A man sitting on the back of a truck underneath an umbrella.
a guy on the back of a truck waiting to go home
There is no mention of the man's purpose so one cannot assume he is waiting to go home.
exists e1 x1 x2 x3 x4 x5.(n_back(x3) & a_topic(x1) & on(e1,x3) & of(x3,x4) & underneath(x4,x5) & n_umbrella(x5) & n_truck(x4) & Actor(e1,x2) & v_sit(e1) & (x1 = x2) & n_man(x1))
exists e1 p1 x1 x2 x3 x4.(n_back(x2) & a_topic(x1) & on(x1,x2) & of(x2,x3) & Topic(e1,p1) & Actor(e1,x4) & v_wait(e1) & exists e2 x5.(Theme(e2,x5) & Actor(e2,x4) & v_go(e2) & n_home(x5)) & (x3 = x4) & n_truck(x3) & n_guy(x1))