A black dog is in midair as a woman behind it cheers.
A woman watches a dog catch the frisbee in midair
The first sentence does not imply that the reason the dog is in midair is to catch the frisbee.
exists p1 p2 s1 x1.(exists e1 x3.(Actor(e1,x3) & v_cheer(e1) & behind(x3,x1) & n_woman(x3)) & n_thing(x1) & as(p1,p2) & exists x2.(in(x1,x2) & n_midair(x2)) & n_dog(x1) & a_black(s1) & Theme(s1,x1))
exists e1 x1 x2 x3 x4 x5 x6 x7.(Theme(e1,x5) & Actor(e1,x1) & v_watch(e1) & n_frisbee(x7) & (x5 = x7) & n_catch(x5) & of(x5,x6) & n_dog(x6) & in(x3,x2) & n_catch(x3) & of(x3,x4) & n_dog(x4) & n_midair(x2) & n_woman(x1))