Infinitary Expressibility of Necessity in Terms of Contingency

This paper consists of two parts. In the first part we present an axiomatization of the “epistemic” modal logic KD45 in the language with noncontingency operator as the sole modal primitive symbol. The second part, having a certain philosophical flavour, is devoted to the old question about the possibility of defining the necessity operator in terms of the contingency operator. Here we give a new, positive answer to this question by constructing an infinitary operator defined in terms of contingency which behaves like some necessity.