Facebook Kiosk Logout

We have a facebook website app for use as a public event kiosk. Many people will be logging into facebook through our site on the same device (set up at a booth, like a ipad or similar).

We need to log the person out of facebook itself after they are done; not simply destroy the graph api session for our site.

Here is the problem:

User walks up to our ipad, which has a browser loaded to our website. He or she clicks "facbook login", and is redirected to facebook to log in.
They log in, grant our app permission, and facebook redirects them back to our site.
After they use our site (post comment, etc...) they click log out on our site.
Next user sits down, clicks "facebook login", and is redirected to facebook. Upon reaching facebook.com, the browser is still logged in for the previous user, granting this user access to the first user's facebook (just a small problem =)

My hope is that I can send the user to facebook, to a page with nothing but a logout button, and have facebook redirect the browser back to my site, ready for the next user. This is how the login works, and I need a logout equivalent.

Edit:

Thank you very much for the answer. We spent like 3 days trying to figure this out; I hope you will forgive us if we post generic code that anyone can plug in. Placing this on an HTML page, then visiting that page, logs the user out of Facebook and your site.

<div id="fb-root"></div>
<script>
  window.fbAsyncInit = function() {
    FB.init({
      appId      : 'your APP ID', // App ID
      channelUrl : '//WWW.YOURSITE.COM/channel.php or channel.html or whatever yours is', // Channel File
      status     : true, // check login status
      cookie     : true, // enable cookies to allow the server to access the session
      xfbml      : true  // parse XFBML
    });
    // Additional initialization code here
    FB.getLoginStatus(function(response) {
    if (response.status === 'connected') {
      var uid = response.authResponse.userID;
      var accessToken = response.authResponse.accessToken;
      FB.logout();
      alert('Thanks!  You have been logged out of facebook.');
    }
   });            
  };
  (function(d){
     var js, id = 'facebook-jssdk', ref = d.getElementsByTagName('script')[0];
     if (d.getElementById(id)) {return;}
     js = d.createElement('script'); js.id = id; js.async = true;
     js.src = "//connect.facebook.net/en_US/all.js";
     ref.parentNode.insertBefore(js, ref);
   }(document));
</script>

If you use the Facebook Javascript SDK, you can call FB.logout when they click your logout link as the documentation states: