 Secondly, Carnap extended Tarski’s extensional semantics by a new intensional one, in which the truth values of sentences with operators creating intensional contexts (such as a sentential operator for necessity) can also be determined compositionally. Carnap’s invention of what would become “possible worlds semantics,” which he showed one could spell out in an extensional metalanguage, had a decisive influence on the development of modal logic and intensional semantics. Even though there are significant differences between modern “Kripke semantics” (which is rightly associated with Saul Kripke’s work), Carnap’s intensional semantics is still a possible worlds semantics in the sense that it evaluates formulas at possible worlds (“state-descriptions” in Carnap’s terminology), and the semantic rule for Carnap’s operator ‘N’ for (logical) necessity invokes universal quantification over worlds: \(N(A)\) holds in state-description s if and only if A holds in every state-description (see §41 of Meaning and Necessity; the differences and similarities to Kripke semantics are explained in detail in the supplement  Semantics (Section 1)).  On the side of theoretical linguistics, Richard Montague’s later intensional semantics for natural language built on Carnap’s semantics (see Partee 2011).