## Reasoning within Fuzzy Description Logics (2001)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 150 - 21 self |

### BibTeX

@ARTICLE{Straccia01reasoningwithin,

author = {Umberto Straccia},

title = {Reasoning within Fuzzy Description Logics},

journal = {Journal of Artificial Intelligence Research},

year = {2001},

volume = {14},

pages = {2001}

}

### Years of Citing Articles

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### Abstract

Description Logics (DLs) are suitable, well-known, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e. set of individuals with common properties. The experience in using DLs in applications has shown that in many cases we would like to extend their capabilities. In particular, their use in the context of Multimedia Information Retrieval (MIR) leads to the convincement that such DLs should allow the treatment of the inherent imprecision in multimedia object content representation and retrieval. In this paper we will present a fuzzy extension of ALC, combining...

### Citations

271 | An analysis of first-order logics of probability
- Halpern
- 1990
(Show Context)
Citation Context ...reasoning in a probabilistic framework is generally a harder task, from a computational point of view, than the relative non probabilistic case and in most cases a complete axiomatization is missing (=-=Halpern, 1990-=-; Roth, 1996). As a consequence, the computational problems have to be addressed carefully (Koller et al., 1997). We will proceed as follows. In the following section we first introduce ALC. In Sectio... |

251 | Using an expressive description logic: FaCT or fiction
- Horrocks
- 1998
(Show Context)
Citation Context ...r expressiveness, their complexity and the completeness of their algorithms, and they have been used for building a variety of applications (Peltason, 1991; Brachman, 1992; Baader & Hollunder, 1991a; =-=Horrocks, 1998-=-). Experience in using DLs in applications has also shown that in many cases we would like to extend the representational and reasoning capabilities of them. In particular, the use of DLs in the conte... |

250 |
Representing and reasoning with probabilistic knowledge
- Bacchus
- 1990
(Show Context)
Citation Context ...n). An impressive work has been carried out in the last decades, resulting in a number of concepts being investigated, a number of problems being identified and a number of solutions being developed (=-=Bacchus, 1990-=-; Dubois & Prade, 1996; Kruse, Schwecke, & Heinsohn, 1991; Pearl, 1988). For most knowledge representation formalisms, First-Order Logic (FOL) has been the basis: its basic units –individuals, their p... |

185 | Decidable reasoning in terminological knowledge representation systems
- Buchheit, Donini, et al.
- 1993
(Show Context)
Citation Context ...tailment problem; the problem of determining whether C ⊑KT D is called subsumption problem; and the problem of determining whether K is satisfiable is called satisfiability problem. It is well known (=-=Buchheit, Donini, & Schaerf, 1993-=-a; Donini, Lenzerini, Nardi, & Schaerf, 1994; Nebel, 1990) that in ALC K |= (a, b):R iff (a, b):R ∈ K (10) K |= a:C iff K ∪{a:¬C} is not satisfiable (11) C ⊑ ∅ D iff a:C |= a:D, for a new a (12) C ⊑KT... |

95 | A terminological knowledge representation system with complete inference algorithms
- Baader, Hollunder
- 1991
(Show Context)
Citation Context ...differ with respect to their expressiveness, their complexity and the completeness of their algorithms, and they have been used for building a variety of applications (Peltason, 1991; Brachman, 1992; =-=Baader & Hollunder, 1991-=-a; Horrocks, 1998). Experience in using DLs in applications has also shown that in many cases we would like to extend the representational and reasoning capabilities of them. In particular, the use of... |

79 | Deduction in concept languages: From subsumption to instance checking
- Donini, Lenzerini, et al.
- 1994
(Show Context)
Citation Context ...ermining whether C ⊑KT D is called subsumption problem; and the problem of determining whether K is satisfiable is called satisfiability problem. It is well known (Buchheit, Donini, & Schaerf, 1993a; =-=Donini, Lenzerini, Nardi, & Schaerf, 1994-=-; Nebel, 1990) that in ALC K |= (a, b):R iff (a, b):R ∈ K (10) K |= a:C iff K ∪{a:¬C} is not satisfiable (11) C ⊑ ∅ D iff a:C |= a:D, for a new a (12) C ⊑KT D iff C′ ⊑ ∅ D ′ (13) and substituting ever... |

77 |
an d P ra d e, H ., Fuzzy Sets and Systems
- Dubois
- 1980
(Show Context)
Citation Context ...he complement of S1 in U. Alternative restrictions on membership functions have been proposed in the literature, but it is not our aim to investigate them here (the interested reader may consult e.g. =-=Dubois & Prade, 1980-=-). A justification of the choice of the min and the max was given by Bellman and Giertz (1973), which have shown that under certain reasonable conditions min and max are the unique possible choice for... |

68 |
Probabilistic description logics
- HEINSOHN
- 1994
(Show Context)
Citation Context ...s to their popularity. Note that our fuzzy extension for the management of imprecise knowledge is complementary to other DL extensions for the management of uncertainty, e.g. probabilistic extension (=-=Heinsohn, 1994-=-; Jäger, 1994; Koller, Levy, & Pfeffer, 1997; Sebastiani, 1994) with some exceptions like shown by Hollunder (1994) where a possibilistic DL has been considered. Even 138Reasoning within Fuzzy DLs th... |

52 |
Fuzzy logic and the resolution principle
- LEE
- 1972
(Show Context)
Citation Context ... this sentence has truth-value 0.8, i.e. r is likely about a Ferrari; • from a proof theoretical point of view, as there exist well-known techniques for reasoning in fuzzy logics (Chen & Kundu, 1996; =-=Lee, 1972-=-; Xiachun, Yunfei, & Xuhua, 1995). In the following we will present a quite general fuzzy DL, in the sense that it is based on the DL ALC, a significant and expressive representative of the various DL... |

49 |
Uncertainty and Vagueness in Knowledge Based Systems Ů Numerical Methods
- Kruse, Schwecke
- 1991
(Show Context)
Citation Context ...ed out in the last decades, resulting in a number of concepts being investigated, a number of problems being identified and a number of solutions being developed (Bacchus, 1990; Dubois & Prade, 1996; =-=Kruse, Schwecke, & Heinsohn, 1991-=-; Pearl, 1988). For most knowledge representation formalisms, First-Order Logic (FOL) has been the basis: its basic units –individuals, their properties, and the relationship between them– naturally c... |

45 | Reducing” CLASSIC to practice: Knowledge representation meets reality
- Brachman
- 1992
(Show Context)
Citation Context ...sing DLs, which differ with respect to their expressiveness, their complexity and the completeness of their algorithms, and they have been used for building a variety of applications (Peltason, 1991; =-=Brachman, 1992-=-; Baader & Hollunder, 1991a; Horrocks, 1998). Experience in using DLs in applications has also shown that in many cases we would like to extend the representational and reasoning capabilities of them.... |

38 | On the analytic formalism of theory of fuzzy set - Bellman, Giertz - 1973 |

35 |
KRIS: Knowledge representation and inference system—System description
- BAADER, HOLLUNDER
- 1991
(Show Context)
Citation Context ...differ with respect to their expressiveness, their complexity and the completeness of their algorithms, and they have been used for building a variety of applications (Peltason, 1991; Brachman, 1992; =-=Baader & Hollunder, 1991-=-a; Horrocks, 1998). Experience in using DLs in applications has also shown that in many cases we would like to extend the representational and reasoning capabilities of them. In particular, the use of... |

32 | An alternative proof method for possibilistic logic and its application to terminological logics - Hollunder - 1994 |

18 | Prade: Can we enforce full compositionality in uncertainty calculi
- Dubois, H
(Show Context)
Citation Context ...istic extensions enlarge the applicability of DLs they do not address the issue of reasoning about individuals and imprecise concepts, as imprecise knowledge and uncertain knowledge are “orthogonal” (=-=Dubois & Prade, 1994-=-). Moreover, reasoning in a probabilistic framework is generally a harder task, from a computational point of view, than the relative non probabilistic case and in most cases a complete axiomatization... |

12 |
A sound and complete fuzzy logic system using Zadeh’s implication operator
- Chen, Kundu
- 1996
(Show Context)
Citation Context ...” and establish that this sentence has truth-value 0.8, i.e. r is likely about a Ferrari; • from a proof theoretical point of view, as there exist well-known techniques for reasoning in fuzzy logics (=-=Chen & Kundu, 1996-=-; Lee, 1972; Xiachun, Yunfei, & Xuhua, 1995). In the following we will present a quite general fuzzy DL, in the sense that it is based on the DL ALC, a significant and expressive representative of the... |

8 |
Approximate and Commonsense Reasoning: From Theory to Practice
- Dubois, Prade
- 1996
(Show Context)
Citation Context ...ve work has been carried out in the last decades, resulting in a number of concepts being investigated, a number of problems being identified and a number of solutions being developed (Bacchus, 1990; =-=Dubois & Prade, 1996-=-; Kruse, Schwecke, & Heinsohn, 1991; Pearl, 1988). For most knowledge representation formalisms, First-Order Logic (FOL) has been the basis: its basic units –individuals, their properties, and the rel... |

7 |
Probabilistic reasoning in terminological logics
- Jäger
- 1994
(Show Context)
Citation Context ...arity. Note that our fuzzy extension for the management of imprecise knowledge is complementary to other DL extensions for the management of uncertainty, e.g. probabilistic extension (Heinsohn, 1994; =-=Jäger, 1994-=-; Koller, Levy, & Pfeffer, 1997; Sebastiani, 1994) with some exceptions like shown by Hollunder (1994) where a possibilistic DL has been considered. Even 138Reasoning within Fuzzy DLs though these pr... |

5 | A system of knowledge representation based on formulae of predicate calculus whose variables are annotated by expressions of a fuzzy terminological logic - Silva, Pereira, et al. - 1994 |

1 |
164 within Fuzzy DLs
- Koller, Levy, et al.
- 1997
(Show Context)
Citation Context ...hat our fuzzy extension for the management of imprecise knowledge is complementary to other DL extensions for the management of uncertainty, e.g. probabilistic extension (Heinsohn, 1994; Jäger, 1994; =-=Koller, Levy, & Pfeffer, 1997-=-; Sebastiani, 1994) with some exceptions like shown by Hollunder (1994) where a possibilistic DL has been considered. Even 138Reasoning within Fuzzy DLs though these probabilistic extensions enlarge ... |