The dog plays with a purple toy near a cat.
The dog is playing near the cat.
The dog is playing in both sentences. We can assume he's playing with the purple toy in sentence 2 as well.
exists e1 s1 x1 x2 x3.(n_dog(x1) & with(e1,x2) & near(x2,x3) & n_cat(x3) & n_toy(x2) & a_purple(s1) & Theme(s1,x2) & Actor(e1,x1) & v_play(e1))
exists e1 x1 x2.(n_cat(x2) & n_dog(x1) & near(e1,x2) & Actor(e1,x1) & v_play(e1))