Re: [lojban] RE:Trivalent Logics

[pycyn@aol.com]

I haven't checked xorxes' table to see whether it does give all the cases, 
but I trust that it does.  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).  So we can probably 
replicate a plausible three-valued system in lb for them what wants it 
(complete with abbreviations for common functors).  
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.  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. (In Aymara, negation is something 
like "it is certain that it is controversial that," where certainty and 
controversiality are primitive functors). 
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.  (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.)

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