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Re: [ontolog-forum] Role of definitions (Remember the poor human)

To: Pat Hayes <phayes@xxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 13 Feb 2007 16:20:46 -0500
Message-id: <45D22BAE.40106@xxxxxxxxxxx>
Pat,    (01)

As I said in my previous notes, FOL by itself cannot make
any distinction between levels of entrenchment.  That is
a metalevel statement.  A first-order theorem prover cannot
use the distinction in a proof.    (02)

JFS>>  The usual versions of FOL do not distinguish which,
 >>     if any, axioms are intended to be define a term (type,
 >>     relation, or function) and which merely use a term that
 >>     is defined elsewhere.    (03)

PH> This distinction, and the idea that only some of these
 > sentences constitute a 'definition' which has a different
 > logical status than other sentences, is exactly what I was
 > urging we should put behind us.    (04)

In practice, there are statements such as "every manager is
an employee", which are fundamental to the use of the terms
(or the corresponding types).  They have a different status
from statements such as "every manager has status 'exempt'",
which applies to a particular feature of US labor law.    (05)

PH> Let me ask you, if you think otherwise, to explain what
 > exactly constitutes, in strict logical terms, the difference
 > between formal sentences that this terminology apparently
 > assumes. These are all sentences of CL, let us say for
 > concreteness.    (06)

That distinction cannot be expressed in CL, which does not
recognize metalevels.  But it can be asserted in IKL by
fiat.  The person who defines an ontology may declare that
some particular proposition is a definition, and another
proposition is a constraint that has been derived from
the 2006 tax code, but not the 2007 tax code.    (07)

PH> There are no definitions in the strict sense in a first-
 > order framework.  This fact is something to treasure and
 > preserve as long as possible.    (08)

It will always be treasured and preserved in FOL, but IKL
is designed to support metalevels, which can and will be
used to distinguish levels of entrenchment of propositions
from different sources with different levels of credibility
or verifiability.  Following are typical levels:    (09)

  1. Logical necessity.    (010)

  2. Physical necessity.    (011)

  3. Practical necessity with current technology or resources.    (012)

  4. Deontic obligation according to the laws of various
     countries, states, provinces, or municipalities.    (013)

  5. Obligation according to the rules and regulations of social
     institutions; e.g., businesses, universities, standards
     bodies, religions, clubs, and notions of morality, ethics,
     etiquette, or your mommy's edict "because I said so."    (014)

Definitions that are purely conventional substitutions
of one expression for another have the effect of logical
necessity.  But the choice of words associated with the
types could become entangled with inferences based on
legal pronouncements at levels #4 and #5 that could be
a matter of life or death.    (015)

John    (016)

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