Which very well fits how the vast majority of people subscribing to either have historically described themselves. In fact, admittedly cursory and sleep deprived scanning indicates the term "positive atheist" is younger than I (albeit not by much.)

Prescriptivism aside, "I do not know," is only "I do not know." If you claim knowledge rather than belief then, congratulations: You are an atheist, or "positive atheist," if you prefer; the definition fits both terms. However, that makes it untenable to claim a deity possible. Possibility and refuting evidence (i.e. knowledge there is no deity) cannot coexist. It is contradictory to say something is (not "may be," but IS) both false and possible; things known to be false are also impossible. Admitting Gods possibility therefore precludes stating His non-existence certain, and if it is uncertain we are dealing with agnosticism, not atheism.

According to the 2005 printing of The Encyclopedia of Philosophy, (though the definition has evidently been present since the first printing in 1967:)

According to the 1998 edition of the Routledge Encyclopedia of Philosophy:

"Positive" and "negative" atheism are canards, attempts to claim certainty without the insurmountable inconvenience of having to prove it. When was the last time you heard of a lawyer winning a case with a summation like, "I cannot prove the defendant innocent; his guilt is a possibility—but I KNOW he is innocent"? That is just the kind of bias that gets potential jurors eliminated from pools. Reasonable doubt requires demonstrating evidence of guilt is insufficient (which may be true without INVALIDATING the evidence;) otherwise it is UNreasonable doubt. Yet even reasonable doubt only exists to prevent errant penalties; to the extent the concept is relevant at all, it argues Pascals Wager is "reasonably" certain (though that wager remains wrongly motivated, IMHO.)

Note that substituting "believe" for "know" makes the statement less rather than more convincing. Of course he believes the defendant innocent, else he would have sought a plea bargain or avoided the case entirely, yet that establishes nothing but his extreme overestimation of his ability to prove his case. It makes him a poor defender, not a "negative" one. Believing ones estimate of the odds on Pascals Wager very good makes it no more certainty or less probability. Claiming an undefinable probability is not only high, but high enough to equal certainty, reflects an embarrassingly bad grasp of what "probability" means.

Likewise, "negative atheism" is a poor dodge. It is a case of atheists no longer insisting they have (impossibly) proven a negative, but treating it as proven while insisting they do not, incidentally arguing the far more numerous agnostics are really atheists. That makes as much sense as me telling agnostics who believe in a deity, spirituality or any supernatural phenomenon they are really "negative Christians." Y'know, like Muslims and Hindus are. It is similar to Mormons "posthumously baptizing" Jewish Holocaust victims into their religion; the only difference is that many agnostics are still around to refute the declaration they are atheists.

A small population inventing a meaningless term to obscure dogmatism and feign inclusiveness does not legitimize it, certainly not after a single generation that makes its usage uncommon outside their own ranks and not universal even among them. If I defined "Americans living in Norway" as "negative Martians," in defiance of logic and language, it would be absurd. That would remain true in 2040, even if half of them and ten percent of others used the term that way by then.