All you need to do is allow half day absences and set the half day point in your absence settings - go to Account Settings from the last icon in your tool bar and then on to Absence Settings.
The half day point splits the absence day into two 12 hour periods - if your half day point is at 12:00, your absence day starts at 00:00. If your half day point is at 13:00, the absence day starts at 01:00 etc.
Once you've fixed these settings, you can make an absence start or end at half day when creating it.
Remember - if you have any additional questions or issues at all, you can always shoot us an email at firstname.lastname@example.org - we're here for you!