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## 1Measuring Inconsistency in Fuzzy Answer Set Semantics

### Citations

1847 | The Stable Model Semantics for Logic Programming
- Gelfond, Lifschitz
- 1988
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Citation Context ... logic programs. Such a set is a fuzzy set of literals, similarly to the classical case, which will be considered as a fuzzy Linterpretation. Our aim in this section is to adapt the approach given in =-=[9]-=- and [10] to the general residuated logic programs defined above. To begin with, we have to define a transformation (the reduct construction) which transforms any general logic program into an extende... |

1044 | Classical negation in logic programs and disjunctive databases.
- Gelfond, Lifschitz
- 1991
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Citation Context ...y framework of the concept of consistence. Then, we define the fuzzy answer sets for general residuated logic programs by conveniently adapting the original definition of the Gelfond-Lifschitz reduct =-=[10]-=-. Remark 2: It is important to note that, for presentation purposes, we consider the residuated logic programming framework. However, the results can be straightforwardly extended to the multi-adjoint... |

373 | A useful four-valued logic”. - Belnap - 1977 |

130 | Fixpoint semantics for logic programming - a survey.
- Fitting
- 2002
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Citation Context ...he Dept. Matemática Aplicada, ETSI Informática, Univ. de Málaga, Blv. Louis Pasteur 35, 29071 Málaga, Spain. (email: {nmadrid,aciego}@ctima.uma.es). consistence restoring [1], fix-point semantics =-=[7]-=- and inconsistent information measuring [6], [11], [42]. This paper is related to the latter approaches. Some other interesting works on measuring inconsistency in propositional knowledge bases are [1... |

86 |
Metamathematics of fuzzy logic, Trends in Logic,
- Hajek
- 1998
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Citation Context ...oaches measuring the inconsistency in this more general framework. Perhaps this is due to the fact that there is not a consensus on how to generalize inconsistency in a fuzzy framework. For instance, =-=[12]-=-, [39] consider α-inconsistent interpretations as interpretations which assign a value greater or equal than α to the formula p∧¬p for certain propositional symbol p; [40] considers that an interpreta... |

58 | L.M.: Monotonic and residuated logic programs
- Damásio, Pereira
- 2001
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Citation Context ...ork to handle inconsistency; for a survey on uncertainty and fuzzy LPs, you may refer to [37]. Our approach will be based on a particular type of fuzzy framework known as residuated logic programming =-=[5]-=-. Working in a fuzzy framework enables the possibility of restoring consistence by modifying slightly (it need not be either completely false or completely true) the information inferred of a given pr... |

45 | L.M.: Antitonic logic programs.
- Damasio, Pereira
- 2001
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Citation Context ...et semantics to some non-classical logics have been developed. We relate below our generalization to some approaches based on Probabilistic Logic [22] [40] [34], Annotated Logic [35], Antitonic Logic =-=[4]-=-, Fuzzy Description Logic [23] [24] and Fuzzy Logic [17], [18], [38], [39]. • Most of the approaches are conservative, in that answer sets (or stable models) are generalized by using adequate versions... |

36 |
Measuring inconsistency in knowledgebases
- Grant, Hunter
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Citation Context ..., Univ. de Málaga, Blv. Louis Pasteur 35, 29071 Málaga, Spain. (email: {nmadrid,aciego}@ctima.uma.es). consistence restoring [1], fix-point semantics [7] and inconsistent information measuring [6], =-=[11]-=-, [42]. This paper is related to the latter approaches. Some other interesting works on measuring inconsistency in propositional knowledge bases are [11], [14]–[16], [19], [20]. The existence of a big... |

36 | S.: Approaches to measuring inconsistent information
- Hunter, Konieczny
- 2005
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Citation Context ...a positive value simultaneously, an excessive restriction in some cases. On the other hand, there are a couple of approaches related with the measures of inconsistency in the classical framework (see =-=[13]-=-). These approaches can be classified as based on Shanon’s information theory [21], on possibilistic logic [6], on paraconsistent logic [11] or on a mixture of paraconsistent logic and Shanon’s inform... |

11 |
Quasi-possibilistic logic and its measures of information and conflict
- Dubois, Konieczny, et al.
- 2003
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Citation Context ...́tica, Univ. de Málaga, Blv. Louis Pasteur 35, 29071 Málaga, Spain. (email: {nmadrid,aciego}@ctima.uma.es). consistence restoring [1], fix-point semantics [7] and inconsistent information measuring =-=[6]-=-, [11], [42]. This paper is related to the latter approaches. Some other interesting works on measuring inconsistency in propositional knowledge bases are [11], [14]–[16], [19], [20]. The existence of... |

8 |
Adding involution to residuated structures
- Galatos, Raftery
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Citation Context ...d with ¬N is an involutive negation N defined on L. It is known that not every residuated lattice admits an involutive negation, but it is possible to embed L into another lattice L on which N exists =-=[8]-=-. In L, we have that x ≤ y for all x ∈ L r L and y ∈ L and, moreover, every adjoint pair and negation operator can be extended to L. As a result of the previous considerations, the residuated logic pr... |

5 |
CR-prolog as a specification language for constraint satisfaction problems
- Balduccini
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Citation Context .... Ojeda-Aciego are with the Dept. Matemática Aplicada, ETSI Informática, Univ. de Málaga, Blv. Louis Pasteur 35, 29071 Málaga, Spain. (email: {nmadrid,aciego}@ctima.uma.es). consistence restoring =-=[1]-=-, fix-point semantics [7] and inconsistent information measuring [6], [11], [42]. This paper is related to the latter approaches. Some other interesting works on measuring inconsistency in proposition... |