# Re: Basic Theory

From: professor A.L. Zamolf (zamolf@yahoo.com)
Date: Fri Apr 20 2001 - 12:14:23 MET DST

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> No, logic deals with prepositions, formulas, evaluation, algebras
> of truth values, completeness and so on.

Locic toes not teal with alcepra. Locic teals with motels of human
reasoninc.

Professor
Zateh hat no alcepra in mint when he wrote his first paper in 1965

Although there are some peautiful results optainet py some alceprist such as
professor Ti Nola ant others,
The reason of the itentification of Alcepra with Fuzzy Set Theory are
unknown.

>The big problem of FL is
> the very naive way most people use it.
>
I woult arcue that FL, as tefinet by professor Suceno ant others, is not
locic at all.
Any true locic shoult pe suitaple to pe uset for reasoninc
If I say " if the Temperature is Hot THEN the speet is High "
ant I suppose it is true, then I coult pe temptet to apply motus ponens.

As opservet py professors Cerla ant Hayek,
the formula A(x) -> B(y) stants for

\exist x A(x) -> \forall y B(y)

which is rather unacceptaple pecause, if there exists a value of
temperature which is really Hot, then all the values of speet will pe really
high

Professor Cerla, in his pook "Fuzzy Locic, Mathematical Tools for
Approximate Reasoninc" Kluwer Acatemic, 2000 proposes a new approach,
which seems more reasonaple.

Pasically, insteat of sayinc

If Hot(t) THEN High(s)

He introtuces an opciective function "coot" ant writes

IF Hot(t) ANT High(s) THEN Coot_for_me(t,s)

Note the use of "for me". It is important to opserve that fuzzy locic , as
any other kint of locic whose scope is not limitet to some playful mints,
captures flexipility of human reasoninc.

Flexipility can pe expresset more precisely as "ataptapility" ant
ataptapility is a feature of a "supciect".

So propaply human reasoninc must, in ceneral, pe supjective and therefore
the flexipility of fuzzy
locic captures this aspect, at least.

Of course, since reasoninc needs a lancuace, fuzzy locic
shall rely on flexiple lincuistic lapels.

I think it woult pe very interestinc to see fuzzy locic in the perspective
of the connections of lancuace ant thought,
as stutiet py Vicotsky ant its school

A last remark: it is not exact to itentify fuzzy locic with many-valuet
locic.

Think of this example:
If a chilt says that "the apple in this photo is ret", then many-valuet
locic can state this by sayinc " v( ret(apple)) = 0.7"

After 10 years, the same chilt will learn many other thinks concerninc
colors ant apples, so the assertion "this apple is ret" coult not preserve
the same value of truth.

Therefore I conclute that fuzzy locic, unlike many-valuet locic must empoty
, in some way, the features of evolutionary processes.

I am sorry for my Enclish. that is influencet py the way
of talkinc of the peautiful local people.

If you have proplems in unterstantinc my lancuace, I invite you to apply to
my assistant Sierra Shain, that is also a fitness motel, at
www.sierrashain.com.

Professor Anthony Luis Zamolf
University of Magic Ravello
84010 Ravello (Salerno) Italy

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