Additionally, if you have 11Gb logfiles, you should really be rotating them properly or they will just become unmanageable like this.
Setting up log rotation so that, for example, you get nine individual 1Gb logfiles that cycle each day would mean that once your server's been running for ten days, it's disk requirements will stay pretty much the same all the time. And removing log files from underneath a program can cause problems (although it would have to be a particularly poorly-written program, I have to admit).
What if that program had gone mad and written hundreds of gigs instead of a few? The machine would have come to a halt and nobody would have been able to use it until you cleared it. Also, if the program that generated them was running as root, there's the possibility that you wouldn't have been ABLE to log in, even as root or in single-user-mode, to fix it because it would have written every byte it could onto the disk and filled it up completely, including the default 5% root-only emergency space.
And the next question is, how often do you (or anyone else) ever look at those logs? What's the point of spooling off logs to the disk if they get to 11Gb and then just get deleted? Either turn off logging, tone it down a bit or put in some form of log rotation/management.