Could you define a " half figure " in art ?

Answer 1

You mean this?
http://www.lib.iastate.edu/spcl/gwc/images/bust.jpg
It is called a bust.
If it is missing at least some part of the legs ... say knees down ... you'd call it a bust.

Also a bust:
http://www.nataliegreen.com/oldsite/img/dr_bust.jpg