A young boy and his dog lay together on the floor.
A young boy with his dog.
As a young boy and his dog lay together on the floor, it means that the  young boy must be with his dog.
exists e1 s1 s2 x1 x2 x3 x4.(n_floor(x4) & a_together(s2) & Manner(e1,s2) & on(e1,x4) & Actor(e1,x1) & v_lay(e1) & subset_of(x3,x1) & n_dog(x3) & of(x3,x2) & n_male(x2) & subset_of(x2,x1) & n_boy(x2) & a_young(s1) & Theme(s1,x2))
exists s1 x1 x2.(a_topic(x1) & with(x1,x2) & n_dog(x2) & of(x2,x1) & n_male(x1) & n_boy(x1) & a_young(s1) & Theme(s1,x1))