  That is, a sentence is possible just in case its negation isn't  necessary. Since, semantically speaking, the necessity  operator is literally a universal quantifier, the definition corresponds exactly to the definition   (7)  of the existential quantifier. For, unpacking the right side of  definition (10) according to the negation and necessitation clauses above (and invoking the definitions of truth and truth at a world simpliciter), we have: 