Modal definability in Kripke's theory of truth

In Outline of a Theory of Truth, Kripke introduces some of the central concepts of the logical study of truth and paradox. He informally defines some of these – such as groundedness and paradoxicality – using modal locutions. We introduce a modal language for regimenting these informal definitions. Though groundedness and paradoxicality are expressible in the modal language, we prove that intrinsicality – which Kripke emphasizes but does not define modally – is not. We characterize the modally definable relations and completely axiomatize the modal semantics.