Curley
There is an application for KDE, which is KSystemLog.
For it :
sudo pacman -S ksystemlog
This automatically records the logs. So, you should open the application and note the time when it is happening. By this you can navigate to the logs which you wanted.
Also
when you want to hard-reboot the computer, perform the following key combination:
press and hold the Alt key the entire time. Now, one after another, with about a second in between, press (tap) the following keys: SysRq, R, E, I, S, U, B.
This prevents the issues which can happen by force shutdown.