Chris and John, (01)
Actually, Nand and Nor logic is no more complex than And and Or logic, in my
opinion. I used it extensively in digital circuit design once upon a time
and never noticed any inconvenience or confusion at all. (02)
In fact, I consider it actually simpler, because And functions are
intuitively there to detect conjoint conditions in which, when detected, you
want to remove from the inputs of the logic function that is inhibited by
the Nand gate. (03)
Using Karnaugh maps, or Yates transforms, or algebraic simplification for
balancing evidence, is every bit as easy, clear and intuitive in Nand/Nor as
in And/Or, IMHO. (04)
Popper says that a falsifiable theory must have at least one ground case
that is detected (usually defined as And conditions) to falsify the theory.
Alternatively, a variable that ranges over a specific set of ground cases
suffices for the same action. Whether that is implemented in Nand/Nor or
And/Or is immaterial. Note that And/Or gates are electronically more
complex, with more circuitry actually REQUIRED, than for Nand and Nor gates. (05)
-Rich (06)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2 (07)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
Sent: Tuesday, March 30, 2010 10:49 AM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping (08)
Chris, (09)
CM> Whoa, combinatory logic is way stronger than ordinary FOL.
> (I suspect you have in mind syntactically (and historically)
> related systems like the predicate functor calculi of Quine
> and Schönfinkel that do away with the apparatus of quantifiers
> and variables.) ... (010)
Yes. I agree that combinatory logic in its full glory goes
far beyond the bounds of FOL. I was indeed thinking of the
use of combinators for eliminating quantifiers and variables. (011)
In any case, simplicity is not a simple notion that can be
characterized in any simple way. Reducing the number of axioms
and primitives can sometimes make a system simpler. But if you
go too far, the overall structure can become more complex. (012)
For example, all the operators of Boolean algebra can be
defined in terms of just one: either Nand or Nor. Those
definitions are actually useful for reducing the number of
transistors in logic circuits. (013)
But the definitions of the most common operators, such as
And, Or, and Not become more complex. When you combine a
Boolean algebra based on Nand or Nor with the quantifiers,
it can obscure rather than clarify many relationships. (014)
John (015)
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