Sorry, this is such a ridiculous response that I feel the need to butt in instead of leaving it to RoboTimbo.
First of all, he didn't even begin to suggest that everything has an opposite.
Second, "is true" and "is false" are opposites, and there are no other positions which count as being exactly opposite of them.
Theism: It is true that I believe God exists.
Atheism: It is false that I believe God exists.
Gnostic: It is true that I know whether or not God exists.
Agnostic: It is false that I know whether or not God exists.
Atheism and agnosticism are positions on two separate questions.
1. You can present a problem with binary classifications based on opposites or not.
1.1. They are different ways to represent.
1.2. Classifications are not true, but useful.
2. My classification is not binary.
2.1. My first criterion is the belief in gods (or to affirm that gods exist).
2.1.2. Atheists don’t believe in gods; theists believe in gods; agnostics neither affirm nor deny that gods exist (they neither believe nor disbelieve).
2.2. My second criterion is rational justification.
2.2.1. Rationalists think their belief can be rationally justified; irrationalists think their belief cannot be rationally justified.
3. My classification and yours (with the criteria of knowledge and belief) are similar.
4. Your classification is useful because is easy to understand.
5. My classification is useful because…
5.1. It fits correctly with scholars’ uses of the words “atheist” and “agnostic”. I have presented some examples of this.
5.2. It introduces more nuances. (My classification includes six possible categories; yours only four). For example, the refraining of judgement, that is a relevant feature of historic agnosticism, is not well reflected in your classification.
6. The debate in this forum takes place because some members have a dogmatic position.
6.1. They think that their classification is the only possible or excludes other alternatives.
6.2. They think that a simple change of names can revolutionize the whole history of ideas and solve some complex problems.
6.3. They are unable to put themselves in the place of the opponent. This is evident by their reluctance to answer some “compromising questions”.
7. The problem of classifications is not a big problem, except if a classification is used to mask an ideology.
7.1. I don’t think this is my case, because I offer a classification where all the categories are included, even AA, GA, AT and GT of your classification.
7.2. The resistance to admit so is surely due to a hidden agenda that I don’t completely understand.
7.3. Some insults that begin to be used here are much less understandable to me. Be calm, please. This is only a forum.