I'm not sure if KSystemLog has the ability to view logs from the previous boot but if it's there, it's not accessible to the user. I don't see it in the UI and you can't open the help page because the log viewer gui runs as root.

So I'm not sure if this option is missing or just extremely difficult to find but as far as the user is concerned it doesn't exist. This means it's impossible to use the program to troubleshoot critical system failures (ones that end with a shut down)