Hi, Welcome to Linux Questions!
You need to give us the syslog files showing time stamps to shutdown plus ones showing the following restart, not just a bit clipped out at random. (everything's logged at 22:41:19!!)We need to see what was happening over the shutdown and subsequent restart. If you wait a minute before restarting, it'll be easier to identify when it shut down. My system identifies a power button as a PNP ACPI device so I don't think that's relevant.
What sort of system is it; desktop, laptop? Some laptops will shut down with overtemp errors as the CPU heat exchanger fins become blocked with fluff and dust.