From: owner-uai@cs.orst.edu on behalf of Paulusnix@cs.com
Sent: 8 września 2003 19:10
To: uai@cs.orst.edu
Subject: Re: [UAI] Decision theories, and other threads

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.