A man with his young children.
They are a family.
Sentence 1 states a man with his young children doesn't logically imply they are a family. This is not  a logical implication.
exists s1 x1 x2.(a_topic(x1) & with(x1,x2) & n_child(x2) & a_young(s1) & Theme(s1,x2) & of(x2,x1) & n_male(x1) & n_man(x1))
exists p1 x1.(n_thing(x1) & exists x2.((x1 = x2) & n_family(x2)))