On Measuring Inconsistency Using Maximal Consistent Sets

Ammoura, Meriem; Raddaoui, Badran; Salhi, Yakoub; Oukacha, Brahim

doi:10.1007/978-3-319-20807-7_24

Cited by 9 publications

(26 citation statements)

References 15 publications

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“…Inconsistency measures, firstly mentioned in (Grant, 1978), can be used to analyse inconsistencies and to provide insights on how to repair them. An inconsistency measure I is a function on knowledge bases, such that the larger the value I(K) the more severe the inconsistency in K. A lot of different approaches of inconsistency measures have been proposed, mostly for classical propositional logic (Hunter and Konieczny, 2004Ma et al, 2010;Mu et al, 2011;Xiao and Ma, 2012;Grant and Hunter, 2011;Ma et al, 2012;Grant and Hunter, 2013;McAreavey et al, 2014;Jabbour et al, 2015Jabbour et al, , 2014bBesnard, 2016;Thimm, 2016b;Ammoura et al, 2015Ammoura et al, , 2017, but also for classical first-order logic (Grant and Hunter, 2008), description logics (Ma et al, 2007;Zhou et al, 2009), default logics (Doder et al, 2010), answer set programming (Ulbricht et al, 2016) probabilistic and other weighted logics (Thimm, 2013;Potyka, 2014;De Bona and Finger, 2015), and relational databases (Decker, 2011), see also (Thimm, 2017b(Thimm, , 2018 for some recent surveys.…”

Section: Introductionmentioning

confidence: 99%

“…More recent measures also take the relationships between minimal inconsistent subsets into account . Other measures belonging to the syntactic approach may exploit other notions such as maximal consistent subsets (Ammoura et al, 2015(Ammoura et al, , 2017 but the commonality of these approaches is that they focus on conflicts between formulas of the knowledge base. On the other hand, measures belonging to the semantic approach focus on conflicts between language components.…”

Section: Introductionmentioning

confidence: 99%

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On the complexity of inconsistency measurement

Thimm

Wallner

2019

Artificial Intelligence

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the complexity of inconsistency measurement

Thimm

Wallner

2019

Artificial Intelligence

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“…This poses the question of which further desiderata could be imposed on inconsistency measures to preclude such cases. Discussions on how reasonable are the inconsistency measuring postulates in the literature have claimed that they are over-constraining to some extent (Ammoura, Raddaoui, Salhi, & Oukacha, 2015;Besnard, 2014;Thimm, 2016a). In contrast, the absence of strong rationality postulates leave a vacuum for rather meaningless proposals to arise, such as I e and I e .…”

Section: From Inconsistency Measures To the Inconsistency Graphmentioning

confidence: 99%

Classifying Inconsistency Measures Using Graphs

Bona¹,

Grant²,

Hunter³

et al. 2019

jair

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The aim of measuring inconsistency is to obtain an evaluation of the imperfections in a set of formulas, and this evaluation may then be used to help decide on some course of action (such as rejecting some of the formulas, resolving the inconsistency, seeking better sources of information, etc). A number of proposals have been made to define measures of inconsistency. Each has its rationale. But to date, it is not clear how to delineate the space of options for measures, nor is it clear how we can classify measures systematically. To address these problems, we introduce a general framework for comparing syntactic measures of inconsistency. It is based on the notion of an inconsistency graph for each knowledgebase (a bipartite graph with a set of vertices representing formulas in the knowledgebase, a set of vertices representing minimal inconsistent subsets of the knowledgebase, and edges representing that a formula belongs to a minimal inconsistent subset). We then show that various measures can be computed using the inconsistency graph. Then we introduce abstractions of the inconsistency graph and use them to construct a hierarchy of syntactic inconsistency measures. Furthermore, we extend the inconsistency graph concept with a labeling that extends the hierarchy to include some other types of inconsistency measures.

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“…Understanding the nature of inconsistency of a set of formulas is an important topic which aroused a great amount of research during the past decade The purpose is to analyze to which degree a set of formulas is inconsistent. A lot of inconsistency measures have been proposed according to different points of view: some of them are based on minimal inconsistent subsets [15,16,25,20] or on maximal consistent subsets [10,1], some consider paraconsistent models such as three valued logic [17,10], some consider probabilistic functions over the underlying propositional language [29], some consider model distance [11] and finally some are proof-based [19]. For a detailed review of these inconsistency measures we refer the reader to [30].…”

Section: Measuring the I C -Inconsistency Of Communication Setsmentioning

confidence: 99%

Using inconsistency measures for estimating reliability

Cholvy

Perrussel

Thévenin

2017

International Journal of Approximate Reasoning

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Any decision taken by an agent requires some knowledge of its environment. Communication with other agents is a key issue for assessing the overall quality of its own knowledge. This assessment is a challenge itself as the agent may receive information from unknown agents. The aim of this paper is to propose a framework for assessing the reliability of unknown agents based on communication. We assume that information is represented through logical statements and logical inconsistency is the underlying notion of reliability assessment. In our context, assessing consists of ranking the agents and representing reliability through a total preorder. The overall communication set is first evaluated with the help of inconsistency measures. Next, the measures are used for assessing the contribution of each agent to the overall inconsistency of the communication set. After stating the postulates specifying the expected properties of the reliability preorder, we show through a representation theorem how these postulates and the contribution of the agent are interwoven. We also detail how the properties of the inconsistency measures influence the properties of the contribution assessment. Finally we describe how to aggregate different reliability preorders, each of them may be based on different inconsistency measures.

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On Measuring Inconsistency Using Maximal Consistent Sets

Cited by 9 publications

References 15 publications

On the complexity of inconsistency measurement

On the complexity of inconsistency measurement

Classifying Inconsistency Measures Using Graphs

Using inconsistency measures for estimating reliability

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