Dear all :-
For the last few months, we have been discussing the shortcomings
of probabilistic uncertainty management as seen from the fuzzy
viewpoint. Fittingly, our exchange takes place during the tenth
anniversary of another prominent and protracted debate, that time
about the perceived shortcomings of the fuzzy enterprise, the Elkan
affair.
A decade later, parts of that debate, like forecasts of the
scalability of fuzzy controllers, seem quaint. Elkan's
honorable-mention-winning 1993 AAAI conference paper can now be seen
as a last hurrah of the 'logicist' movement in the larger AI
community, as much anti-probabilist as anti-fuzzy, today blessedly
given way to better ideas about the automated handling of uncertainty.
What stands the test of time is Elkan's core concern about the
fitness of fuzzy logic as a vehicle for syntactical reasoning about
realistic subject matter.
Elkan was uninterested in the familiar surface violations of
non-contradiction, that "A and not-A" might be taken as something
other than double-talk. Rather, he emphasized the failure of more
elaborate Boolean equivalences, such as that of (not-A or B) with [(
not-A and not-B ) or B].
This tactical choice was pertinent to Elkan's principal thesis,
that fuzzy logic would perform poorly in chained inferences. His focus
is also apt for a topic closer to the interests of readers of this
list, reasoning about evidence.
Two descriptions of the same evidence, different only in the form of the
expressions used, must have the same bearing. Probabilists, and others who use
probabilistic orderings under various names, need not worry about complying
with this requirement, since their calculus is equivalence-preserving and
complies automatically.
Without such moorings, it is easy to go adrift. For example, suppose
Charles and Catherine recall a stillness of the air in the woods, in order to
reason about local weather conditions at that time.
Charles: There was no wind, or the trees absorbed what wind there was.
Catherine: There was no wind and the trees did not absorb it, or the
trees did absorb the wind.
Charles: That's what I said.
Catherine: No, you did not.
Charles and Catherine fully agree about what happened, and their
perceptions perfectly coincide. In a fuzzy regime, Catherine can find
significance for her distinction without a difference. She can go on
to reach conclusions incompatible with Charles', the difference being
based only upon that distinction.
This sort of thing promptly puts some probabilists' neglect of the
nuances of _approximately_ into perspective.
In bringing this up, I am no critic of the logic
itself. Lukasiewicz, whose logic it once was, made parallel
observations about syntactical reasoning using his logic in the
domains which concerned him. Under some circumstances, and with
precautions to ensure Charles and Catherine's agreement, what the
logic says about the bearing of evidence can be normatively justified
from probabilistic desiderata.
The Elkan affair was remarkable not only for its substance, but
also for what it revealed about the quality of discourse in our
community. Many papers discussing Elkan's appeared in a special issue
of _IEEE Expert_. Some displayed _ad hominem_ attacks. Elkan's
scholarship, cognitive abilities, motivations, and originality were
flayed. It is stunning to see this in print; usually such trash-talk
appears only in referee reports.
Professor Zadeh also participated in that discussion. In contrast
to the works just described, his contribution was a model of reasoned
and civil argument, what ought to occur in a scholarly forum. The
little Zadeh addressed personally to Elkan honored both its subject
and its author.
That is yet another reason why probabilists are fortunate to have
a critic like him.
Paul
Elkan's "The paradoxical success of fuzzy logic" is found on pages
698-703 of the 1993 AAAI Proceedings. The special issue of _IEEE
Expert_ appeared in August of the following year. How heated the
moment was can be seen in a letter to the editor of _AI Magazine_
15(1), 1994, pages 6-8. One example of Lukasiewicz' concerns is
discussed in his lecture "On determinism," in S. McCall (ed.), _Polish
Logic 1920-1937_, Clarendon, 1967, pages 19-39.
