Considering facebook application is to be developed in PHP, which PHP framework (code igniter, Yii, cake php etc.) would you use?
None. I'd core-code it. I'm not a fan of frame-works, instead of actually simplifying things, they complicate things.
I wouldn't use a framework for that. Considering that facebook has a really nice API and an SDK for development - I would write my own framework.
But that's just my opinion.
well it also depends on the what scale you are building your FB app
for small app i would not consider any framework
but if the app is big then i will prefer codeigniter or Zend framework