The woman is holding the harness that the brown and white dog is wearing.
The woman is walking the brown and white dog.
Holding the harness doesn't necessarily imply that the woman is walking the dog.
exists e1 p1 s1 s2 x1 x2 x3.(Topic(x2,p1) & exists e2.(Actor(e2,x3) & v_wear(e2)) & n_dog(x3) & a_white(s2) & Theme(s2,x3) & a_brown(s1) & Theme(s1,x3) & n_harness(x2) & n_woman(x1) & Theme(e1,x2) & Actor(e1,x1) & v_hold(e1))
exists e1 s1 s2 x1 x2.(n_dog(x2) & a_white(s2) & Theme(s2,x2) & a_brown(s1) & Theme(s1,x2) & n_woman(x1) & Theme(e1,x2) & Actor(e1,x1) & v_walk(e1))