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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: Wed, 19 Mar 1997 16:42:46 GMT
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WSiler (wsiler@aol.com) wrote:

: In fact, there definitely exist logics which obey Lemke's axioms.

: Buckley and Siler's family of logics obeys the following:
: Idempotency: A AND A = A, A OR A = A
: Commutativity: A AND B = B AND A, A OR B = B OR A
<snip>
: These hold for all rational truth values between 0 and 1 inclusive. Paper
: submitted to FS&S but still in review.

: I understand that Thomas' logic obeys all (or most all) of these except
: for distributivity.

I concluded that associativity and distributivity (Thomas, 
1995, p.120) did not hold *in general*.  However, in light of 
the algebraic parallel between your (Siler/Buckley) development 
and mine, and in light of your result that, *under certain restrictions*, 
associativity and distributivity hold, I would expect associativity and
distributivity, *with similar restrictions*, also to hold in my 
development... as a matter of algebraic necessity.
  
: Bill Siler 

Regards,
S. F. Thomas
