On the expressivity of inconsistency measures

Thimm, Matthias

doi:10.1016/j.artint.2016.01.013

Cited by 44 publications

(56 citation statements)

References 12 publications

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“…The problem of measuring inconsistency in knowledge bases over logical languages has increasingly received attention during recent years (for a survey, see [42,43]). An inconsistency measure is a function I : K → [0, ∞) ∪ {∞} 7 , which takes knowledge bases and returns non-negative real numbers or ∞.…”

Section: New Inconsistency Measuresmentioning

confidence: 99%

“…To better characterise I and I C , we consider some additional properties for inconsistency measures from the literature [41]: Another way of assessing the behaviour of an inconsistency measure is through its expressivity power. Thimm [42] proposes a method to quantify this expressivity in four dimensions, defined via bounding either the size of, or the number of atoms in, either the whole knowledge base or each formula. Although we do not formally present Thimm's whole framework, it can be proved that, for any Tarskian Cn , I and I C , similarly to I M IS and I M IS C , have the highest possible expressivity for three of out the four dimensions.…”

Section: New Inconsistency Measuresmentioning

confidence: 99%

“…To answer the second question in a qualitative way, inconsistent knowledge bases were classified by the severity of their inconsistency [17]. Recently, to numerically quantify the extent to which a knowledge base is inconsistent, many inconsistency measures have been proposed [29,24,25,19,28,27,20,42,43]. In contrast, the first question appears quite underdeveloped, and it is the subject of the present work.…”

Section: Introductionmentioning

confidence: 99%

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Localising iceberg inconsistencies

Bona

Hunter

2017

Artificial Intelligence

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In artificial intelligence, it is important to handle and analyse inconsistency in knowledge bases. Inconsistent pieces of information suggest questions like "where is the inconsistency?" and "how severe is it?". Inconsistency measures have been proposed to tackle the latter issue, but the former seems underdeveloped and is the focus of this paper. Minimal inconsistent sets have been the main tool to localise inconsistency, but we argue that they are like the exposed part of an iceberg, failing to capture contradictions hidden under the water. Using classical propositional logic, we develop methods to characterise when a formula is contributing to the inconsistency in a knowledge base and when a set of formulas can be regarded as a primitive conflict. To achieve this, we employ an abstract consequence operation to "look beneath the water level", generalising the minimal inconsistent set concept and the related free formula notion. We apply the framework presented to the problem of measuring inconsistency in knowledge bases, putting forward relaxed forms for two debatable postulates for inconsistency measures. Finally, we discuss the computational complexity issues related to the introduced concepts.

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Section: New Inconsistency Measuresmentioning

confidence: 99%

Section: New Inconsistency Measuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Localising iceberg inconsistencies

Bona

Hunter

2017

Artificial Intelligence

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“…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]. In this section, we first review some well-known inconsistency measures then we show our requirements to adapt them to our context.…”

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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“…With the advent of a number of new inconsistency measures (see e.g. [9] as well as the special issue [11] in the Journal of Approximate Reasoning) or related approaches [4,19], further investigations are afoot.…”

Section: Exhibiting Conjunctionsmentioning

confidence: 99%

Basic Postulates for Inconsistency Measures

Besnard¹

2017

Lecture Notes in Computer Science

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Postulates for inconsistency measures are examined, the set of postulates proposed by Hunter and Konieczny being the starting point. The focus is on two postulates that were questioned by various authors. Studying the first suggests a systematic transformation to guard postulates against a certain kind of counter-examples. The second postulate under investigation here is devoted to independence, for which a general version is proposed that avoids the pitfalls mentioned in the literature. Combining these two additions with some postulates previously introduced by the same author, a set of basic postulates alternative to the core set given by Hunter and Konieczny arises.Formally, for I denoting an inconsistency measure, I(K 1 ) < I(K 2 ).

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On the expressivity of inconsistency measures

Cited by 44 publications

References 12 publications

Localising iceberg inconsistencies

Localising iceberg inconsistencies

Using inconsistency measures for estimating reliability

Basic Postulates for Inconsistency Measures

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