The knowledge of Quantities and Units (Q&U) is: (01)
1) A physical theory;
2) Mathematically structured;
3) A set of standards. (02)
Each of these has significant meaning. (03)
First and foremost, it Q&U a physical theory. This means that it is
a new set of observations could upset the existing theory. It means that the
theory can change over time. It also means that concepts like "mass" have a
meaning that is defined operationally, by measurement procedures, which are
observations. Measurement procedures are extensions of our sensory capabilities. (04)
The mathematical structure is an abstraction of the observations, but
proven/validated for its utility in making predictions. The mathematical
properties are not mathematical truths, however. If we find they no longer
the mathematical concepts themselves are not invalidated, only the particular
way they've been applied to the physical theory. (05)
Finally, since there are many possible terms and systems of units, one set of
terms and units must be selected for common usage to support mutual
Mass is defined operationally by a measurement procedure, i.e., weighing. This
definition is also consistent, by a validated physical theory, with using that
measurement, along with Newton's law, to make predictions on the future state
propelled objects. This provides a concrete, ostensive definition of mass. (07)
A Quantity is an element of the set of all things that can be measured.
It is certainly not undefined. When we wish, however, to describe the
mathematical properties alone, we can take it as a primitive, e.g., a scalar
quantity is represented by the ordered pair (real number, mass-unit).
Now we have a mathematically structured definition. Expressing the algebra is
only part of the theory, not the whole theory. (08)
The standard requires that mass be measured in kilograms and force in newtons.
This provides further definition, e.g., (1.3, pound) is not a valid SI mass,
a newton is proportional to kilogram*meter/sec/sec with proportionality
of one. (09)
I think we need to have these three aspects of the meaning of Quantities and
Units for meaningful definitions. (010)
My question is, "Do we need more than this?". (011)
Joe Collins (012)
Ed Barkmeyer wrote:
> John F. Sowa wrote:
>> 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.
> 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.
> 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?
> 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?
>> 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.
> Well, John, what precisely is the problem at hand? That is the question
> Gunther was trying to answer.
> 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.
> 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.
> As Gunther pointed out, this is a critical question for the project.
> So, instead of Zen Principles of Ontology Design, what you could
> contribute is a position on the question.
Joseph B. Collins, Ph.D.
Code 5583, Adv. Info. Tech.
Naval Research Laboratory
Washington, DC 20375
(202) 767-1122 (fax)
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