shibboleth SP logout question

[Sam Jacob]

we implemented the Shibboleth.sso/Logout
but have a question:
1. user logs out of SP application and calls Shibboleth.sso/Logout
2. then user logs out of the single-sign on ,ie. iDP logout
3. close the browser
 Can the user still access the SP application if logged out of iDP?
 if the user can still access the SP application without logging into iDP
(after iDP logout) , what will be the reason for that ?

does SP has any control on the iDP session , or is it iDP's  responsibility
to expire or remove the cookie on iDP logout?

thanks
-- 
Sam Jacob
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