People in black hats gathered together downtown.
The people are part of the same group.
Just because people in black hats gathered toget, it doesn't mean they are of the same group.
exists e1 s1 s2 x1 x2 x3.(a_together(s2) & Manner(e1,s2) & Theme(e1,x3) & Actor(e1,x1) & v_gather(e1) & n_downtown(x3) & in(x1,x2) & n_hat(x2) & a_black(s1) & Theme(s1,x2) & n_people(x1))
exists p1 s1 x1 x3.(n_group(x3) & a_same(s1) & Theme(s1,x3) & n_people(x1) & exists x2.((x1 = x2) & of(x2,x3) & n_part(x2)))