On a website I have implemented the login using OpenID (based on StackOverflow).
But I can\'t seem to logout.
On my host I can logout but when the user tries to logi
OpenID authenticates users to your site, when then starts a session on your site. You destroy or invalidate your site's session separately from the user's session with their OpenID provider.
User visits joewidgets.com > User logs in with OpenID (with a new or existing provider session) > ... User clicks logout > joewidgets.com destroys/invalidates the session.
If the user has their OpenID provider keep them logged in, and your system automatically checks, then it will create a new local session. (Un)fortunately, you don't/can't worry about what the user does or does not do at their provider, which is a pro/con of OpenID.
There is an argument at Social Lipstick which calls for "Single Sign-Out", but OpenID does not currently provide this function.