People are crossing a busy street at night.
people crossing the street across their home
There is nothing about the people crossing the street at night to imply that the street is across from their home. With the qualification "across their home" there is information as to the relationship of the people, as "their home" implies they are part of the same family.
exists e1 s1 x1 x2 x3.(at(e1,x3) & n_night(x3) & Theme(e1,x2) & Actor(e1,x1) & v_cross(e1) & n_street(x2) & a_busy(s1) & Theme(s1,x2) & n_people(x1))
exists e1 x1 x2 x3 x4.(n_home(x4) & of(x4,x3) & n_thing(x3) & n_street(x3) & a_topic(x1) & across(e1,x4) & Theme(e1,x3) & Actor(e1,x2) & v_cross(e1) & (x1 = x2) & n_people(x1))