Re: looking for a predicate hierarchy

"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 because 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?


WIth your implication connective, the modified logic cannot potentially
handle contradiction with formulas using the connective, that's what.
Originally, every formula in the logic had a model, with the
implication it's no longer the case. It's not surprising because the
defect is inherited from the '~' connective ! The whole point if using
'b' as a designated truth value was to block the explosion
principle/avoid trivialization.
.