facebook应用程序多次登录，逻辑错误

我有这个脸书应用程序可以在我的网站上显示fb通知。然后我遇到了这个问题，假设两个用户Alice&上下快速移动爱丽丝是我网站的常客，她把它推荐给了鲍勃。她让他用自己的笔记本电脑在我的网站上注册。当bob尝试添加应用程序时，Alice的fb通知出现了。事实上，当Bob点击登录链接时，由于alice已经登录到facebook，它只是提取了她的详细信息（同一会话），如何解决这种情况，我们必须让alice从facebook注销并让Bob登录吗，类似于"alice已经登记，以不同用户身份登录"，有人能提出一些解决方案和如何做到这一点吗？

以下是我用于登录的代码

        require_once('sdk/src/facebook.php');
        $facebook = new Facebook(array(
          'appId'  => 'xxxxxxxxxxxxxxxx',
          'secret' => 'xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx',
          'cookie' => true
        ));

        // Get User ID
        $user = $facebook->getUser();

        // Login or logout url will be needed depending on current user state.
        if ($user) {
          $logoutUrl = $facebook->getLogoutUrl();
        } else {
          $loginUrl = $facebook->getLoginUrl();
        }

        //check permissions list
        if ($user) {
            $permissions_list = $facebook->api('/me/permissions','GET', array('access_token' => $access_token));

             //check if the permissions we need have been allowed by the user
            //if not then redirect them again to facebook's permissions page
            //
            $permissions_needed = array('manage_notifications','publish_stream', 'read_stream');
            $login_url_params = array(
                        'scope' => 'manage_notifications,publish_stream,read_stream',
                        'fbconnect' =>  1,
                        'display'   =>  "page",
                        'next' => 'http://'.$_SERVER['HTTP_HOST'].$_SERVER['REQUEST_URI']
                    );
            foreach($permissions_needed as $perm) {
                if( !isset($permissions_list['data'][0][$perm]) || $permissions_list['data'][0][$perm] != 1 ) {
                    $login_url_params = array(
                        'scope' => 'manage_notifications,publish_stream,read_stream',
                        'fbconnect' =>  1,
                        'display'   =>  "page",
                        'next' => 'http://'.$_SERVER['HTTP_HOST'].$_SERVER['REQUEST_URI']
                    );
                    $login_url = $facebook->getLoginUrl($login_url_params);
                    echo $login_url;
                    header("Location: {$login_url}");
                    exit();
                }
            }               
            //if the user has allowed all the permissions we need,
            //get the information about the pages that he or she managers
            $accounts = $facebook->api(
                '/me',
                'GET',
                array(
                    'access_token' => $access_token
                )
            );              
        } 
          else {
            //if not, let's redirect to the ALLOW page so we can get access
            //Create a login URL using the Facebook library's getLoginUrl() method
            $login_url_params = array(
                'scope' => 'manage_notifications,publish_stream,read_stream',
                'fbconnect' =>  1,
                'display'   =>  "page",
                'next' => 'http://'.$_SERVER['HTTP_HOST'].$_SERVER['REQUEST_URI']
            );
            $login_url = $facebook->getLoginUrl($login_url_params);
            //redirect to the login URL on facebook
            $facebook_login = $login_url;
             echo "<a href='$login_url'>Login Facebook</a>";