Inherit permissions

I have an application which creates rotating log files in a directory. Because this application can only run as root, the log files are created with root permissions. Is there any way I can force newly created files to automatically inhherit the permissions of their parent directory or other specified permissions? (i.e. I don’t want to change the file permissions using chown/chgrp/chmod)

OS is Redhat 9 and just in case it’s relevant, the application is Tethereal.