Argument and rhetoric is a whole field of study. Prof. David Zarefsky at Northwestern has a good set of lectures on the subject which are on Amazon. The outline is here: http://thefulldialectician.synthasite.com/resources/ZAREFSKY...

My exposure to the subject has been in the legal context. This is a popular textbook on legal argumentation: Gardner, Legal Argument: The Structure and Language of Effective Advocacy. Someone has an older edition for cheap on EBay: http://www.ebay.com/itm/LEGAL-ARGUMENT-THE-STRUCTURE-AN-/310.... The text is quite general, not all that specific to the legal context.

Thanks very much! I'll definitely look into these.