A man and woman with a dog.
A dog with people.
People refers to more than one person, such as a man and a woman. If a man and a woman are with a dog, then that dog is with people.
exists s1 x1 x2 x3.(a_topic(s1) & with(s1,x3) & n_dog(x3) & n_woman(x2) & n_man(x1) & subset_of(x2,s1) & subset_of(x1,s1))
exists x1 x2.(a_topic(x1) & with(x1,x2) & n_people(x2) & n_dog(x1))