 In the 1932 Appendix C.I. Lewis introduces five different systems. The modal primitive symbol is now the operator of possibility \(\Diamond\), strict implication \((p\Rightarrow q)\) is defined as \(\neg \Diamond(p\wedge \neg q)\), and \(\vee\) is ordinary extensional disjunction. The necessity operator \(\Box\) can also be introduced and defined, though Lewis does not, in the usual way as \(\neg \Diamond \neg\).