You can log people out of your app by attaching the JavaScript SDK function FB.logout to a button or a link, as follows:
Note: This function call may also log the person out of Facebook. Consider the 3 scenarios below:
1. A person logs into Facebook, then logs into your app. Upon logging out from your app, the person is still logged into Facebook.
2. A person logs into your app and into Facebook as part of your app's login flow. Upon logging out from your app, the user is also logged out of Facebook.
3. A person logs into another app and into Facebook as part of the other app's login flow, then logs into your app. Upon logging out from either app, the user is logged out of Facebook.
Additionally, logging out is not the same as revoking login permission (removing previously granted authentication), which can be performed separately. Because of this your app should be built in such a way that it doesn't automatically force people who have logged out back to the Login dialog.