I linked to the previous post. That begins with something like an abstract: a statement of intent, at least.
This isn't an article or a paper: it's a blog post.
For anyone still following this, I have tried to restate my arguments in a new way here:
I calculated the result for about three different sets of probabilities before making the original post. The equation was correct each time. I could have just been mistaken, of course, but even Zack (the commenter above) conceded that the equation is true.
EDIT: Oh, I see now. You have changed all my disjunctions into conjunctions. Why?
Well, it wasn't actually an equation. That's why I used the =||= symbol. It was a bientailment. It asserts logical equivalence (in classical logic), and it means something slightly different than an equals symbol. The equation with the plus signs and the logical equivalence shouldn't be confused.
I am the author. It wasn't a mistranslation. The logical equivalence was not translated into anything. It was merely intended to break down A according to its logical consequences shared with B. I never wrote "P(A v B) + P(A v ~B)," because that would be irrelevant.
Hi, I am the author.
The =||= just means bientailment. It's short for,
A |= (A v B) & (A v ~B) and (A v B) & (A v ~B) |= A
Where |= means entailment or logical consequence. =||= is analogous to a biconditional.
The point is that each side of a bientailment is logically equivalent, but the breakdown allows us to see how B alters the probability of different logical consequences of A.