Clarification

are you saying you're switching from a session variable to a cookie?

delete the cookie altogether by setting the expiration to a time in the past (negative value). don't forget that you'll then have to reload a page in order to reread the cookie data.

so if you have a cookie with a logged_in value = true, and you set it to logged_in value = false, you're still logged_in = true, until you reload that page (or another page) and it rereads the cookie data and now determines that logged_in = false.

make sense? write the logged_in=false to the cookie, then force a url redirection to reload the page is my suggestion.