David Leal wrote:
> Dear Pat,
>
> I agree except for one thing - a scale is not a set of items/symbols in
> itself, but a mapping from a set of "magnitudes of quantity" to a set of
> items/symbols. Hence re-expressing the consensus in these terms we have:
>
> scale: a mapping f from Q (set of magnitudes of quantity) to S (set of
> symbols - commonly numbers), such that:
>
> f(q1) = f(q2) if and only if q1 = q2
>
> ordinal scale: a scale where both Q and S are ordered, such that:
>
> f(q1) > f(q2) if and only if q1 > q2
>
> ratio scale: a scale where ratios can be defined for both Q and S, such that:
>
> r.f(q1) = f(q2) if and only if r.q1 = q2
>
I agree with all this. The one David left out is the "interval scale".
I'm not quite sure what an "interval scale" is, because time and
temperature are not similar in nature. (01)
The Celsius temperature scale assigns symbols to amounts/magnitudes of
temperature. It is essentially just a ratio scale with 0 corresponding
to a magnitude of temperature that isn't "none". So the scale is based
on a ratio to the amount that is the difference in temperature between 1
degrees and 0 degrees -- the degree Celsius -- offset by the magnitude
at 0. It doesn't name "intervals" in any sense. It is just a "ratio
scale with an offset" that maps symbols to (relative) magnitudes. And
that is why it is easily converted to Kelvin. (02)
A "duration scale" is a ratio scale that assigns symbols to
amounts/magnitudes of time. But a clock or a calendar is an "interval
scale" that maps a set of symbols to a set of intervals on the
(putative) Time Axis. It is not a map to "magnitudes of quantity" (my
Q3) at all. In a similar way, the mileposts on a measured roadway
constitute an "interval scale" of this kind. What characterizes it
structurally is that there is a fixed reference point (in space time)
that is the 0 point (without loss of generality) and each symbol denotes
the interval that has size equal to the granularity of the scale and
starts (or ends, depending on how you number them) at a point whose
"difference" from the 0-point is equal to the magnitude that corresponds
to the symbol on the corresponding ratio scale. (03)
The Celsius scale measures "magnitudes", whereas the clock/calendar kind
of "interval scale" identifies intervals. So I don't know what an
"interval scale" is. (04)
I raise this particular example, because it came up in the OMG date/time
ontology effort and bogged down the process for months. My view of this
is that "one size fits all" will waste everyone's time. We can write
down the axioms we clearly want and see the differences in scales that
don't satisfy certain axioms, and that may enable us to see other
classes of scales and other relationships among them. And for OWL
purposes, common axioms define classification hierarchies. So I what I
am suggesting is that we formulate the applicable axioms and learn the
classifications, rather than imposing them a priori. That is in essence
what David is doing above. (05)
-Ed (06)
--
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 (07)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (08)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
Shared Files: http://ontolog.cim3.net/file/work/UoM/
Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard (09)
|