A subset $H\subset \mathsf{Int}(\mathsf{At})$ is called a hitting set of $\mathcal{K}$ if for every $\alpha\in\mathcal{K}$ there is $\omega\in H$ with $\omega\models \alpha$. $H$ is called a card-minimal hitting set if it is minimal wrt. cardinality. Let $h_{\mathcal{K}}$ be the cardinality of any card-minimal hitting set (define $h_{\mathcal{K}}=\infty$ if there does not exist a hitting set of $\mathcal{K}$). Then the hitting set inconsistency measure $\mathcal{I}_{hs}$ is defined as \[ \mathcal{I}_{hs}(\mathcal{K}) = h_{\mathcal{K}} - 1 \] The hitting set inconsistency measure has been proposed in [Thimm:2014d].