Dear All, (01)
I agree with John and Pat that that ontology should have layers, so that
there is a minimal "micro-ontology" that covers the basics of quantities and
units, which can extended with other ontologies which embody additional
theories or assumptions about the world. (02)
Our discussion has been muddied by a loose use of the term "unit". The VIM
says that a quantity value may make reference to different things including
a measurement unit, a measurement procedure and a reference material. We
should not loosely use the term "unit" to refer to any of these. (03)
The use of the term unit implies some axioms. Somehow it must be possible to
define a times operator such that if u is a measurement unit in the kind of
quantity Q, then: (04)
1) For each q in Q there exists a real r, such that r.u = q.
2) For each q1 and q2 in Q such that q1 > q2 and r1.u = q1 and r2.u = q2, r1
> r2. (05)
This may be enough for the use of a unit to be well founded, but probably
the route to the times operator involved additional axioms such as: (06)
a) For all real r and q in Q, r.q is in Q. (this is not true for temperature
- so some more work needs to be done)
b) A plus operator is defined (i.e. has a physical meaning) for Q.
c) For all real r1 and r2 and q in Q, (r1 + r2)q = r1.q + r2.q. (07)
Has anybody done any work on this? Do we need to? Perhaps we just have two
subclasses of kind of quantity:
- kind of quantity for which a unit can be defined
- kind of quantity for which a unit cannot be defined (08)
Even if a kind of quantity can have a unit defined, you do not have to use
it. An example is temperature. You can express a temperature with respect to
Kelvin or with respect to ITS90. (09)
Best regards,
David (010)
At 08:03 08/08/2009 -0400, you wrote:
>Chris,
>
>I agree with everything that Pat said in his last note,
>and he agreed with me.
>
>In summary,
>
> 1. The assumption of an extensional or intensional position
> is independent of, but compatible with either a 3-D or
> a 4-D ontology.
>
> 2. The formulation of an extensional or intensional 3-D
> position could be mapped to or from an extensional or
> intensional 4-D position by the same methods used to map
> any 3-D statement to or from 4-D.
>
> 3. The methods of measurement have improved enormously from
> the 19th to the 21st centuries, and the units such as meter,
> second, ampere, volt, etc., are specified with far greater
> precision, but they are independent of any changes in the
> physical theories. (The kilogram, by the way, hasn't
> changed in any way -- it's still defined by the same lump
> of metal stored in a vault in Paris.)
>
> 4. An ontology for UoM does not depend in any way on the
> assumptions of extensional vs. intensional, 3-D vs. 4-D,
> or Newtonian vs. relativistic vs. quantum mechanical vs.
> quantum electrodynamical vs. string theory or many other
> hypotheses, assumptions, and theories.
>
> 5. Therefore, a microtheory about units of measure can and
> should be stated in a way that it can be used with any
> consistent set of assumptions in point #4 plus many
> others that may be proposed in the future.
>
>Comment about point #3: The reason why the units of measure
>are independent of any theory is that they are defined in terms
>of repeatable physical experiments. The theories that interpret
>the results of those experiments have changed drastically over
>the past 150 years, but every new theory must be consistent
>with the brute facts observed in any repeatable experiment.
>
>John
>
>
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> (011)
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