1. To accept that something is virtually certain to be correct even though there is no proof of it on the grounds that it is extremely likely; to expect; to think to be a fact: Agatha assumed, supposed, or presumed that her children were at school since it was Monday and not Sunday!

Since Mark's firm is prosperous and his work has been very good, he presumes that he will be getting a raise very soon.
2. To behave so inconsiderably, disrespectfully, or over confidently as to do something without being entitled or qualified to do it; usually used in a negative sense: Sarah's fiancé presumed to be very important, bold, and shameless in her mother's home!