 to its nature as a logical atom.  

ok first off, if A is a term, it is a unit of syntax.
then when you talk of 'all A is X' or you talk of 'some A is not X'
I think you are mixing up syntax and semantics.
becasue A as a term can refer to individuals in the world.
(Are these called particulars?)
and it is those individuals that are X or not X.
the 'all' and 'some' quantifiers must semantically be referring
to those individuals. 
This is in contrast to the use of quantifiers as syntax.
In terms of syntax, I