Re: [lojban] RE:Trivalent Logics

["Jorge Llambias" <jjllambias@hotmail.com>]

la pycyn cusku di'e

> Ooops!  For functional completeness the system needs min(x,y), too and that
> seems harder to get.  Once it is gotten, however, it alone generates all of
> the connectives (binary, unary, more-ary), or rather the Sheffer function,
> min(x,y)+1, does.

Is there a simple :) way to see that this is true?

It seems to me that max(x,y) is the most useful "or", and
min(x,y) is the most useful "and", so it is nice that they
are relatively straightforward to generate.

> I think (disclaimer) that min can be defined with f1=f2 :-1 for -1, 0
> otherwise and f3 as 1for 1, 0 otherwise.  But my head is not functioning 
> well
> in -1,0,1 arithmetic at the moment.

It does indeed give the minimum. So this is really the same
situation we have in Lojban with respect to 3-way connectives,
right? They can all be generated but not without repeating
some of the arguments in some cases.

Now the question is, do we have anything like a complete
three-value unary system in Lojban? Obviously not a logic
system (we only have na and ja'a there) but maybe with some
set of attitudinals?

{ju'a} or {je'u} (1,0,-1)
{ju'o} (1,-1,-1)
{la'a} (1,0,0)
{ca'e} or {se'o} or {ai} (1,1,1)
{pe'i} (0,0,0) ??

Could we produce some coherent system out of what we have?

co'o mi'e xorxes



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