I wrote:
> > So an ontology that defines such a KoQ must necessarily express
> > the formulation per the theory that was used by the community
> > that expressed it.
>
>
John Sowa wrote:
> The UoM ontology should be little more than a compendium of the
> values of the units and the relations among them. The details
> of how they were derived is not necessary for using them.
>
> Adding more detail to the UoM ontology will just create conflicts
> when engineers try to use the values for different applications
> that may use different versions of physics.
>
We may be talking past one another here, John. (01)
We can cite the SI definitions for base units without modeling the
definitions formally. I doubt that we can write meaningful axioms for
them, beyond such things as
(base-unit SI second) read "'second' is a thing that is a base-unit in
the SI system", and
(not (= second metre)) read "'second' and 'metre' are different things", and
(measures SI time second) (read "In the SI system, 'second' measures
(quantity kind) 'time'".
That is what I meant by "primitive" concepts. (02)
But I strongly believe that we must model 'derived unit' as having a
derivation, and 'derived quantity' as having a derivation. That means
that the (derived) quantity kind 'force' is defined to be a product of
mass and acceleration (F=ma), and the newton is a unit of 'force' and is
defined as derived by
1/1 * m^1 * kg^1 * sec^-2.
The newton will also have accompanying text that is not modeled formally. (03)
I'm not asking for anything more interesting or esoteric than that. And
I hope that is what you mean by:
"little more than a compendium of the values of the units". (04)
Per John's previous comments, the question is: Is 'force' part of some
microtheory or part of the main units ontology? Is 'newton' part of
some microtheory? What is the characteristic of a units/quantities
concept that makes it necssary to put it in a microtheory, thus
permitting the existence of conflicting axioms for the ostensibly same
concept in a different microtheory? (05)
I see no reason to relegate force and the newton to some microtheory
(but I don't hold that position with any fervor). It seems to me that
the Newtonian v. Einsteinian physics issues are primarily about the
relationships among the fundamental quantities: mass, time, length. The
SI Newtonian model presumes them to be "orthogonal" and simultaneously
primitive. That is a weaker theory than the relativity theory, in that
it has fewer axioms, but probably no conflicting ones. So relativity
adds relationships and related axioms, but they won't be in conflict
with the few axioms that we state, because we won't be trying to state
or define orthogonality. For any given system of units, 'base unit' is
essentially an extensional concept -- the system enumerates the
instances. And that avoids the orthogonality issue. We may have to be
careful about what 'comparable' means. (06)
-Ed (07)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (08)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (09)
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