Log out of Facebook Connect, but not Facebook

Question

I'm using Facebook PHP SDK to implement authorization through Facebook Connect on my website. It works fine, however, when a user logs out, he or she logs out of Facebook as well. I understand this is normal behaviour for clicking on a link which was generated using getLogoutUrl() method.

Is it possible for a user to log out of Facebook Connect, but not Facebook as well? If so, how can this be achieved?

Thank you in advance.

UPD, sort of an answer: For me, what it basically boiled down for was using Facebook Connect this way: user clicks the 'Facebook Connect' button; if they are logged in to Facebook and authorize the app (app is required for using Facebook Connect), we get their ID and set a cookie that he's logged in. This cookie has no relation to Facebook, it's created by my script. When the user wants to log out, we simply delete this cookie.

So, login and logout logic are based entirely in my script. FB Connect only aids the process by removing the need to get a password and a login for a user.

Answer 1

Simply clear the facebook-connect-related cookies manually.