According to this article, http://www.ntdiscourse.org/2010/03/background-and-foreground-an-introduction/, "grounding" in discourse analysis refers to the difference between "core elements that advance a discourse [and] the peripheral elements that flesh it out," foregrounding pertaining to the former and backgrounding pertaining to the latter. For instance, in narrative, bits of discourse that denote events (e.g. George drove up the old driveway ...) that happen in temporal succession tend to be foregrounded, and bits of discourse that denote non-events (e.g. "... whose winding course reminded Milicent of a gargantuan dead snake") tend to be backgrounded.
Which, if any, natural languages have morphemes or syntactic construction that mark grounding specifically?