The big dog is carrying an object is its mouth.
The dog carried the object back to it's owner.
Carrying an object is its mouth doesn't mean it is for the owner.
exists e1 p1 s1 x1 x2 x3 x4.(n_mouth(x4) & of(x4,x1) & n_thing(x1) & n_dog(x1) & a_big(s1) & Theme(s1,x1) & Theme(e1,x2) & Actor(e1,x1) & v_carry(e1) & (x3 = x4) & (x2 = x3) & n_object(x2))
exists e1 p1 x1 x2 x3 x4.(n_thing(x2) & n_object(x2) & n_dog(x1) & Theme(e1,x2) & Actor(e1,x1) & v_carry(e1) & exists x5.((x4 = x5) & n_owner(x5)) & (x2 = x4) & to(x3,x2) & back(x2,x3) & n_thing(x3))