A Method to Determine the Expressive Power of a Set of Connectives

If a set of connectives is not functionally complete, then there is no simple way of deciding whether or not an arbitrary truth-function is expressible by a proposition-letter formula which has only the connectives in this set. In order to assert that a set of connectives is not complete with respect to a particular truth-function, it is often necessary to give a formal proof by some inductive argument. To come up with such an inductive argument is not always easy. An algorithm by which the expressive power of a set of connectives may be determined is described.