Half day leaves are not possible yet, however "hourly absences" are our #1 priority for next big release
Please, follow it or vote for it on our Roadmap:
Workaround
As a workaround you could create a new vacation type like "Half day off" (make it a one time vacation type, without end date and without suggested days, remember to assign it to users - just by picking all users and setting up start date for this vacation type).
That vacation type would indicate (by its name) users request for a half of the day off. With new vacation type you would get access to its statistics, which then could be used to count, used by user, full days (number of documents / 2). Later on that number would need to be used to reduce number of available days from the original vacation type - please check out the screenshot (“Half day off.png”).
Reducing number of vacation days would require some additional work from the HR team (it could be done at the end of each month).
This could cover most of the usecaseses (at least for now).
Stay tuned!