A man with a red hat holding up one finger.
The man is wearing a red hat.
To say "with a red hat" generally implies that a man is wearing a red hat.
exists e1 s1 s2 x1 x2 x3 x4.(a_topic(x1) & with(x1,x2) & a_up(s2) & Manner(e1,s2) & Theme(e1,x4) & Actor(e1,x3) & v_hold(e1) & n_finger(x4) & card_eq_1(x4) & (x2 = x3) & n_hat(x2) & a_red(s1) & Theme(s1,x2) & n_man(x1))
exists e1 s1 x1 x2.(n_man(x1) & Theme(e1,x2) & Actor(e1,x1) & v_wear(e1) & n_hat(x2) & a_red(s1) & Theme(s1,x2))