Subject: Re: UI for 'possible' (was: Re: [lojban] Bible translation style question)

From: [email-masked]
Date: Thu, 31 Jan 2002 18:07:24 EST

In a message dated 1/30/2002 8:33:35 PM Central Standard Time, 
[email-masked] writes:

> The system was:
> 
> cai (1,-1,-1)
> sai (1,0,0)
> ru'e (1,1,-1)
> cu'i (0,1,-1)
> nai (-1,0,1)
> 
> and the operator (0,1,-1) is essential in order to be able
> to have a complete system. You need either that one or (-1,1,0).
> 

Strictly, the requirements for the smallest complete set are that there be on 
rotation (not used here, since it is derivable with extra functions -- 
(-1,1,0) or (0,-1,1)), one exchange (here (0,1-1), exchanging the first and 
second places) and one identification (the first three above). These three 
give the whole system and do so in a normative way (identifications at 
beginning and end, rearrangements only in between). This pattern works for 
any finite number of truth values from 2 up, with the peculiarity that for 2, 
the rotation and exhange are the same: negation.