Children dig through dirt.
children dig via their hands
Dig through dirt does not specifically refer to digging via their hands.
exists x1 x2 x3.(a_topic(x1) & through(x1,x3) & n_dirt(x3) & n_dig(x1) & (x1 = x2) & ne_nam_children(x2))
exists e1 x1 x2.(via(e1,x2) & n_hand(x2) & of(x2,x1) & n_thing(x1) & Actor(e1,x1) & v_dig(e1) & n_child(x1))