I 'believe" that the switch analogy is valuable in expressing belief, however, I have trouble making a bridge between this analogy and your explanation. In this post I will make a feeble attempt to make that bridge.
To avoid confusion between my Switch belief function and the one you use, let me rename my three state switch belief function from B to S. So now, what I had expressed in an earlier post as qBp becomes qSp, where q is the switch control line, p is the input and qSp is the output.
So your Bp becomes my 1Sp and your ~Bp becomes my 0Sp.
Note that pSp is never 0. (the control line and the input line carry the same information.) This reminds me of the anthropic principle.
Bruno Marchal wrote:
Just remember that Bp means the machine has print, or prints, or
will print, sooner or later the proposition p.
From "Bp is true" you cannot infer that the machine will print Bp, only that she
will print p.
Using the switch analogy and paraphrasing what you said:
If q = 1 (i.e. Bp is true) then you cannot infer that qSp is true (the machine will print Bp) only that p is known (only that she will pring p)
ie., if the control line is on, you still don't know what is the output of the switch. However you know that p is known.
Could you pursue this analogy further?