fuzzy logic

["John E. Clifford" <pcliffje@CRL.COM>]

Not too surprisingly, logicians have been involved with Loglan/Lojban
from almost the start and so provisions have been made for extended
logics from early on -- originally just many-valued or
probability-valued bu t fuzzy soon after Zadeh's original paper.  In one
sense, this has been pretty easy, since the *language* of even the most
extreme Wooky logics differ hardly at all from that of a standard logic
and certainly not from such a language modified to be speaka ble in
real-world contexts.  In short, as xorxes has pointed out, lojban is
equipped already to do fuzzy logic -- linguistically at least.

A couple of distinction make the discussion clearer, however.  Zadeh --
and some even madder epigones -- have developed at least three fuzziness
theories:  set theory, logic, and arithmetic.  The set theory takes the
range of the characteristic function of a set from the usual {0,1} to
[0,1], from a set with two members to a closed real interval.  But the
underlying logic of this theory is two-valued:  c-set(object)=r gives
the right value or it does not.  The fun comes in figuring out how the
values for derivative sets comes from that for basic sets -- various
kinds of intersections and unions and (worst, since it does not work at
all regularly) subselections (red horses as opposed to things red and
horses).  Considering the range of possible members, each set could be
seen to have a characteristic membership gradient (thank you, and) and
one of the developments finding sets related to a given set but with
different gradients, sharper ("very," "extremely," "perfectly" -- this
lasted tended to be almost perpendicular) or flatter ("sorta,"
"somewhat," "more or less" and so on).  In lojban these are the tanrus
and the lujvos with _mutce_ and its compounds and opposites (and
probably other words as well, if we need them).