You can uninstall or removes an installed logcheck-database package itself from Ubuntu 14.04 LTS (Trusty Tahr) through the terminal,
$ sudo apt-get remove logcheck-database
If you would like to remove logcheck-database and it's dependent packages which are no longer needed from Ubuntu,
$ sudo apt-get remove --auto-remove logcheck-database
If you use with purge options to logcheck-database package all the configuration and dependent packages will be removed.
$ sudo apt-get purge logcheck-database
If you use purge options along with auto remove, will be removed everything regarding the package, It's really useful when you want to reinstall again.
$ sudo apt-get purge --auto-remove logcheck-database