Full Idea
The modal syntax and axiom systems of C.I.Lewis (1918) were formally interpreted by Kripke and Hintikka (c.1965) who, using Z-F set theory, worked out model set-theoretical semantics for modal logics and quantified modal logics.
Clarification
Z-F stands for Zermelo-Fraenkel
Gist of Idea
The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s
Source
Dale Jacquette (Ontology [2002], Ch. 2)
Book Reference
Jacquette,Dale: 'Ontology' [Acumen 2002], p.70
A Reaction
A historical note. The big question is always 'who cares?' - to which the answer seems to be 'lots of people', if they are interested in precision in discourse, in artificial intelligence, and maybe even in metaphysics. Possible worlds started here.