Hi, an agnostic here ... just agnostic.

[GrandizerII]

Person A and Person C make no sense. Unless I'm misunderstanding the notations.

Must be misunderstanding. 

X = gods exist

A: has a belief "gods exist", has no belief "gods do not exist"
B: has no belief "gods exist", has no belief "gods do not exist"
C: has no belief "gods exist", has a belief "gods do not exist"

b:g|~b:~g
~b:g|~b:~g
~b:g|b:~g

Ummm... 

If you believe the store is open, you're not believing the store is closed.
If you have no clue if the store is open, or closed, then you have no belief, either way.
If you believe the store is closed, you're not believing the store is open.

Your wording confused me.

If I have a belief that "God exists" is true, then I also have a belief that "God does not exist" is false.

But I get what you're saying now.