Initial Models (ADF)

A three-valued interpretation $v$ of an ADF is an initial model iff $v$ is admissible with $v \neq v_\mathsf{u}$ and there is no admissible model $v' \neq v_\mathsf{u}$ with $v' <_i v$ in the information ordering, where $v_\mathsf{u}$ maps every argument to $\mathsf{u}$.