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Re: [ontolog-forum] {Disarmed} Reality and Truth

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 17 May 2007 13:47:06 -0400
Message-id: <464C951A.1000304@xxxxxxxxxxx>
Kathy and Wacek,    (01)

There's a very important distinction between fuzzy set theory
(which was the topic of the first paper on the subject by
Lotfi Zadeh) and fuzzy logic (which was the topic of some
later papers by Zadeh and others).    (02)

Many people who have studied the subject are more convinced
in the usefulness of fuzzy sets than fuzzy logic.  In fact,
many of the useful results in practical applications of fuzzy
logic can be reformulated as first-order logic statements about
fuzzy sets and fuzzy membership.    (03)

That point, however, is controversial, since many advocates of
fuzzy logic believe that there is considerable value in it.
Other people, however, gracefully avoid the controversy by talking
about "fuzzy sets and systems" without mentioning fuzzy logic.    (04)

KBL> I personally think, therefore, that it is misleading to say
 > I am uncertain about whether Waclaw is tall.  I think it is less
 > misleading to say that (according to a given system of assigning
 > fuzzy memberships) he has membership degree 0.73 in the set of
 > tall people.    (05)

That is a good example of how fuzzy logic can be avoided by making
statements (in classical FOL) about fuzzy sets.    (06)

vQ> But this still seems to me to be far from degrees of truth,
 > even if the fuzzy logic community agreed to use the term 'degree
 > of truth'.  It either is that I am 73% in the set, or it is not.    (07)

Yes, that is why it is better to talk about "fuzzy sets and systems".    (08)

There are other formalisms, such as "rough sets", which consist of
pairs of conventional sets that give the upper and lower approximations
to the rough set.  There are also variations of rough sets, in which
the upper and lower approximations are fuzzy sets.    (09)

These are all interesting methods, which can be formalized in terms
of classical FOL -- such as Common Logic, for example.    (010)

John    (011)

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