Pat Hayes wrote: (01)
>I guess I was assuming there was more to it than this. I can speak of
>the ultimate tensile strength of a given material (or object?) just as
>I can speak of the width of my third finger, and that is just as
>particular a value. David, correct me if I have this wrong, but were
>you meaning to draw a distinction between for example the category of
>lengths, and the category of strengths (stresses?)? If so, can you
>expand on what you see as the difference between them? (02)
Dear Pat, (03)
I was trying to make a very simple point at the time:
- length is a category which contains instances of "particular quantity";
- there are also a categories of categories such as length categories (e.g.
radius, circumference, waterline_length), or stress categories (e.g.
ultimate tensile strength, yield stress in compression) (04)
This introduces a larger point which we have only just touched upon, which
is how these domain specific, and often measurement method specific
categories are included in the ontology. Maybe the straightforward approach,
which regards radius as a function with domain circle and range length, will
stand up to scrutiny. (05)
The language of the VIM suggests a classification of tropes. Hence the trope
"radius of circle A" is of type length and also of type radius. With this
view, radius is a subclass of length. I don't think that this is useful. On
the other hand one of the symbols suggested in the VIM for radius of circle
A is "r(A)" :). (06)
Best regards,
David (07)
At 06:23 16/07/2009 -0500, you wrote:
>
>On Jul 15, 2009, at 6:42 PM, Ed Barkmeyer wrote:
>
>> David Leal wrote:
>>
>>>>> Probably we need to look at two "kinds of quantity":
>>>>> - categories such as that which includes Ed Barkmeyer's height,
>>>>> width of the
>>>>> Thames at London Bridge, the diameter of the earth's orbit;
>>>>> - categories such as that which includes ultimate tensile
>>>>> strength, yield
>>>>> strength in tension, yield strength in compression (all are
>>>>> stresses).
>>> Can anyone elaborate on the distinction here? I don't follow it.
>>
>> The distinction I see is between 'particular quantities' in the
>> first group, and categories of particular quantity in the second.
>
>I guess I was assuming there was more to it than this. I can speak of
>the ultimate tensile strength of a given material (or object?) just as
>I can speak of the width of my third finger, and that is just as
>particular a value. David, correct me if I have this wrong, but were
>you meaning to draw a distinction between for example the category of
>lengths, and the category of strengths (stresses?)? If so, can you
>expand on what you see as the difference between them?
>
>Pat H
>
>> Each of the examples in the first group is an individual physical
>> phenomenon; no example in the second group is a particular quantity
>> -- each of the examples in the second group is a class of
>> phenomena. So if I understand David correctly, one 'kind of
>> quantity' is a class whose instances are individual phenomena; the
>> other 'kind of quantity' is a class whose instances are classes of
>> phenomena.
>>
>> VIM has only one category of the second kind: 'kind of quantity'.
>> The instances of 'kind of quantity' are categories of the first
>> kind: each instance of 'kind of quantity' is a subclass of the
>> general class 'particular quantity'.
>> (forall (k)(if (kind-of-quantity k)
>> (forall (x) (if (k x) (particular-quantity x)))
>> ))
>>
>> "length", as the class of phenomena that are one-dimensional spatial
>> displacements, is a 'kind of quantity'. That is, "length" is a
>> subtype of 'particular quantity' and an instance of the class 'kind
>> of quantity'.
>>
>> Further, a 'kind-of-quantity' has the property that all particular
>> quantities of the same kind are comparable.
>> (forall (k)(if (kind-of-quantity k)
>> (forall (x y) (if (and (k x) (k y))
>> (comparable x y)))
>> ))
>>
>>>> There is a set of categories that are
>>>> 'kinds of quantity', such that all instances of any 'kind of
>>>> quantity'
>>>> category are comparable and no pair of instances from two different
>>>> kinds of quantity are comparable.
>>> Why the second requirement? If length and width are different
>>> quantities (why not?) they are nevertheless comparable.
>>
>> As I said above, the VIM only introduces one class whose instances
>> are subtypes of 'particular quantity', but that class does not
>> include all subtypes of 'particular quantity'! To make this clearer
>> we might define 'kind of quantity' with only the axioms above, and
>> then 'length' and 'width' and 'circumference' and 'diameter', etc.,
>> would all be instances of it.
>>
>> But then we need the concept VIM has: 'special kind of quantity',
>> which is a subtype of 'kind of quantity' with the additional
>> property that no pair of instances from two different special kinds
>> of quantity are comparable.
>> (forall (s1 s2)
>> (if (and (special-kind-of-quantity s1)
>> (special-kind-of-quantity s2))
>> (forall (x y) (if (and (s1 x) (s2 y))
>> (not (comparable x y))
>> ))
>> ))
>>
>> The reason for this is the concept 'system of measurements'. A
>> system of measurements selects a set of special kinds of quantity to
>> be base quantities (reference dimensions), and it assigns to each
>> 'base quantity' a particular measurement unit to be the reference
>> unit for all instances of that 'base quantity'.
>>
>> So 'length' is a 'base quantity' or 'reference dimension' of SI and
>> the MKS system assigns 'metre' as the reference unit for 'length'.
>> MKS does not assign units to 'width' and 'diameter' and
>> 'circumference', etc., because they are all subtypes of 'length' and
>> can all be measured in metres.
>>
>> Now, velocity is not a base quantity; it is a 'derived quantity'.
>> 'Derived quantities' are all the special kinds of quantity that are
>> not base quantities. Each derived quantity can be defined/expressed
>> as a relationship among base quantities, i.e., in terms of the
>> reference dimensions. So velocity can be described as length/
>> duration.
>>
>> This is the idea that underlies the International System of Units
>> (SI).
>>
>> We need these "maximal subtypes" of 'particular quantity' to create
>> a uniform scheme for magnitudes of things that can be compared.
>> But the VIM has no need to deal with all the other subtypes -- those
>> are just the particular relations, like 'circumference' and
>> 'ultimate tensile strength', which are irrelevant to the system of
>> measurements and the system of units.
>>
>> Pat noted this, but he devised an alternative model:
>>
>>> It would make sense to allow each KOQ to have an associated
>>> dimension, but the association be many-one, so that length, width,
>>> distance, etc. all are different KOQs but all associated with the
>>> one physical dimension, which is spatial distance. But that
>>> requires relaxing the 'incomparable with other kinds' restriction
>>> you mention above. NOt sure about this.
>>
>> The VIM model is 1-to-1 by choosing a maximal KOQ that represents
>> the dimension. That makes the KOQ and the dimension the same
>> concept. The alternative model, which Pat sketched, separates the
>> two concepts: KOQ and dimension, and makes the relationship many-
>> to-1. In that model, there is no concept for the maximal SKOQ, but
>> the comparability property is then based on the dimension, not the
>> KOQ; so the reason for the SKOQ may also disappear.
>>
>> I hope this is clearer.
>>
>> One other observation: SI treats mass and energy as 'special kinds
>> of quantity', with the property that no mass is comparable to an
>> energy. We have known for almost 100 years that this is not correct
>> at the atomic particle level. But there have been as yet no
>> international commerce measurement issues that have had to be
>> concerned about this. So, an ontology that supports SI implicitly
>> supports only Newtonian physics! (But mass is a base quantity,
>> while energy is a derived quantity, so perhaps that can somehow be
>> fudged.)
>>
>> -Ed
>>
>> --
>> 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
>>
>> "The opinions expressed above do not reflect consensus of NIST,
>> and have not been reviewed by any Government authority."
>>
>>
>
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CAESAR Systems Limited
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