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Re: [ontolog-forum] Requesting Opinions on the Benefits of Predicates as

To: Pat Hayes <phayes@xxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Mon, 16 Jun 2014 12:07:22 -0400
Message-id: <539F163A.6080506@xxxxxxxxxxx>
On 6/16/2014 3:14 AM, Pat Hayes wrote:
> But my point is that the IKL 'that' operator is not metalanguage
> in the usual sense of that term. Metalanguage usually refers to
> language  *about language", ie about sentences. But the (that ...)
> construction  denotes a proposition, not a sentence.    (01)

I agree that is a crucial distinction.  You can use CL to talk
about the character strings that represent CL expressions, and you
can define a grammar in CL that let's you talk about sentences.    (02)

With Tarski's stratified levels, you can use level N to talk about
the syntax and semantics of levels N-1, N-2...  But you can't use
sentences at level N to talk about the semantics of level N.    (03)

> I do not know if this construction can be smoothly adapted to other
> formalisms: in any case, one should not claim or assume that it can
> without doing the actual work of checking that the resulting system
> is internally coherent, as this stuff skirts very close to paradox.    (04)

That is why Tarski insisted on stratified levels.  I was discussing
this topic with Fred Thompson, a former student of Tarski's.  Fred
and his wife had designed a very nice controlled English called REL.
But Fred was adamant about not allowing metalanguage.    (05)

>> What's unique about the IKL semantics is the ability to avoid
>> paradox without requiring stratified metalevels.
> Well, we hope.  This is still an open research issue, in fact.    (06)

That reminds me of a story that George Polya told about "typical"
mathematicians.   One professor was covering the blackboard with
equations.  At the end, he triumphantly announced, "QED!"    (07)

Whereupon, a student said "But professor, if you take one more
step, you get a contradiction."  The professor replied, "Yes,
but I did not take that step."    (08)

That's the way people use NLs.  They're so flexible that they
allow you to say anything in FOL, HOL, metalanguage, modal
logics, etc.  That let's you get into all kinds of trouble,
if you push the limits.  But people rarely push the limits.    (09)

That's why I recommend expressive KR languages.  Instead of
restricting what people can say, develop tools that check what
subset of logic they're using.  For most cases, simple syntactic
checks are sufficient to determine the complexity class.    (010)

If somebody says something that might be inefficient, undecidable,
or paradoxical, the system can warn "Here be dragons".  If they want
to ignore the warning, tell them "If you click CONTINUE, you're on
your own -- goodbye."    (011)

John    (012)

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