On the expressivity of inconsistency measures

Abstract

We survey recent approaches to inconsistency measurement in propositional logic and provide a comparative analysis in terms of their expressivity. For that, we introduce four different expressivity characteristics that quantitatively assess the number of different knowledge bases that a measure can distinguish. Our approach aims at complementing ongoing discussions on rationality postulates for inconsistency measures by considering expressivity as a desirable property. We evaluate a large selection of measures on the proposed characteristics and conclude that the distance-based measure IΣdalal from [Grant and Hunter, 2013] has maximal expressivity along all considered characteristics.