Is it safe to delete system logs? I'm using DaisyDisk to clean my hard drive and it is showing nearly 8GB of files in /private/var/log/asl. Are those files safe to delete?
Yes, you can safely delete log files. In the case of an application needing to write a new entry and the file not being found, it will be re-created automatically.

Just bear in mind that these ASL (Apple System Log) files may contain some useful information to trace or debug any issues you could be experimenting with your computer, which, of course, will be lost with the deletion of the files. 

So, in case you might want to take a look at these files before deleting them, you could use the syslog command as follows: syslog -f /private/var/log/asl/nameOfTheFile.asl