Full Idea
C.I.Lewis's S4 system develops a sense of necessity as 'provability' in some fairly informal sense.
Gist of Idea
Equating necessity with informal provability is the S4 conception of necessity
Source
report of C.I. Lewis (works [1935]) by Stephen Read - Thinking About Logic Ch. 4
Book Reference
Read,Stephen: 'Thinking About Logic' [OUP 1995], p.118