A young girl is sitting at a table writing.
A girl is doing her English homework before a roaring fire.
Sentence 1 does not indicate that the girl at the table is writing any kind of homework, or if she's near a roaring fire.
exists e1 s1 x1 x2 x3.(at(e1,x2) & n_writing(x2) & of(x2,x3) & n_table(x3) & Actor(e1,x1) & v_sit(e1) & n_girl(x1) & a_young(s1) & Theme(s1,x1))
exists e1 s1 x1 x2 x3 x4.(before(e1,x3) & n_fire(x3) & of(x3,x4) & n_roaring(x4) & Theme(e1,x2) & Actor(e1,x1) & v_do(e1) & n_homework(x2) & a_english(s1) & Theme(s1,x2) & of(x2,x1) & n_female(x1) & n_girl(x1))