At 11:54 06/10/04 -0700, George Levy wrote:

`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.
`

This seems nice and you could perhaps elaborate.
Now, I don't think, indeed, that your S logic
is related to the B logic, where B is really
an a priori higher level notion (like an affirmation
that some machine stops after having done some search).
Your S is closer to the belief function theory than
the Smullyan/Gödel slef-referential "belief".

To test the degree of resemblance of your S and the
B, you could test S on the original knight/knave problem.
Knights always tell the truth, Knaves always lie. A native
of the Island tells you "You will never believe I am a Knight"
What will you (or your S machine) believe about
the native's nature?

And here is another puzzle, which is not entirely
unrelated with both the KK puzzles and the current probability
discussion: I put three cards, two aces and a jack, on their
face in a row. By using only one yes-no question and pointing
one of the card, you must with certainty find one of the aces.
I know where the cards are, and if you point on a ace, I will
answer truthfully (like a knight), but if you point on the jack, I
will answer completely randomly!
How will you proceed? (The puzzle is one invented by Boolos,
as a subpuzzle of a harder one by Smullyan & McCarthy.
Cf Boolos' book "Logic, logic, and logic". According to
Boolos, it illustrates something nice about the practical
importance of the excluded middle principle. And this is
a hint, perhaps.)

Bruno

http://iridia.ulb.ac.be/~marchal/