Higher Order Predicate Logic :
In the very first order predicate logic, we are only allowed to quantify over objects. If we are considered to allow ourselves to quantify over predicate or function symbols, then we have to moved up to the very much expressive higher order predicate logic. Because of that we can represent meta-level information about our knowledge, just like as: "For all the functions we've specified, they return the number 10 if the number 7 is input":
∀ f, (f(7) = 10).