On the expressivity of inconsistency measures

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 16 different measures on the proposed characteristics and conclude that the distance-based measure IdalalΣ from Grant and Hunter (2013) [8] and the proof-based measure IPm from Jabbour and Raddaoui (2013) [16] have maximal expressivity along all considered characteristics. In our study, we discovered several interesting relationships of inconsistency measurement to e.g. set theory and Boolean functions and we also report these findings.