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







In a message dated 1/30/2002 8:33:35 PM Central Standard Time, jjllambias@hotmail.com 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.