A man in a cowboy hat rides a horse.
There's a man riding a horse and he has a hat on.
The cowboy hat could be anything and doesn't have to be that he has a hat on.
exists e1 x1 x2 x3 x4.(Theme(e1,x4) & Actor(e1,x1) & v_ride(e1) & n_horse(x4) & in(x1,x2) & n_hat(x2) & of(x2,x3) & n_cowboy(x3) & n_man(x1))
exists e1 p1 s1 x1 x2 x3.(n_male(x2) & a_on(s1) & Manner(e1,s1) & Theme(e1,x3) & Actor(e1,x2) & v_have(e1) & n_hat(x3) & exists e2 x4 x5 x6.((x1 = x4) & Theme(e2,x6) & Actor(e2,x5) & v_ride(e2) & n_horse(x6) & (x4 = x5) & n_man(x4)))