A singer on stage singing to fans.
The singer is singing to nobody.
The singer is either singing to fans or to nobody.
exists e1 x1 x2 x3 x4.(a_topic(x1) & on(x1,x2) & to(e1,x4) & n_fan(x4) & Actor(e1,x3) & v_sing(e1) & (x2 = x3) & n_stage(x2) & n_singer(x1))
exists e1 x1.(n_singer(x1) & -exists x2.(to(e1,x2) & n_person(x2)) & Actor(e1,x1) & v_sing(e1))