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From: sthomas@decan.com (S. F. Thomas)
Subject: Re: Defining fuzzy descriptors (was  NOT and DIFF)
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Date: Thu, 13 Mar 1997 12:43:39 GMT
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WSiler (wsiler@aol.com) wrote:
: Maurice, your reply to Thomas' and my question (why worry about NOT?)
: cleared up a whole lot.

: Assuming NOT = 1 minus, Thomas, Hisdal and Buckley and I have spent a good
: deal of thought on the (AND, OR, NOT) triad for consistency. However, as
: you say, I know of no work on the triad with NOT freed up. Of course, we
: must have restrictions, and the restriction that all the laws of classical
: logic should hold seems reasonable to me. I would be interested to hear
: from Thomas and Hisdale as to their thoughts on whether these laws could
: still hold for other formulations than 1 minus for NOT.

I have just posted a longish reply in this thread to a post from 
Stephan Lehmke which incidentally also addresses this question.  
As you will note, if the one minus rule for NOT is taken away,
the linkage (along with the insight which flows from that)
between the min-max and bounded-sum rules for AND/OR
is lost, along with laws of excluded middle and contradiction.
If that is true in my development, I would expect it to be true
in the Siler/Buckley one as well, given the algebraic parallels
between the two.

Regards,
S. F. Thomas
