A man looking for something possibly left by the horse.
horse dropped its shoe
A man looking for something left by the horse does not mean it dropped its shoe.
exists e1 e2 s1 x1 x2 x3 x4.(n_horse(x4) & Actor(e2,x4) & Theme(e2,x1) & v_leave(e2) & a_possibly(s1) & Manner(e1,s1) & for(e1,x3) & n_thing(x3) & Actor(e1,x2) & v_look(e1) & (x1 = x2) & n_man(x1))
exists e1 x1 x2.(Theme(e1,x2) & Actor(e1,x1) & v_drop(e1) & n_shoe(x2) & of(x2,x1) & n_thing(x1) & n_horse(x1))