Re: The L3 Revolution

Hi

Confutus wrote:
> It's [](_ -> _} and [](_< -> _} applied to
> the Lukasiewicz conditional that seem to have
> gone unappreciated.

What are the curly braces above ("}"), and the
plonked less than sign ("<") ?

> Granted, but without a well-behaved conditional
> this is only a fragment of a full-featured logic.

BTW:
(A->B)+ = A- v (A+ & B+) v (~A- & ~A+ & ~B-)
(A->B)- = A+ & B-

Which can easily be read off from your 3-valued
table, thus if you had the constant u in your
system L3 you could represent A->B by the other
connectives. Namely by combining (A->B)+ and (A->B)-
as I suggested in my other post.

But you dont need the constant u in your system.
You can use an arbitrary propositional variable p,
then we have:

u == ~p+ & ~p-

Or when we translate it back to your "modal" operators,
we then have:

u == ~[]p & <>p

further notice that ~[]~A == <>A. Thus your whole
system could be reduced to &, v, ~ and [].

Bye
.