 K is a fundamental principle common to all the modal logics we will survey here: if a conditional is necessary, then its consequent is necessary if its antecedent is. T expresses that necessity implies truth, and 5 expresses that what is possible is not a mere matter of happenstance; no possibility could have turned out to be impossible; or again: what is possible in the actual world is possible in every world. The basic normal deductive system K is the result of adding (every instance of) K and the rule of Necessitation to PL; the system T is the result of adding all instances of T to K; and the system S5 is the result of adding all instances of 5 to  T.[39]