Is there such a thing as a half day sick leave?

i landed up with severe neck pain and spasms due to a mechanical arthritis from a car accident so i left to see the Dr at 1pm. 

i also had the next day off for treatment. 

My HR /bookkeeper wont accept the Dr note, she says it doesn't say i am unfit for work so i could have worked, it just says i am off for treatment. 

then the day i worked until 1pm, she is taking as half day sick. 

another day i went to the dentist for an emergency and came to work 1hr 20min late. with a doctors note saying it was urgent. she is taking 1,5 hours off my salary.

my colleague has just found out that she is pregnant. 

she is 4 months, and went to see a Dr in a state clinic- she has not got medical aid. 

on returning with  the doctors note, from the state clinic to check on the pregnancy ...the note was not accepted, the HR is taking it off her salary. because the note does not say that she is unfit for work. 

please can someone shed some light on this.