This is less a category of logic and more of a general technique that can be applied to nearly every other type of reasoning. Traditional logic is the use of premises that are generally accepted by both parties or society as a whole, and then using purely logical methods to form a conclusion.
Traditional reasoning is going to be brought up multiple times as we explore the different types of reasoning, and appealing to something that has already been settled can serve as a handy tool for shortening the amount of time spent arguing and reducing the amount of opposition, so it is important for you to be able to discern when it is appropriate to use.
Of course, it only works when both parties agree on the validity of the premises. It can only be used when there is a true common context for the two parties involved to work from. Avoid appealing to assumptions when you don’t have common ground on the issue with your opponent as it can reduce your reputability in their eyes and cause even more fierce opposition.