Analysing inconsistent information using distance-based measures

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Highlights

  • A class of inconsistency measures for propositional logic based on distance between models is proposed.

  • Conformance of the inconsistency measures with a range of postulates is investigated.

  • Significance of inconsistency is evaluated through a cost function that is related to distance.

  • Options for specifying a cost function are proposed and compared.

Abstract

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.

Keywords

Inconsistency measurement
Inconsistency analysis
Inconsistency management
Inconsistency tolerance
Propositional logic
Distance measures

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