Without stating reasons for demanding resignation, as rightly pointed out, any advice would be futile. As a true HR professional, you should examine the propriety of demanding resignation. Your query of whether to pay half salary or not is misconceived without the proper knowledge of terms of employment and grounds for resignation/termination.
I am getting the impression that you are doing what you have been told to do without sharing your mind on the issue. Maybe I am wrong, but you have to advise the management on the right action arising from your own conviction supported by legality, ethics, and best practice. Remember, HR is the 'conscience keeper' of the organization.
Regards, Vinayak Nagarkar HR Consultant