From pycyn@aol.com Fri Jun 23 09:10:04 2000
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Date: Fri, 23 Jun 2000 12:09:59 EDT
Subject: RE:Trivalent logics
To: lojban@egroups.com
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From: pycyn@aol.com
The formula I gave overestimates the number of distinct binary functions that
can be defined with the formula given, since symmetric functions get defined
twice at even the basic level (f1(x) + f2(y) and f2(x) + f1(y)). And some
get defined even more times: the fixed value functions (always the same value
whatever the input) can be worked off the corresponding unary fixed value
function as any of f1, f2, f3, with the others being fixed 0. There are
obviously other ways of doing these as well. The max function (greater value
of x,y) can also be done in a variety of ways, including using functions that
are 1 for 1, 0 otherwise as f1 and f2, -1 for 1 and 0 otherwise for f3. The
three fixed functions and max, however, make a functionally complete system,
one in which every three valued binary connective can be defined -- though
often by very complex formula indeed.