For defining the $\eta$-inconsistency measure we need to consider probability functions $P$ of the form $P:\mathsf{Int}(\mathsf{At})\rightarrow [0,1]$ with $\sum_{\omega\in\mathsf{Int}(\mathsf{At})} P(\omega)=1$. Let $\mathcal{P}(\mathsf{At})$ be the set of all those probability functions and for a given probability function $P\in\mathcal{P}(\mathsf{At})$ define the probability of an arbitrary formula $\alpha$ via $P(\alpha)=\sum_{\omega\models\alpha}P(\omega)$. The eta inconsistency measure $\mathcal{I}_{\eta}$ is then defined as \[ \mathcal{I}_{\eta}(\mathcal{K}) = 1-\max\{\xi\mid\exists P\in \mathcal{P}(\mathsf{At}):\forall \alpha\in\mathcal{K}:P(\alpha)\geq \xi\} \] The eta inconsistency measure has been proposed in [Knight:2002].