints. In the generic framework, we view a rule as a conditional statement. As such, let α be some value from the certainty lattice, a conditional constraint of the ... |

78 | Probabilistic reasoning in terminological logics
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Citation Context ...− a2, 1 − a1]. Note that this allows us to express both interval probability (such as [0.4, 0.8]) and exact probability (e.g., [0.8, 0.8]). Currently existing probabilistic extensions to DLs, such as =-=[3, 4, 7, 8]-=-, support mainly conditional constraints. In the generic framework, we view a rule as a conditional statement. As such, let α be some value from the certainty lattice, a conditional constraint of the ... |

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Citation Context ...certainty lattice as L = 〈V, ≤〉, where V = C[0, 1] is the set of closed intervals [α, β] in [0, 1] such that α � β. The negation operator in this case is defined as ∼([a1, a2]) = [1 − a2, 1 − a1]. In =-=[5, 13, 15, 16, 18]-=-, the meet operator is inf (infimum) and the join operator is sup (supremum). On the other hand, [17] uses min as the meet operator, and max as the join. The conjunction function used in all these pro... |

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Citation Context ...e. Hence, although our framework can easily handle simple probabilities, such as independent events and mutually exclusive events, more complex probability modes such as positive/negative correlation =-=[9]-=-, ignorance [9], and conditional independence [14] are still under investigation. Example 4 (Possibilistic DL). Hollunder [6] is the only proposal that gives a possibilistic extension to DL. Here, the... |

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Citation Context ...od compromise between expressive power and computational tractability. Uncertainty management has been a challenge for over two decades in database (DB) and artificial intelligence (AI) research (see =-=[10, 12]-=-), and has recently attracted the attention of the DL community. Uncertainty is a form of deficiency or imperfection commonly found in the real-world information/data. A piece of information is uncert... |

47 | A parametric approach to deductive databases with uncertainty
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Citation Context ... different applications may require using different aspects. It may even be desired in some cases to model different aspects within the same application. Following the parametric approach proposed in =-=[11]-=-, we propose a generic DL framework with uncertainty in this paper as a unifying umbrella for several existing frameworks for DLs with uncertainty. This not only provides a uniform access over knowled... |

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Citation Context ...certainty lattice as L = 〈V, ≤〉, where V = C[0, 1] is the set of closed intervals [α, β] in [0, 1] such that α � β. The negation operator in this case is defined as ∼([a1, a2]) = [1 − a2, 1 − a1]. In =-=[5, 13, 15, 16, 18]-=-, the meet operator is inf (infimum) and the join operator is sup (supremum). On the other hand, [17] uses min as the meet operator, and max as the join. The conjunction function used in all these pro... |

40 |
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Citation Context ...e simple probabilities, such as independent events and mutually exclusive events, more complex probability modes such as positive/negative correlation [9], ignorance [9], and conditional independence =-=[14]-=- are still under investigation. Example 4 (Possibilistic DL). Hollunder [6] is the only proposal that gives a possibilistic extension to DL. Here, the possibility (Π) and necessity (N) degrees can be ... |

35 |
An alternative proof method for possibilistic logic and its application to terminological logics
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(Show Context)
Citation Context ...ents, more complex probability modes such as positive/negative correlation [9], ignorance [9], and conditional independence [14] are still under investigation. Example 4 (Possibilistic DL). Hollunder =-=[6]-=- is the only proposal that gives a possibilistic extension to DL. Here, the possibility (Π) and necessity (N) degrees can be represented by the certainty lattice L = 〈V, ≤〉, where V = C[0, 1], with ne... |

33 |
A Bayesian Approach to Uncertainty Modeling
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(Show Context)
Citation Context ...− a2, 1 − a1]. Note that this allows us to express both interval probability (such as [0.4, 0.8]) and exact probability (e.g., [0.8, 0.8]). Currently existing probabilistic extensions to DLs, such as =-=[3, 4, 7, 8]-=-, support mainly conditional constraints. In the generic framework, we view a rule as a conditional statement. As such, let α be some value from the certainty lattice, a conditional constraint of the ... |

26 | Generalizing quantification in fuzzy description logics
- Sánchez, Tettamanzi
- 2004
(Show Context)
Citation Context |

25 | A fuzzy description logic with hedges as concept modifiers
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Citation Context |

22 |
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(Show Context)
Citation Context |

4 |
Logic programming and deductive databases with uncertainty: A survey
- Lakshmanan, Shiri
- 2001
(Show Context)
Citation Context ...od compromise between expressive power and computational tractability. Uncertainty management has been a challenge for over two decades in database (DB) and artificial intelligence (AI) research (see =-=[10, 12]-=-), and has recently attracted the attention of the DL community. Uncertainty is a form of deficiency or imperfection commonly found in the real-world information/data. A piece of information is uncert... |

1 |
A fuzzy description logic
- Stracia
- 1998
(Show Context)
Citation Context ...The negation operator in this case is defined as ∼([a1, a2]) = [1 − a2, 1 − a1]. In [5, 13, 15, 16, 18], the meet operator is inf (infimum) and the join operator is sup (supremum). On the other hand, =-=[17]-=- uses min as the meet operator, and max as the join. The conjunction function used in all these proposals is min, whereas the disjunction function uses max. Note that existing proposals rarely allow c... |