From Facebook Developer Wiki

You can use this tag to determine if your canvas is being viewed publicly or not.

e.g.

<fb:is-logged-out>
  Please sign up to use this application with your friends.
<fb:else>
  Welcome valued user!
</fb:else>
</fb:is-logged-out>

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This doesn't appear to be determining public/non-public viewing status but instead it shows if the user has authorized/logged into the app.

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I second that -- I'm trying to distinguish between the following three cases: 1. anonymous user, not logged into Facebook, accesses an application page 2. user, logged into Facebook but hasn't given the app authorization, accesses an application page 3. user of the application (has given it authorization already) accesses the application page

I was hoping this tag would distinguish between cases (1) and (2), but apparently it doesn't.

How about using Fb:if-is-app-user? Also, check out Authorizing_Applications#Parameters_Passed_to_Your_Application. You can determine 2 by looking for the fb_sig_canvas_user parameter, and 3 by looking for fb_sig_user, tho these parameters are only passed when a user arrives at your application from a link within facebook.com and provided the user's privacy settings allow the user to be seen. I'll confirm this next, but wouldn't the absence of any parameters indicate your first use case? -- Pete (User:563683308)