Dear David,
Thanks for your explanation about power sets. It is clear to me now.
Pleas allow me to go back to your figure now: http://www.caesarsystems.co.uk/uom_ontology_progress/uom_ontology_progress-files/quantity_meta-levels.gif.
I leave the power sets out of consideration for a moment.
Below is a class diagram that I could draw up from the example. It is based on VIM. (|_ indicates a class or an instance; underlined indicates an instance; - indiates a property, and 1.3 is a float):
|_ quantity (Q1)
|_ length
|_ length of my table at my instant
|_ magnitude/measure (Q3)
|_ 1.3 metre
- numerical value: 1.3
- unit of measure: metre
|_ Unit
|_ metre
Here we do not need Q2 (kind of quanity) (it is inherent to classification), Q4 (I think we do not need a classification of magnitudes/measures), and length - as class of magnitude (which is only necessary because of, I think, mixing up quantities and magnitudes/meaures).
Am I talking sense? I believe the above is still VIM, but now I have translated it to ontology. Which does not mean, in principle, that every concept in VIM is a class in UoM.
Maybe the seemingly difference in our views is that you focus more on set theory and I do more on ontology?
However, I do think our views are very close already, which is good. However, the devil may be in the detail, which I see more often in ontology.
Best regards, Hajo
-----Original Message-----
From: uom-ontology-std-bounces@xxxxxxxxxxxxxxxx [mailto:uom-ontology-std-bounces@xxxxxxxxxxxxxxxx] On Behalf Of David Leal
Sent: 10 September 2009 11:56
To: uom-ontology-std
Subject: Re: [uom-ontology-std] FW: Quantity kinds
Dear Hajo,
This is on fringe of set theory - see http://en.wikipedia.org/wiki/Power_set .
The powerset (or powerclass) of the set S is the set of all subsets of S.
Sometimes the powerset/powerclass of S is denoted S*. (Neither the term "powerclass" nor the notation S* is used in the Wikipedia page.)
Hence if S is {a, b, c}, then S* is {{}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}.
L* is the set of all subsets of "length as a class of particular quantity".
Therefore any set of particular lengths, chosen on any basis, is a member of L*.
A useful set of particular lengths can be defined that consists of ALL particular lengths that are equal in magnitude to a chosen reference particular length. The set of particular lengths called "1.3 metres" is an example of this. This set is a member of L*.
The set of all sets of this type with different magnitudes is a subset of L*. This subset is called "length as a class of magnitude" in the picture.
The object "the metre" is not a particular length but a set of particular lengths that are equal in magnitude. Therefore it is a member of "length as a class of magnitude".
The set "length as a class of magnitude" seems to have some useful properties which enable us to define one member with respect to another.
Hence we can define the member "1.3 metres" with respect to "the metre".
Best regards,
David
At 11:11 10/09/2009 +0200, you wrote:
>Dear David,
>
>Thanks for the picture showing the objects and their meta-levels.
>Please allow me to ask a few questions, for my understanding:
>1. What is the difference between Q1* and Q1?
>2. What is L*? A symbol, perhaps?
>3. What is the difference between Q3 and Q3*?
>
>Thanks in advance.
>
>Best regards, Hajo
>
>________________________________
>
>Van: uom-ontology-std-bounces@xxxxxxxxxxxxxxxx namens David Leal
>Verzonden: zo 6-9-2009 11:36
>Aan: uom-ontology-std
>Onderwerp: Re: [uom-ontology-std] FW: Quantity kinds
>
>
>
>Dear Mike,
>
>Alas, everything is abstract except the members of particular_quantity.
>The
>different abstractions are at different meta-levels, which it is why it
>is so confusing.
>
>I have taken Hajo's example, and shown the objects and their
>meta-levels in
>http://www.caesarsystems.co.uk/uom_ontology_progress/uom_ontology_progr
>e
>ss-f
>iles/quantity_meta-levels.gif .
>
>The bottom left of the diagram has exactly what Hajo wishes. The top
>right of the diagram is entirely abstract and may seem unnecessary, but
>I do not think that this is so. Its utility is justified as follows:
>
>1) "1.3 metres" and "the metre" are both members of "magnitude of
>quantity"
>and of "length as a class of magnitude" (neither are members of "length
>as a class of particular quantity" because both are abstractions and
>not members of "particular quantity");
>2) that "1.3 metres" can be expressed in terms of its relationship with
>a unit, such as "the metre", is a property of the class "length as a
>class of magnitude";
>3) a subclass of "Q4, kind of quantity as class of magnitude" can be
>defined that contains all members for which a simple relationship with
>a unit exists.
>
>Best regards,
>David
>
>At 00:39 05/09/2009 +0100, you wrote:
>>Would it be less confusing if one of those had a parent class of
>>"Abstract Thing" and the other had a parent class of " Concrete thing"
>>or "Particular thing" or some such? Because I think you've hit the
>>nail on the head about what the actual distinction is, and therefore
>>it should be possible to represent that in the upper ontology.
>>
>>More broadly, all these distinctions would surely lend themselves to
>>modeling such that the model, and not the reader's understanding of
>some
>>paragraph, is what captures or fixes the meaning?
>>
>>Mike
>>
>>Ed Barkmeyer wrote:
>>> Rijgersberg, Hajo wrote:
>>>
>>>> 1. Maybe the most important question is (and probably only for my
>information and understanding): why do we base the vocabulary on VIM?
>>>>
>>> VIM is the International Vocabulary for Measurement, a publication
>>> of BIPM -- the people who maintain the international standards for
>>> units
>of
>>> measure. http://www.bipm.org/en/publications/guides/vim.html
>>> It seemed like adopting their vocabulary would be good, and we have
>>> tried to stay close to that.
>>>
>>>
>>>> (I'm very interested in studying VIM, but couldn't find the
>document.
>Could someone please send me a link?) There are also other documents
>that we could base our vocabulary on.
>>>>
>>>>
>>> Yes. For example, we could use the model in DOLCE or Cyc or SUMO or
>>> some other published upper ontology that provides formal axioms for
>the
>>> quantity and measurement concepts. We have a work item that says we
>>> should look at these.
>>>
>>>
>>>> 2. But then I ignore VIM, and repeat myself: couldn't we have:
>>>>
>>>> "length of my table" ---"member of" ---> "length quantity"
>>>> "length quantity" ---"subclass of" ---> "quantity"
>>>>
>>>> This is in accordance with some standard documents I know.
>>>>
>>>>
>>> And it is in accordance with the model that David has produced. But
>he
>>> uses "instance of", instead of "member of" ("instance" is an
>>> "intensional" characterization; "member" is an "extensional"
>>> characterization; although probably only an ontology purist would
>care.)
>>>
>>>
>>>>
>>>> 3. Also, according to these documents, e.g. "1.3 metre" is not a
>quantity, but a measure.
>>>>
>>> Agreed. VIM calls it a "quantity value", which is an "_expression_ of
>the
>>> magnitude of a quantity". VIM uses "measure" to talk about a
>>> process for determining a quantity value and for the results of that process.
>>>
>>>
>>>> (A quantity is like a variable, it is a reference to a value, like
>"1.3
>metre".)
>>>>
>>>>
>>> We are careful to distinguish the class "quantity", whose instances
>are
>>> particular quantities, like "the length of your table", from the
>class
>>> "quantity magnitude", whose instances are the abstractions --
>>> amounts
>of
>>> length stuff. So if you have two chairs next to your table and they
>are
>>> identical in size and shape, "the height of the first chair" is a
>>> (particular) quantity, and "the height of the second chair" is a
>>> (particular) quantity, and they are _different_ instances of
>"quantity",
>>> but they have the same "magnitude". That is, there is one amount of
>>> 'length' that they both have.
>>>
>>> "1.3 metre" is a quantity value, which is an _expression_/name for a
>>> "quantity magnitude". If your chairs are 1.3 metres high, then "1.3
>>> metres" is a name for the magnitude of the height of each chair. And
>of
>>> course, the same magnitude can have other names, such as "51 inches".
>
>>> "51 inches" and "1.3 metres" are two different quantity values, but
>they
>>> express the same "magnitude". That is the model we are proposing.
>>>
>>> But then there are two (or more) different classifiers that are
>called
>>> "length". length-1 is a subclass of "(particular) quantity". The
>>> length of your table is a length-1, the height of the second chair
>>> is
>a
>>> length-1. But the magnitude of the height of the second chair is
>>> not
>a
>>> length-1. length-2 is a subclass of 'quantity magnitude'. The
>>> magnitude of the height of the second chair, which is the same as
>>> the magnitude of the height of the first chair, is a length-2. So
>>> we
>must
>>> choose one of these to be what we mean by "length". VIM is very
>clear
>>> that it means length-1. But then we must not say that "1.3 metres
>>> expresses a length"; we must say (as VIM does) that "1.3 metres
>>> expresses the magnitude of a length".
>>>
>>> I personally think this usage is confusing for everyone. I would
>prefer
>>> that we use "particular quantity" to be the class of things like the
>>> height of the second chair, and use "quantity" to be what VIM calls
>the
>>> "magnitude". But, on the other hand, you can't ever measure a
>>> "magnitude"; you can only measure a particular quantity -- the
>>> height
>of
>>> the second chair. The "magnitude" itself is not a physical
>phenomenon;
>>> it is an abstraction. So it is very important that we agree on what
>>> definition we choose for each term we use. Otherwise, everyone is
>confused.
>>>
>>>
>>>> Again, hopefully this discussion is appreciated; it is meant to be
>constructive, with the aim of working together to achieve a
>high-quality vocabulary.
>>>>
>>> Me, too. But we keep going around these same issues, because people
>>> don't understand the definitions.
>>>
>>> -Ed
>>>
>>>
>>
>>
>>--
>>Mike Bennett
>>Director
>>Hypercube Ltd.
>>89 Worship Street
>>London EC2A 2BF
>>Tel: +44 (0) 20 7917 9522
>>Mob: +44 (0) 7721 420 730
>>www.hypercube.co.uk
>>Registered in England and Wales No. 2461068
>>
>>
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>>
>>
>
>============================================================
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>CAESAR Systems Limited
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