The brown and white dog is running to catch something.
The dog runs through the field to catch a stick.
The dog is not necessarily running through a field and the something he is trying to catch may not be a stick.
exists e1 p1 s1 s2 s3 s4 x1.(n_dog(x1) & a_white(s4) & Theme(s4,x1) & a_brown(s3) & Theme(s3,x1) & a_white(s2) & Theme(s2,x1) & a_brown(s1) & Theme(s1,x1) & Topic(e1,p1) & exists e2 x2.(Theme(e2,x2) & Actor(e2,x1) & v_catch(e2) & n_thing(x2)) & Actor(e1,x1) & v_run(e1))
exists e1 p1 x1 x2.(n_field(x2) & n_dog(x1) & Topic(e1,p1) & exists e2 x3.(Theme(e2,x3) & Actor(e2,x1) & v_catch(e2) & n_stick(x3)) & through(e1,x2) & Actor(e1,x1) & v_run(e1))