Edit own comments in other users' posts

On my site I am only going to allow logged in users to post comments. I would like to allow logged in users to edit (and remove) only there own comments in another users' post (e.g. admin). For the subscriber role I tried without success:

`$user_role = get_role('subscriber'); // get the user role you want to edit $user_role->add_cap('edit_comment');'

and

$subscriber= get_role('subscriber'); $subscriber->add_cap('edit_comment');

Using URE I then added to the subscriber role publish posts, edit posts and edit published posts also without success.

Thank you for your time

Jerry