Re: looking for a predicate hierarchy

[ Sorry guys, for it became a shameless off-topic in comp.object ]

On Fri, 22 Dec 2006 18:59:17 +0100 (CET), V.J. Kumar wrote:

"Dmitry A. Kazakov" <mailbox@xxxxxxxxxxxxxxxxx> wrote in
news:jctw61m4fitf.or6bzp94wggz.dlg@xxxxxxxxxx:

On Fri, 22 Dec 2006 12:40:46 +0100 (CET), V.J. Kumar wrote:

If this is the case, your logic is trivializable becaus it has formulas
that do not have a model, and in the 4-valued logic all the formulas
are supposed to have models. Consider for example ^(A=>A) for any
valuation where ^ is the ordinary negation (0->1, 1->0, _|_->_|_, T-> T).

not(A=>A) is false for any A. So what?

Formulas with your implication potentially cannot handle contradiction,
that's what. The whole point of having 'T' as a designated truth value
is to allow models for expressions like (F /\ ^F).

You forgot that everything is in the inference rules. Yes, a contradiction
cannot be constructed from 0 and 1 using /\ (AND), or any conventional
logic operators. This was a *desired* property, that 1 /\ 0 = 0, 1 V 0 = 1,
after all. That alone does not make it trivial, because the contradiction
and uncertainty can still be produced. For example by operations like
consensus(+) and gullibility(*):

1 + 0 = _|_ 1 * 0 = T

for further information see:

http://www.dmitry-kazakov.de/ada/fuzzy.htm#fuzzy_proposition

--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
.

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