  The layered perovskite cobaltite RBaCo$_2$O$_{5.5}$ (R: rare-earth elements
or Yttrium) exhibits an abrupt temperature-induced metal$-$insulator transition
(MIT) and has been attributed to spin-state ordering (SSO) of Co$^{3+}$ ions.
Here we investigated the hole doping member of PrBaCo$_2$O$_{5.5+x}$ ($0 \le x
\le 0.24$) with multiple techniques. The analysis on crystal and magnetic
structures by electron and neutron diffraction confirm the SSO in the
insulating phase of undoped PrBaCo$_2$O$_{5.5}$, which is melted by increasing
the temperature across the MIT. In addition, we discovered that hole doping to
PrBaCo$_2$O$_{5.5}$ also melts the SSO in conjunction with an insulator-metal
transition. The experimental results from electron/neutron diffraction and soft
x-ray absorption spectroscopy (XAS) all lead to the conclusion that hole-doping
induced MIT occurs is in the same manner as the temperature-induced MIT.
Therefore, we propose a unified mechanism that dominates the temperature- and
hole-doping-induced MITs in the PrBaCo$_2$O$_{5.5+x}$ system. Specifically,
this mechanism involves symmetry breaking coupled with a SSO in the
paramagnetic phase.
