John F. Sowa wrote: (01)
> The UoM ontology should be compatible with a very wide range
> of incompatible ontologies that people have developed or
> proposed. If we start defining too many upper-level concepts,
> we will end up with one more incompatible ontology.
>
> Therefore, I propose that we take the terms that lead to
> endless rounds of discussion and declare them to be
> undefined primitives. That would allow them to be linked
> to a wide range of different upper levels that other people
> have proposed. (02)
Most of this debate is about first getting past the terms to agree on
the concepts, and then getting agreement on whether specific concepts
are needed. (03)
But if we take John's guidance at his word, the following are undefined
primitives: Quantity, Kind of Quantity, Quantity Magnitude, Dimension,
Unit of Measure. Now, what sort of ontology will we make with those
undefined terms? Do they have any properties? What axiom can we write? (04)
Well, we can do what UCUM does: There are relationships among units of
measure and those relationships can be expressed mathematically as an
algebra. But comparability and equality are only partly defined by the
algebra. In effect, the algebra defines two units to be either
'incomparable' or 'possibly comparable', and it defines two 'possibly
comparable' units to be 'unequal' or 'possibly equal'. The user needs
to add an external rule to get from 'possibly comparable' to
'comparable' and thence to 'equal'. Would you be satisfied with that, John? (05)
> Fundamental principle: Detailed axioms and definitions create
> incompatibilities and inconsistencies. Never define anything
> that you don't absolutely need for the problem at hand.
>
> This strategy is one more example of my general approach
> to axioms:
>
> When in doubt, throw it out.
> (06)
Well, John, what precisely is the problem at hand? That is the question
Gunther was trying to answer. (07)
He avers that you don't need to understand 'quantities' in the VIM and
SI sense, in order to produce a useful (mathematical) semantics for
units of measure. And that is true from the point of view of
manipulation -- a units of measure calculus does not require the
semantics of quantity, anymore than Newton's calculus required a
semantics of physics. In that view, if there is a right answer, the
UCUM mathematical model will produce it. But the mathematical model can
also produce meaningless answers. Gunther's position is that the
avoidance of meaningless answers requires a further ontology that
conveys the science of the problem space, and there are many of those. (08)
NIST (Martin Weber and I) have argued that the ontological model of a
unit of measure that supports knowledge engineering _in general_ cannot
be purely mathematical. We don't want a reasoner to use valid
mathematics and nonsense physics to produce the proof of a conjecture.
But unlike Gunther, we believe that the general science of measurement
is not specific to the science of particular problem spaces, and the
exceptions (like particle physics) are very few. We also believe that
to be the position of the BIPM, which is why their publications do not
get deeply into electricity or mechanics or chemistry. And we believe
that most science, most engineering and almost all business uses of
units of measure would benefit from an ontology that understands the
semantics of units in terms of the semantics of quantity. (09)
As Gunther pointed out, this is a critical question for the project. (010)
So, instead of Zen Principles of Ontology Design, what you could
contribute is a position on the question. (011)
-Ed (012)
--
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 (013)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (014)
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