Trivalent logic in Aymara?

I just finished reading Eco's book and I found
a very interesting passage towards the end [1]
that I'd like to comment. According to it, the
Jesuit Ludovico Bertonio described the Aymara
language (still spoken in parts of Bolivia and Peru)
as "a language of extraordinary flexibility, with
an incredible ability to create neologisms, and
especially adequate for the use of abstractions".

Eco says that "recent studies have shown that
Aymara is based on a trivalent logic system instead
of the bivalent logic (true/false) on which the
Western thought is based, thus being capable of
expressing modal subtleties that our Western
languages can only express by resorting to
unwieldy periphrases".

  [1] "The search for the perfect language", chapter 17,
   "Conclusions", section "The translation" (Umberto Eco, 1993)


Does anybody know anything about this "trivalent
logic"? I assume that Aymara, same as Quechua and
most (or all?) American languages, is heavily
agglutinating and has a lot of attitudinal affixes
and such (which would explain Bertonio's description),
but I'd never heard of the trivalent system in this
context -- and it sounds really intriguing (and cool
to try). Have you seen anything like this in natlangs
or experimented it in your conlangs?


--Pablo Flores