The woman is holding the harness that the brown and white dog is wearing.
The man is walking a dog.
It can be either the woman or the man. Holding the dogs with the harness and walking a dog are different actions.
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 x1 x2.(n_man(x1) & Theme(e1,x2) & Actor(e1,x1) & v_walk(e1) & n_dog(x2))