Declarative processing : a person argues his or her position by bringing forward a number of separate reasons for it. The reasons are separate in the sense that each is brought forward individually, on its own, and no connection is made with any of the other reasons: for example “Here’s is one reason for my idea, here’s another, I could give you others as well.” This method of processing has a disjunctive, declarative quality.
Cumulative processing: a person argues his or her position by bringing together a
number of different ideas, none of which is sufficient to make the case, but taken together they do; for example, a detective might argue, “If you take this first point (clue), and put it together with these three other items we have observed, then it becomes clear that such-and-such has occurred. “This method of processing has a pulled-together, conjunctive quality.
Serial processing: a person argues his or her position by constructing a line of thought made up of a sequence of reasons, each one of which leads on to the next, thus creating a chain of linked reasons; for example, “I would do A because it would lead to B, and B will lead to C, and C would lead on to where we want to get”. This method of processing had a conditional quality in the sense that each reason in the series sets the conditions that lead to the next reason.
a person argues his or her position by examining a number of possible positions as well, each arrived at by means of serial processing. The several lines of thought are held in parallel and can be linked to each other. It becomes possible to take useful points from less favored positions to bolster up a favored one. This method of processing has a double conditional quality, in the sense that the various scenarii are not only linked with each other, but they can condition each other as well.
Elliott Jacques (Requisite Organizations)