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

From: "Jorge Llambias" <[email-masked]>
Date: Thu, 31 Jan 2002 02:28:57

la xod cusku di'e

> > > Why ru'e and not cu'i?
> >
> > Basically because it's 'ru'e' that glossed as 'possibility' in the
> > lojban version of trivalent logic
> > (http://nuzban.wiw.org/wiki/index.php?Three-value%20Logic), but other
> > than that 'cu'i' is just as good, if not better.
>
>I prefer cu'i, for cu'i has no negative, it being in the center of the
>scale, whereas ru'e is opposed by ru'enai.

There was a reason to choose {ru'e} though, as {cu'i} was needed for
something else. 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).

To remind us what we're talking about: In two-valued logic
there are only four unary operators, which in lojban can be
represented by:

ja'a (1,-1)
na (-1,1)
xukau (1,1)
na xukau (-1,-1)

This means that {ja'a} returns true from true and false from false,
{na} returns false from true and true from false, {xukau} returns
true from either true or false, and whatever the contradiction
operator is it always returns false.

In three-valued logic, there are 27 unary operators. We don't have
27 words for them, but fortunately we can get them from combinations
of up to three of the above six. (In two-value the combination {nana}
for example is equivalent to {ja'a}.)

The reason I chose {ru'e} for (1,1,-1) (which means that any value
but false gives true, and false gives false) is that it is the
weakest of the three affirmations that differ minimally from the
transparent operator (1,0,-1). The three are:

cai (1,-1,-1) necessarily
sai (1,0,0) probably
ru'e (1,1,-1) possibly

The truly most natural operator for {cu'i} would probably
be (0,0,0) in any case, total non-commital, but we need something
for (0,1,-1) or for (-1,1,0) or else we can't generate the 27 to
have a full system, so I assigned (0,1,-1) to {cu'i}, which gives
neutral for true and true for the neutral value. I think that's
a good enough "neutral".

"Possible" is not "neutral". In terms of probablity for example,
any value but zero gives possible, only zero gives impossible.
Something like (1,1,-1).

mu'o mi'e xorxes

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