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*> No, logic deals with prepositions, formulas, evaluation, algebras
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*> 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
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*> the very naive way most people use it.
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*>
*

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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