Modal logic proper enables possible worlds semantics
In modal logics, the meaning of a sentence does not only depend on the current world, but also on related related worlds. Modal logic proper introduces two modal operators: necessity and possibility. Kripke’s key idea was that accessibility relations reflect relative possibility. Inductive truth definitions are very similar for modal logic proper compared to propositional logic if you only consider one world. Validity requires designated values for all models in all worlds at once.