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KI - Künstliche Intelligenz
Published in: KI - Künstliche Intelligenz 1/2017

02-08-2016 | Technical Contribution

On the Compliance of Rationality Postulates for Inconsistency Measures: A More or Less Complete Picture

Author: Matthias Thimm

Published in: KI - Künstliche Intelligenz | Issue 1/2017

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Abstract

An inconsistency measure is a function mapping a knowledge base to a non-negative real number, where larger values indicate the presence of more significant inconsistencies in the knowledge base. In order to assess the quality of a particular inconsistency measure, a wide range of rationality postulates has been proposed in the literature. In this paper, we survey 15 recent approaches to inconsistency measurement and provide a comparative analysis on their compliance with 18 rationality postulates. In doing so, we fill the gaps in previous partial investigations and provide new insights into the adequacy of certain measures and the significance of certain postulates.
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Footnotes
1
Note that slightly different formalizations of this idea have been given in [16, 29, 30].
 
3
Consider a lottery of n tickets and let \(a_{i}\) be the proposition that ticket i, \(i=1,\ldots ,n\) will win. It is known that exactly one ticket will win (\(a_{1}\vee \ldots \vee a_{n}\)) but each ticket owner assumes that his ticket will not win (\(\lnot a_{i}\), \(i=1,\ldots ,n\)). For \(n=1000\) it is reasonable for each ticket owner to believe that he will not win but for e. g., \(n=2\) it is not. Therefore larger minimal inconsistent subsets can be regarded less inconsistent than smaller ones.
 
5
Note that proofs of [43] are for propositional probabilistic logic. As this is a generalization of propositional logic, the results apply here as well.
 
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Metadata
Title
On the Compliance of Rationality Postulates for Inconsistency Measures: A More or Less Complete Picture
Author
Matthias Thimm
Publication date
02-08-2016
Publisher
Springer Berlin Heidelberg
Published in
KI - Künstliche Intelligenz / Issue 1/2017
Print ISSN: 0933-1875
Electronic ISSN: 1610-1987
DOI
https://doi.org/10.1007/s13218-016-0451-y

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