Is there a linux log for when a user is denied access to files due to permissions

Is there a log file which keeps track of things users try to do and are denied due to regular unix file permissions. I know selinux does things, but a lot of the time the good ole' file permissions stop them first. When this happens, is there a log that gets printed to.

Thanks

How to set up and use auditd in Linux:

http://www.cyberciti.biz/tips/linux-audit-files-to-see-who-made-changes-to-a-file.html

No, that's not logged.

Auditctl allows you to log access to files, including access denied.

From the manpage:

To see unsuccessful open call's:

auditctl -a exit,always -S open -F success!=0