This is not about the way you fight with a spouse, (mostly) it is about a classification of the arguments themselves. Better minds than mine have devoted much more time to this; and for my part, I have ignored them. I will only be covering tactics and methods used in discussions, not sales tactics, and not actual violence. Instead I present a half-assed overview of the way people try to make a point, or perform stage magic. More on that in a bit.
First, we will present the Mathematical Argument. A+B=C. This is also referred to as "Reason" It is the most rare and precious of arguments. Never seen in the wild, and only a few examples exist in captivity, in the groves of academia. The reason being that if your argument is so easily proved, you normally don't have to make it at all.
A close cousin is the False Mathematical Argument. These are typically multi-step equations, that introduce an error, that may go unnoticed. This is not necessarily intentional.
Next is the Geometric Proof. It begins with items which are "Given". Based on those, other items are Proven. (http://www.cliffsnotes.com/study_guide/Testing-for-Parallel-Lines.topicArticleId-18851,articleId-18780.html) (for example). This argument, which is also fact based, is almost as rare as the Mathematical Argument.
This brings us to the False Geometric Proof. It follows the same methodology as the Geometric Proof, but begins with assumptions, rather than facts. It can be hard to identify since the false assumption can be shared by both parties and it superficially resembles...
Circular Reasoning. The difference is that in circular reasoning, the loop is closed. A cunning debater can even use so large of a circle that it no longer seems round, and the other party quite forgets that A proved B, which proved C, and so on,... and therefore Z proves A, cannot possibly be correct.
We have now seen the two types of reasoning, and three types of false reasoning. We will now examine the stage magic. Each of these types of argument are designed to make you look elsewhere, so you forget what the point of the argument was. This is broadly termed, "Derailing".
The Emotional Plea: This is the one most used by politicians and other weak-minded imbeciles, who do not want you to examine the facts. (See Mathematical Argument, above) There is typically tears, imagery, or both, involved. This takes advantage of the strong emotional response most people have toward certain topics. It is designed to make the facts appear irrelevant.
Next up is the Attack. This tactic is as simple as it is effective. It involves berating the other party about anything and everything in general, to distract them from the point being discussed. This is also known as Arguing like a Man. It is designed to make you forget the point of the discussion.
Then we have the Dredging Tactic. In this tactic one party brings up a time in the past when the other party was wrong, in order to "Prove" they are wrong now. It need not be related, or even have been previously discussed. Also, the second party need not even have been wrong. They will normally be so blindsided by this tactic as to concede the point being dredged up, just to see where the discussion is headed. This is also known as Arguing like a Woman. It is designed to change the point of the argument.
Next is Button Pushing. This can only be used when at least one party has intimate knowledge of the other's points of irritation. It is another derailing tactic, and the lowest of all of them, as there is no premise of ever trying to make a point. Much like the Emotional Plea, it is designed to make you forget about the argument that was begun.
I will close with the Forced Agreement. This employs the same method as Button pushing, but leads one party to a point where both agree. At this point one of the other methods is introduced to convince the second party that despite appearances, they actually agree. This, most insidious of arguments, can be employed whether there is actual agreement or not. It cannot be used by itself.
There are more, so feel free to add some in the comments. Please though, keep it clean, no personal attacks, and above all, well reasoned. In this case please also insure that you are not just calling a tactic a different name. Thanks, and happy arguing.
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Keep it clean and well thought out.