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From: mackw@bytex.com
Subject: Re: Fuzzy theory or probability theory? 
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> : S. F. Thomas (sthomas@decan.gate.net) wrote:
> 
> : : I still insist that any utterance "A and not A" has no meaning 
in 
> : : natural language, at least not in the normal sense of the 
conjunctive
> : : "and".  

I'll agree that in most common usage the English statement "A and not 
A" is not meaningful, but there are lesser used cases where this 
statement is used either for humor or emphasis where it does have 
meaning.  Let me rewrite our burglar example using "6 foot" instead of 
tall.

WITNESS: The burglar was 6 foot tall.
ATTORNEY: But my client is 6 foot one.
WITNESS: Your client is the burglar.
ATTORNEY: But 6 foot one is not 6 foot.  Are you saying the burglar
	was both 6 foot tall and not 6 foot tall?
WITNESS: In this case yes, the burglar was 6 foot tall and not
	6 foot tall.

Yes, the example sounds contrived, but the point is the statement 
"6 foot tall and not 6 foot tall" is meaningful in this context.  We 
would not consider the information useful and we probably accuse the 
attorney of arguing a trivial point, but we can understand the 
statement (likewise "A and not A" is meaningful but not terribly 
useful in fuzzy logic).

A fuzzy logic interpretation of the witness's final statement is that 
the burglar has a high degree of membership in the fuzzy set "6 foot," 
but being 6 foot one, he also has a low degree of nonmemebership in 
this set.  This is explicitly stating some of the implicit meaning in 
the witness's statement.  In this regard, fuzzy logic does a fairly 
good job of translating the meaning of the english statement into a 
form which a computer (or computer programmer) may be able to handle.

Wayne Mack

