The notion of grounded truth has been very prominent in recent work on formal truth theories as it oers a philosophically justied way to evade the Liar paradox. We first discuss a novel way to construe the notion of groundedness and compare that to Kripke's and Leitgeb's notions of grounded truth. We offer a formalisation for this notion of groundedness that relies on an intensional semantics given by inverse systems with limit. We nally discuss the type of truth theory that such formalisations give rise to