## How to Infer from Inconsistent Beliefs without Revising? (1995)

Venue: | Proc. IJCAI'95 |

Citations: | 44 - 5 self |

### BibTeX

@INPROCEEDINGS{Benferhat95howto,

author = {Salem Benferhat and Didier Dubois and Henri Prade},

title = {How to Infer from Inconsistent Beliefs without Revising?},

booktitle = {Proc. IJCAI'95},

year = {1995},

pages = {1449--1455}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper investigates several methods for coping with inconsistency caused by multiple source information, by introducing suitable consequence relations capable of inferring non-trivial conclusions from an inconsistent stratified knowledge base. Some of these methods presuppose a revision step, namely a selection of one or several consistent subsets of formulas, and then classical inference is used for inferring from these subsets. Two alternative methods that do not require any revision step are studied: inference based on arguments, and a new approach called safely supported inference, where inconsistency is kept local. These two last methods look suitable when the inconsistency is due to the presence of several sources of information. The paper offers a comparative study of the various inference modes under inconsistency. 1 Introduction Inconsistency can be encountered in different reasoning tasks, in particular: - when reasoning with exception-tolerant generic knowledge, where ...

### Citations

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Citation Context ...n inference captures the cases when we believe in two mutually consistent properties of some object for conflicting reasons. This situation also happens in numerical settings such as evidence theory (=-=Shafer, 1976) since -=-we may have Belief(f)>0, Belief(y)>0 and Belief(f��y)=0 with Shafer belief functions. Besides, the set of argued consequences of �� can be inconsistent (Benferhat et al., 1993a), while the set... |

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Citation Context ...�=S 1 ��...��S n , such that formulas in S i have the same level of priority or certainty and are more reliable than the ones in S j where j>i. This stratification is modelled in possibilist=-=ic logic (Dubois et al., 1994) by attachin-=-g a weight a��[0,1] to each formula with the convention that (f a i )��S i , "i and a 1 =1>a 2 >...>a n >0. From now on, a stratification is used to represent prioritized knowledge bases,... |

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Citation Context ...j is the cardinality of A. From now on, we denote by Incl(��) and Lex(��) the set of inclusion-preferred subbases and Lex-preferred subbases of ��. Inclusion-preferred subbases have been p=-=roposed by (Brewka, 1989) under th-=-e name "preferred sub-theories" and have also been independently introduced by (Dubois et al., 1992a) in the setting of possibilistic logic under the name of strongly maximal consistent subb... |

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Citation Context ...h its level of certainty corresponding to the layer to which it belongs. The use of priorities among formulas has been shown to be very important to appropriately revise inconsistent knowledge bases (=-=Fagin et al., 1983). I-=-n particular, G��rdenfors (1988) has proved that any revision process that satisfies natural requirements is implicitly based on priority ordering. In the context of merging several knowledge base... |

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Citation Context ...995). We now give a procedure to compute safely supported conclusions of a belief base. Algorithms for computing conclusions obtained using coherence theories are largely described in the literature (=-=Baral et al., 1992-=-; Benferhat et al., 1993b), and a theorem prover has been developed in (Cholvy, 1993). A procedure for computing argued consequences can be found in (Benferhat et al., 1993a). We use an ATMS for compu... |

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Citation Context ...an combining the knowledge bases attached to each source before the inference process takes place. Our dichotomy coherence versus foundation is somewhat different from the one used in the literature (=-=Harman, 1986), (-=-G��rdenfors, 1990), (Rao & Foo, 1989), (Doyle, 1992), (DelVal, 1994). In this paper, we do not assume any particular structure on the beliefs in the knowledge base (contrary for example to RMS def... |

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Citation Context ...bbases. Baral et al. (1992) have also used a similar approach to combine belief bases. The definition of Lex(��) has been proposed in another form in (Dubois et al., 1992a) and also independently =-=in (Lehmann, 1993). T-=-he idea of selecting a subset of the set of maximally consistent subbases of �� using a cardinality criterion was used independently in diagnostic problems (De Kleer, 1990; Lang, 1994). It corresp... |

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Citation Context ... corresponds to the most conservative inferences. lo-Consequence lo ; SS-Consequence ; SS Incl-Consequence ; Incl p-Consequence ; p Lex-Consequence ; Lex Argued-Consequence ;A Proofs can be found in (=-=Benferhat et al., 1994). N-=-otice that all the consequence relations described above collapse with the possibilistic entailment ; p when �� is consistent. Moreover, when the base is flat then the safely supported inference i... |

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Citation Context ... most log(n) satisfiability (SAT) tests. However, this approach is very drastic ("liberal") and the amount of the formulas given up may be important. Nebel(1994), elaborating on a suggestion=-= made in (Dubois & Prade, 1991-=-), has proposed a less liberal way to select one consistent subbase. The idea is to consider each stratum as composed of one element obtained by the conjunction of the formulas inside this stratum. Su... |

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Citation Context ... before the inference process takes place. Our dichotomy coherence versus foundation is somewhat different from the one used in the literature (Harman, 1986), (G��rdenfors, 1990), (Rao & Foo, 1989=-=), (Doyle, 1992-=-), (DelVal, 1994). In this paper, we do not assume any particular structure on the beliefs in the knowledge base (contrary for example to RMS defined in (Doyle, 1992)). Nor do we assume any (in)depend... |

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Citation Context ...gorithms for computing conclusions obtained using coherence theories are largely described in the literature (Baral et al., 1992; Benferhat et al., 1993b), and a theorem prover has been developed in (=-=Cholvy, 1993-=-). A procedure for computing argued consequences can be found in (Benferhat et al., 1993a). We use an ATMS for computing safely supported inferences. This tool can compute minimal inconsistent sets, a... |

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Citation Context ...ched to each source before the inference process takes place. Our dichotomy coherence versus foundation is somewhat different from the one used in the literature (Harman, 1986), (G��rdenfors, 1990=-=), (Rao & Foo, 1989-=-), (Doyle, 1992), (DelVal, 1994). In this paper, we do not assume any particular structure on the beliefs in the knowledge base (contrary for example to RMS defined in (Doyle, 1992)). Nor do we assume... |

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Citation Context ...gument which supports f. Proposition 1: Let y be a safely supported consequence of ��, then there exists an argument, say A, for y in �� such that none of the formulas of A is defeated. See pr=-=oof in (Benferhat et al., 1995-=-). The previous proposition means that the safely supported inference is based on undefeated arguments, and therefore the conclusions produced by this consequence relation are safe. The converse of Pr... |

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Citation Context ...nce process takes place. Our dichotomy coherence versus foundation is somewhat different from the one used in the literature (Harman, 1986), (G��rdenfors, 1990), (Rao & Foo, 1989), (Doyle, 1992), =-=(DelVal, 1994-=-). In this paper, we do not assume any particular structure on the beliefs in the knowledge base (contrary for example to RMS defined in (Doyle, 1992)). Nor do we assume any (in)dependence relations b... |

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Citation Context ...maximally consistent subbases of �� using a cardinality criterion was used independently in diagnostic problems (De Kleer, 1990; Lang, 1994). It corresponds to the property of parsimony advocated =-=in (Reggia et al., 1985). Once Incl-=-(��) and Lex(��) are computed, we define the nonmonotonic consequence relation in the following way: Def. 5: A formula f is said to be a Incl-consequence (resp.Lex-consequence) of ��, deno... |

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Citation Context ...asoning for handling exceptions. There also exist approaches to reasoning with inconsistent knowledge bases which, for instance, identify a consistent part and an inconsistent part in the base as in (=-=Lin, 1994-=-), or which combine the consequences obtained from each source of information as in (Dubois et al., 1992b) rather than combining the knowledge bases attached to each source before the inference proces... |

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Citation Context ...ently in (Lehmann, 1993). The idea of selecting a subset of the set of maximally consistent subbases of �� using a cardinality criterion was used independently in diagnostic problems (De Kleer, 19=-=90; Lang, 1994). It co-=-rresponds to the property of parsimony advocated in (Reggia et al., 1985). Once Incl(��) and Lex(��) are computed, we define the nonmonotonic consequence relation in the following way: Def. 5:... |

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Citation Context ...w, the first class is very interesting (with computational complexity close to one of the classical logic), while selecting several maximal consistent subbases is computationally very difficult (see (=-=Nebel, 1994-=-), (Cayrol & Lagasquie-Schiex, 1994) for a discussion of complexity results of inconsistency handling approaches). However, from the minimal change point of view, the second class seems more satisfact... |

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