An operator (i.e. Something which if added to one or more propositions makes a (molecular) proposition) is non-truth-functional if and only if the truth value of a proposition in which it appears is not wholly determined by the truth value of the subsidiary propositions on which it operates. E. G. The truth value of "It is necessary that there are nine planets" and "It is believed that there are nine planets" is not determined by the truth value of "There are nine planets. " Hence the operators "It is believed that" are non-truth-functional operators. See truth-functional.