The extension we make to the general framework presented above in order to include discourse adverbials as discourse anaphors is to allow more general functions f α to be associated with lexically specified anaphors.
for the discourse adverbials considered in this article, the function associated with an adverbial maps its anaphoric argument-an eventuality derived from the current discourse context-to a function that applies to the interpretation of the adverbial's matrix clause (itself an eventuality).