@Interlocutor: Atheists Actually Believe In God

Yes. I believe in the oh god of orgasms and hangovers. I also believe in the oh god of terminal boredom trying to sift through a disjointed and meandering collection of non sequiturs.

Otherwise, nope.

Is it safe to assume then that Christians actually believe in Odin, even though they claim not to?
Or Ra?
Or Vishnu?
Or Lolth?
Or Morgoth?
Etc, etc, etc...

@The Interlocutor -
Since every definition and usage of the word "Atheist" that I have ever come across specifically applies to those people who disbelieve in or deny the existence of deities, this renders your thread title (and premise) abjectly void of soundness. Unless, of course, you are completely bastardizing the meaning of the word, and purposefully ignoring everyone else's usage of the word for your own devices. In which case - who cares? Whatever you're calling "atheist" isn't me, because I don't believe that God exists due to a complete lack of compelling evidence, and the horrid, confusing, shit-stained state of the evidence that does exist. I can't claim that I know for sure that He doesn't exist, but I hold no positive belief in His existence whatsoever. Whatever you want to call that, that's what I am. Whatever other thing you want to construct and label "atheist" - all I can say is, good luck with that. Based on this kind of "semantic circus" kind of activity, I don't believe it worth my time to read anything you've written.

My article is based on a standard evidentialist epistemology in aced mic philosophy

In short, it's a sophomoric outing into an arena regarded as troublesome by far greater minds than yours.

It can be basically summed up as the following:

This is going to be interesting ...

Based on the laws of logic - and particularly the logical law of excluded middle

Actually, the term "excluded middle" is better known to many here as the name of a logical fallacy, as covered here.

we only have a proposition (P) and its negation/opposite (~p) - no in between. So a proposition is either P or ~P. For example:

P: There is an apple on my desk.
--OR--
~P: There is NO apple on my desk.

Which fails to be rigorous, because it fails to state precisely the number of apples involved. There is merely a presumption in your above construction of P, that we are dealing with one apple. P fails to constitute an exclusive proposition, because it will also be true, as it stands, if there are three apples on your desk.

However, the moment we start specifying number precisely, you fall foul of the excluded middle fallacy, because doing so would re-cast your propositions as:

P: There is precisely one apple resting upon my desk;

~P : There is not precisely one apple resting upon my desk.

In this case, ~P is true for zero, two, three or more apples, and only false for one apple.

To remedy this situation, you end up needing two uncoupled propositions:

P : There is precisely one apple residing on my desk;

Q : There are precisely zero apples residing on my desk.

At which point, you need to provide a whole family of numerically precise propositions to encapsulate the possibilities.

Willard Van Ormand Quine devoted an entire chapter of his Methods of Logic to the problems inherent in integrating number within logical propositions. Which should be telling you much about the quicksand you've waded into here.

For a belief to be rationally justified

And at this point, it's time to introduce you to the rigorous approach to the matter. Quite simply, the word "belief" has so much unwanted baggage associated with it, that any rigorous discourse would insist upon better terminology. People use the word "belief" to cover such diverse processes as [1] treatment of unsupported assertions uncritically as fact (yes, supernaturalists, I'm looking at you) and [2] acceptance of evidence pointing to the truth-value of a postulate. Yet these processes are totally different. Consequently, in rigorous discourse, the word "belief" is restricted to cover [1], and in such rigorous discourse, there is, by definition, no justification for "belief" whatsoever. In the case of [2], one either deduces the truth-value of a proposition via an appropriate error-free derivation in the appropriate formal system, or observes the truth-value of a proposition by noting the consonance thereof with observational data.

At this point, your entire exercise has crashed and burned. But I'll continue ...

some person P must have a REASON which is rationally justified enough in proportion to how strongly a belief is held.

And courtesy of the above paragraph, what we are dealing with in such a case, is not "belief", but deduction or observation.

Which part of this do you have a problem with?

I think you should be able to work out from the above, the nature of the problem with your simplistic presentation.

Of course, this simplistic presentation completely fails to encapsulate the notion, that one can contemplate a concept, at the very least for pedagogical purposes, without once considering that concept to be valid. Indeed, you should have noticed yourself, if you had paid attention in the logic classes you assert as the source of your presentation, that the teachers of those classes routinely present false propositions as part of their teaching of those classes. Yet you failed to notice this manifest fact.

If we move on for a moment to the world of pure mathematics (which takes on board the propositional calculus as the basis for its own deductive processes), one of the methods of proof to be found in that discipline, is the method known as reductio ad absurdum. It consists of the following steps:

[1] Treat a proposition initially as if it were true, without committing oneself to this truth-value (the emphasis I place here is deliberate);

[2] Construct a derivation, based upon the purported truth of the proposition, which leads to a logical contradiction;

[3] Note that the contradiction disappears if the proposition is treated as false;

[4] From [2] and [3] above, conclude that the proposition is indeed false.

Note that treating a proposition temporarily as true, for the purpose of deductive analysis, does NOT in any way, shape or form, require commitment to that truth-value. Your failure to understand this elementary concept tells me that you have failed to pay proper attention in your classes.

As a corollary, your assertion that we need to commit ourselves to supernaturalist assertions about god type entities in order to refute them, is utterly destroyed. Treating an assertion temporarily as true, in order to further a deduction ultimately leading to the falsification of that assertion, is a completely different process to that of committing oneself to a given truth-value for that assertion. That is the elementary mistake you are making here. Indeed, the whole point of any properly conducted analytical process, is to avoid committing oneself to a truth-value before the analysis is complete.

Again, Quine is wonderfully informative on this matter. In my electronic copy thereof, pages 197-200, in the chapter Existence and Singular Inference will be worth your while reading.