A man with a beard sits on a bench with a cloak and fancy hat.
While wearing a fancy hat and cloak sits on a bench stroking his beard
Both sentences say that person is sitting on bench.  The first sentence says that the man has a beard and has a cloak and fancy hat.  Having a cloak and fancy hat is one way of saying that these items are being worn, which is what is stated in the second sentence.
exists e1 s1 x1 x2 x3 x4 x5 x6.(with(e1,x4) & n_hat(x6) & a_fancy(s1) & Theme(s1,x6) & n_cloak(x5) & subset_of(x6,x4) & subset_of(x5,x4) & on(e1,x3) & n_bench(x3) & Actor(e1,x1) & v_sit(e1) & with(x1,x2) & n_beard(x2) & n_man(x1))
exists e3 e1 e2 s1 x1 x2 x3 x4 x5.(for(e2,e3) & Theme(e3,x5) & Actor(e3,x3) & v_stroke(e3) & n_beard(x5) & of(x5,x1) & n_male(x1) & while(e2,e1) & on(e2,x4) & n_bench(x4) & Actor(e2,x3) & v_sit(e2) & n_cloak(x3) & Theme(e1,x2) & Actor(e1,x1) & v_wear(e1) & n_hat(x2) & a_fancy(s1) & Theme(s1,x2) & n_thing(x1))