Subject: Re: [lojban] RE:Trivalent Logics

From: "Jorge Llambias" <[email-masked]>
Date: Sun, 25 Jun 2000 19:26:06 PDT

la pycyn cusku di'e

>The assignments of functions to terms looks about
>right and the means of using the functors in different contexts does recall
>much of the Aymara approach (so far as i understand it).

I realized something else about those assignments after I
posted it. The three assertions:

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

are the three that differ minimally from the simple
assertion (1,0,-1). Maybe that is why they are useful
and the easiest to understand. (The fourth minimal
variation, (0,0,-1) is not an assertion, as it doesn't
start with 1.)

>I also haven't checked to see whether the system xorxes gives is minimal
>(i.e., could we do it with fewer functors), but I suspect it is not -- as I
>am sure that the Aymara system is not.

It is not minimal. For example, {ru'e} is equivalent
to {naicainai}. (Possible = not necessarily not.)

But we don't want a minimal system because some functions
become unusably cumbersome.

>xorxes' system lacks one interesting
>feature of Aymara, that negation is not a primitive functor, but, since
>negation is a given in lb, that would be hard to recreate, in spite of the
>interesting thoughts it brings to mind.

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?

>(In Aymara, negation is something
>like "it is certain that it is controversial that," where certainty and
>controversiality are primitive functors).

Isn't (-1,1,0) just plain controversial? I think "necessarily
controversial" is (-1,1,-1).

With my proposal, "controversial", or trivalent negation, comes
out as {naicu'i}, something like "doubtful that not".

(-1,1,-1) is {cu'icai}, "necessarily doubtful".

>lb does not provide any natural way of upgrading this to a system of binary
>connectives unless the gi's that got us into trouble the last time around 
>can
>be called to our aid.

Maybe it does: do'egi<f1> ... gi<f2> ... vau<f3>

>(I hope they -- or something else -- can be, since
>being able to absorb a totally unexpected and odd system would be a nice
>demonstration of some property or other than lb is supposed to have.)

Yes, it is working out very nicely.

co'o mi'e xorxes

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