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Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 30 Mar 2010 13:08:32 -0500
Message-id: <A90FA473-6D93-4766-9194-4A42F7B7D05F@xxxxxxxx>
On Mar 30, 2010, at 12:49 PM, John F. Sowa wrote:
> Chris,
> 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.) ...
> 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.
> 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.
> 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.
> 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.    (01)

Just so.  Those are good simple examples to illustrate the point.    (02)

-chris    (03)

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