A Syntax-based approach to measuring the degree of inconsistency for belief bases

Mu, Kedian; Liu, Weiru; Jin, Zhi; Bell, David A.

doi:10.1016/j.ijar.2011.04.001

Cited by 39 publications

(17 citation statements)

References 17 publications

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“…Compared with ID 4 and ID Q , the MUS based measure I MI = |MUSes(K)| can distinguish γ 1 and γ 2 . However, as argued in [26], I MI does not satisfy dominance property. In this paper, we further refine the notion of MUS and propose a new one called DMUS (for deduced MUS) which leads to an interesting inconsistency measure that satisfies a new restrictive but more intuitive dominance property, called weak dominance.…”

Section: Introductionmentioning

confidence: 92%

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On the Characterization of Inconsistency: A Prime Implicates Based Framework

Jabbour

Raddaoui

et al. 2014

2014 IEEE 26th International Conference on Tools With Artificial Intelligence

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Measuring inconsistency is recognized as an important issue for handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we emphasize one such property, named dominance, rarely satisfied by syntactic measures. Based on prime implicates canonical representation, we first characterize the conflicting variables allowing us to refine an existing inconsistency measure. Secondly, we propose a new measure, to circumscribe the internal conflicts in a knowledge base. This measure is proved to satisfy a new but weaker form of dominance.

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Section: Introductionmentioning

confidence: 92%

“…In [26], the authors show that the measure I MI does not satisfy the dominance property. To support their claim, they provide the following counterexample:…”

Section: Mus-based Logical Deductionmentioning

confidence: 99%

On the Characterization of Inconsistency: A Prime Implicates Based Framework

Jabbour

Raddaoui

et al. 2014

2014 IEEE 26th International Conference on Tools With Artificial Intelligence

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“…Next we consider several properties that have been studied for inconsistency measures (see [11,12,23]) and show which of them hold for distance-based measures.…”

Section: Definition 15mentioning

confidence: 99%

Analysing inconsistent information using distance-based measures

Grant¹,

Hunter²

2017

International Journal of Approximate Reasoning

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There have been a number of proposals for measuring inconsistency in a knowledgebase (i.e. a set of logical formulae). These include measures that consider the minimally inconsistent subsets of the knowledgebase, and measures that consider the paraconsistent models (3 or 4 valued models) of the knowledgebase. In this paper, we present a new approach that considers the amount by which each formula has to be weakened in order for the knowledgebase to be consistent. This approach is based on ideas of knowledge merging by Konienczny and Pino-Perez. We show that this approach gives us measures that are different from existing measures, that have desirable properties, and that can take the significance of inconsistencies into account. The latter is useful when we want to differentiate between inconsistencies that have minor significance from inconsistencies that have major significance. We also show how our measures are potentially useful in applications such as evaluating violations of integrity constraints in databases and for deciding how to act on inconsistency.

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“…Mu et al claim that dominance is not appropriate for characterizing variable-based measures for the degree of inconsistency (Mu et al, 2011). They argue that {x, ¬x} might be seen as more inconsistent than {x ∧ y, ¬x}, since the latter set contains a non-contradictory information that y holds.…”

Section: Definition 3 (Dominance) An Inconsistency Measurementioning

confidence: 99%

“…Convincing arguments can be constructed even to support the fact that inconsistency is not always a bad thing (Gabbay and Hunter, 1991;Gabbay and Hunter, 1993). The question how to measure inconsistency of a knowledge base has attracted attention of researchers in recent years (Knight, 2002;Hunter and Konieczny, 2005;Hunter and Konieczny, 2008;Hunter and Konieczny, 2010;Mu et al, 2011;Grant and Hunter, 2011b;Grant and Hunter, 2013). In some papers, the measure of inconsistency depends on the proportion of the language that is affected by the inconsistency in a theory (Konieczny et al, 2003;Grant and Hunter, 2006;Hunter and Konieczny, 2010).…”

Section: Introductionmentioning

confidence: 99%

How to Decrease and Resolve Inconsistency of a Knowledge Base?

Doder

Vesic

2015

Proceedings of the International Conference on Agents and Artificial Intelligence

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This paper studies different techniques for measuring and decreasing inconsistency of a knowledge base. We define an operation that allows to decrease inconsistency of a knowledge base while losing a minimal amount of information. We also propose two different ways to compare knowledge bases. The first is a partial order that we define on the set of knowledge bases. We study this relation and identify its link with a particular class of inconsistency measures. We also study the links between the partial order we introduce and information measures. The second way we propose to compare knowledge bases is to define a class of metrics that give us a distance between knowledge bases. They are based on symmetric set difference of models of pairs of formulae from the two sets in question.

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A Syntax-based approach to measuring the degree of inconsistency for belief bases

Cited by 39 publications

References 17 publications

On the Characterization of Inconsistency: A Prime Implicates Based Framework

On the Characterization of Inconsistency: A Prime Implicates Based Framework

Analysing inconsistent information using distance-based measures

How to Decrease and Resolve Inconsistency of a Knowledge Base?

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