Subject: Re: [lojban] RE:Trivalent Logics

From: [email-masked]
Date: Mon, 26 Jun 2000 10:13:11 EDT

In a message dated 00-06-25 22:26:50 EDT, xorxes writes:

<< I tried assigning (-1,1,0) to {nai} but it becomes too different
from the binary meaning of {nai}. In any case, {cu'i} = (0,1,-1)
is -1. What would that be? A counter-negation? >>

What you tried for {nai} was a Post or circular negation, that is +1 to each 
value. It places an important role in the theory of many-value logics, as 
the preferred negation when it comes to looking for minimal connective sets. 
The Sheffer function is always this negation of the min function and it is 
this negation that gives the analog of double negation (triple negation in 
the trivalent case) -- you go round the circle one complete turn by doing n 
negations. Your {nai} always gives double negation, even for zillion-valued 
logics. Although I can't find anyone who messed with it, your {cu'i} is also 
a circular negation, just going the other direction. I wonder if it might 
not play a role in defining the other adequate single connective, the Peirce 
(amphec) function, NOR. Might that be max(x,y)-1? It is in the 2 case, 
which doesn't prove much, and looks at a glance to be in 3 and also to be 
adequate.

The rest of the system looks very promising (Hell, very done, except for 
usage thoughts -- especially for the binary connectives).