A little girl with a pink headband is riding a horse past a fence.
the girl is riding horseback by the fence on her birthday
There is nothing in sentence 1 to imply that this is the girl's birthday. A girl could ride a horse with a pink headband on any other day too.
exists e1 s1 s2 x1 x2 x3 x4.(past(e1,x4) & n_fence(x4) & Theme(e1,x3) & Actor(e1,x1) & v_ride(e1) & n_horse(x3) & with(x1,x2) & n_headband(x2) & a_pink(s2) & Theme(s2,x2) & n_girl(x1) & a_little(s1) & Theme(s1,x1))
exists e1 x1 x2 x3 x4.(n_birthday(x4) & of(x4,x3) & n_female(x3) & n_fence(x3) & n_girl(x1) & on(e1,x4) & by(e1,x3) & Theme(e1,x2) & Actor(e1,x1) & v_ride(e1) & n_horseback(x2))