A woman walking with 4 kids.
The kids are walking the woman.
A woman walking with 4 kids doesn't mean that the kids, too, are walking. She may be pulling them behind her in a wagon or maybe they are running circles around her while she walks.
exists e1 x1 x2 x3.(a_topic(x1) & with(e1,x3) & n_kid(x3) & n_date(x3) & a_date_day_04(x3) & a_date_day_04(x3) & Actor(e1,x2) & v_walk(e1) & (x1 = x2) & n_woman(x1))
exists e1 x1 x2.(n_woman(x2) & n_kid(x1) & Theme(e1,x2) & Actor(e1,x1) & v_walk(e1))