## A Fuzzy Description Logic (1998)

Venue: | In Proc. of the 15th Nat. Conf. on Artificial Intelligence (AAAI-98 |

Citations: | 51 - 9 self |

### BibTeX

@INPROCEEDINGS{Straccia98afuzzy,

author = {Umberto Straccia and Via S. Maria},

title = {A Fuzzy Description Logic},

booktitle = {In Proc. of the 15th Nat. Conf. on Artificial Intelligence (AAAI-98},

year = {1998},

pages = {594--599}

}

### Years of Citing Articles

### OpenURL

### Abstract

Description Logics (DLs, for short) allow reasoning about individuals and concepts, i.e. set of individuals with common properties. Typically, DLs are limited to dealing with crisp, well defined concepts. That is, concepts for which the problem whether an individual is an instance of it is a yes/no question. More often than not, the concepts encountered in the real world do not have a precisely defined criteria of membership: we may say that an individual is an instance of a concept only to a certain degree, depending on the individual's properties. Concepts of this kind are rather vague than precise. As fuzzy logic directly deals with the notion of vagueness and imprecision, it o#ers an appealing foundation for a generalisation of DLs to vague concepts. In this paper we present a general fuzzy DL, which combines fuzzy logic with DLs. We define its syntax, semantics and present constraint propagation calculi for reasoning in it. Introduction Description Logics (DLs, for short) provide...

### Citations

265 | A Schema for Integrating Concrete Domains into Concept Languages
- Baader, Hanschke
- 1991
(Show Context)
Citation Context ...,sf i are features (i.e. functional roles) and A is a fuzzy membership function defined on a concrete domains(called universe of discourse in (Yen 1991)) such that A depends on the features f i (see (=-=Baader & Hanschke 1991-=-) for the formal aspects about concrete domains) . For instance, the concept Tall could be defined as Tall =sTall (height), wheresTall is defined as a lambda abstraction on reals such that it relies o... |

230 | On the hardness of approximate reasoning
- Roth
- 1996
(Show Context)
Citation Context ...ut individuals and vague concepts. Moreover, reasoning in a probabilistic framework is generally a harder task, from a computational point of view, than the relative non probabilistic case (see e.g. (=-=Roth 1996-=-) for an overview) and thus, the computational problems have to be addressed carefully like in (Koller, Levy, & Pfe#er 1997). In the following sections we first introduce crisp ALC, then we extend it ... |

187 | The tractability of subsumption in frame-based description languages
- Brachman, Levesque
- 1984
(Show Context)
Citation Context ...mbership degree of individual a being an instance of concept C is at least n". Extending DLs with fuzzy features has already be done in the past. For instance, in (Yen 1991) the very limited DL F=-=L - (Brachman & Levesque 1984-=-) has been extended with some fuzzy features. In particular, it allows the definition of fuzzy concepts and the only supported reasoning mechanism is determining subsumption 2 . Unfortunately, it does... |

187 | Decidable reasoning in terminological knowledge representation systems - Buchheit, Donini, et al. - 1993 |

148 |
Attributive concept descriptions with complements
- Schmidt-Schau, Smolka
- 1991
(Show Context)
Citation Context ...omplexity point of view, it is easily verified that termination of the above algorithm is guaranteed. Moreover, from Proposition 2 and from PSPACE-completeness of the entailment problem in crisp ALC (=-=Schmidt-Schau & Smolka 1991-=-), PSPACEhardness of the fuzzy entailment problem follows. It can be verified that trace rules as in (Schmidt-Schau & Smolka 1991) can be defined. Therefore, Proposition 5 Let # be a fuzzy KB and and ... |

107 | P-classic: A tractable probabilistic description logic - Koller, Levy, et al. - 1997 |

82 |
Fuzzy Sets and Systems
- Dubois, Prade
- 1980
(Show Context)
Citation Context ...r.t. the # connective, (#R.C) I (d) is the result of viewing #R.C as the first order formula 5 Other membership functions have been proposed in the literature. The interested reader can consult e.g. (=-=Dubois & Prade 1980-=-; Kundu & Chen 1994). #y.R(x, y) # C(y), where F # G is F # G 6 and the universal quantifier # is viewed as a conjunction over the elements of the domain. Similarly, for the # connective (#R.C) I (d) ... |

69 |
Probabilistic description logics
- Heinsohn
- 1994
(Show Context)
Citation Context ...nd expressive power of DLs contributes to their popularity. Finally, note that most existing work in extending DLs for uncertainty management lie in the category of probabilistic extension like e.g. (=-=Heinsohn 1994-=-; Jager 1994; Koller, Levy, & Pfe#er 1997) with some exceptions like (Hollunder 1994). Even though these 2 Roughly, a concept D subsumes a concept C i# from a first order point of view, #x.C(x) # D(x)... |

55 |
Generalizing term subsumption languages to fuzzy logic
- Yen
- 1991
(Show Context)
Citation Context ...) .7#, with intended meaning "the membership degree of individual a being an instance of concept C is at least n". Extending DLs with fuzzy features has already be done in the past. For inst=-=ance, in (Yen 1991-=-) the very limited DL FL - (Brachman & Levesque 1984) has been extended with some fuzzy features. In particular, it allows the definition of fuzzy concepts and the only supported reasoning mechanism i... |

52 |
Fuzzy logic and the resolution principle
- LEE
- 1972
(Show Context)
Citation Context ...ilarly, for the # connective (#R.C) I (d) is the result of viewing #R.C as #y.R(x, y) # C(y), where the existential quantifier # is considered a disjunction over the elements of the domain (see e.g. (=-=Lee 1972-=-)). It is easily verified that for all interpretations I and individuals d # # I , ((C # D)) I (d) = (C # D) I (d) and ((#R.C)) I (d) = (#R.C) I (d). An interpretation I satisfies a fuzzy assertion #C... |

33 |
An alternative proof method for possibilistic logic and its application to terminological logics
- Hollunder
- 1995
(Show Context)
Citation Context ... existing work in extending DLs for uncertainty management lie in the category of probabilistic extension like e.g. (Heinsohn 1994; Jager 1994; Koller, Levy, & Pfe#er 1997) with some exceptions like (=-=Hollunder 1994-=-). Even though these 2 Roughly, a concept D subsumes a concept C i# from a first order point of view, #x.C(x) # D(x) is logically valid. 3 The idea to use DLs in the context of multimedia document ret... |

24 | Describing and Classifying Multimedia Using the Description Logic GRAIL - Goble, Haul, et al. - 1996 |

12 |
A sound and complete fuzzy logic system using Zadeh’s implication operator
- Chen, Kundu
- 1996
(Show Context)
Citation Context ... constraint propagation method, as this method is usually proposed in the context of DLs (see, e.g. (Buchheit, Donini, & Schaerf 1993)). The calculus extends the propositional framework described in (=-=Chen & Kundu 1996-=-) to the DL case. Consider a new alphabet of variables. An Interpretation is extended to variables by mapping these into elements of the interpretation domain. An objects(written w) is either an indiv... |

9 | Reasoning about the form and content for multimedia objects (extended abstract - Meghini, Sebastiani, et al. - 1997 |

7 |
Probabilistic reasoning in terminological logics
- Jäger
- 1994
(Show Context)
Citation Context ...ower of DLs contributes to their popularity. Finally, note that most existing work in extending DLs for uncertainty management lie in the category of probabilistic extension like e.g. (Heinsohn 1994; =-=Jager 1994-=-; Koller, Levy, & Pfe#er 1997) with some exceptions like (Hollunder 1994). Even though these 2 Roughly, a concept D subsumes a concept C i# from a first order point of view, #x.C(x) # D(x) is logicall... |

5 | A four-valued fuzzy propositional logic
- Straccia
- 1997
(Show Context)
Citation Context ...ion of fuzzy concepts and the only supported reasoning mechanism is determining subsumption 2 . Unfortunately, it does not allow reasoning in presence of assertions. Recently, (Meghini, Sebastiani, & =-=Straccia 1997-=-) proposed a fuzzy DL as a tool for modelling multimedia document retrieval 3 . But this work was rather at a preliminary stage and no reasoning algorithm was given. We present a more general framewor... |

3 |
Fuzzy logic or Lukasiewicz logic: A clarification
- KUNDU, CHEN
- 1994
(Show Context)
Citation Context ..., (#R.C) I (d) is the result of viewing #R.C as the first order formula 5 Other membership functions have been proposed in the literature. The interested reader can consult e.g. (Dubois & Prade 1980; =-=Kundu & Chen 1994-=-). #y.R(x, y) # C(y), where F # G is F # G 6 and the universal quantifier # is viewed as a conjunction over the elements of the domain. Similarly, for the # connective (#R.C) I (d) is the result of vi... |