Log File?

Our company is deciding whether to choose Postgresql or not and
have a question. Say we back up our database every night and the
next day at 11am, the hard drive crashes. We then have data from
our back up from last night, but, is there a way to have a log file sitting
somewhere
other than the hard drive that will allow us to retrieve all data
from that morning and add that data to the back up? Therefore, we
will have only lost the trasaction that we would have been working
on because it has not been commited. Any answer would be extremely helpful.