The young girl is running on a sandy beach.
a girl is running on a beach with her dog
Because a person is running on the beach does not necessarily mean she is with her dog.
exists e1 s1 s2 x1 x2.(n_girl(x1) & a_young(s1) & Theme(s1,x1) & on(e1,x2) & n_beach(x2) & a_sandy(s2) & Theme(s2,x2) & Actor(e1,x1) & v_run(e1))
exists e1 x1 x2 x3.(with(e1,x3) & n_dog(x3) & of(x3,x1) & n_female(x1) & on(e1,x2) & n_beach(x2) & Actor(e1,x1) & v_run(e1) & n_girl(x1))