IDP Local Logout behaviour question

[Peter Schober]

* Byte Flinger <byteflinger at gmail.com> [2013-11-13 09:43]:
> We are currently using Shibboleth's IDP local logout functionality
> (/idp/profile/Logout) and it was out understanding that once the user goes
> to that address the session gets destroyed on Shibboleth side and also the
> cookie get removed on the user's browser.

I don't know wheather it's meant to overwrite the HTTP Cookie but is
that even relevant when the session corresponding to that Cookie is gone?
-peter