An approach that is perhaps better aligned with the across-topics setting is to notice that in detailing one's arguments, one tends to utilize a specially structured discourse, and that discourse role could provide a clue to the argumentative function of a sentence, without reliance on what the sentence is actually saying (beyond discourse connectives that are used to help identify the discourse role).
argumentative essays often have a fairly standard structure, where a general claim (or stance, or thesis) on the issue is introduced in the beginning of the essay, followed by a sequence of main points, each elaborated using supporting statements, and finally followed by a conclusion that often re-states the thesis and provides a high-level summary of the argument.