Dear Hajo, (01)
It is good that we are understanding each other - it is a necessary first
step to reaching agreement :). (02)
Unit and magnitude/measure
--------------------------
A difficulty with your taxonomy is that metre and 1.3 metre are unrelated
concepts. (03)
A member of Q3, such as 1.3 metre, is an equivalence class which contains
ALL members of Q1 that are equal. The definition of "the metre", as a unit,
seems to be the definition of just such an equivalence class. Hence in the
diagram, it is assumed that "1.0 metre exactly" and "the metre" are the same
equivalence class which is a member of Q3. This approach has the advantage
of simplicity, therefore to reject it requires an arguement that "the
metre", as defined by the BIPM, is not a member of Q3. (04)
I agree that "length - as class of magnitude" and Q4 are largely
mathematical constructs. Nonetheless the set of all length magnitudes {1.0
metre, 1.1 metre, 1.2 metre, etc. } is a useful one. The statement that
'each can be expressed as a real number times "the metre"' is not a trivial
one and therefore it implies something about the object "length - as class
of magnitude". (05)
Property of a magnitude/measure
-------------------------------
It is probably not correct to say that a magnitude/measure has a "unit of
measure" property. Any length magnitude/measure can be expressed using any
"unit of measure", so we can equally say that 1.3 metre has a "unit of
measure" of "the inch". (06)
A better way of looking at it is to regard the (number, reference) pair as a
whole as the property. Hence using your notation, we have: (07)
> |_ 1.3 metre
> - expressed as: (1.3, metre)
> - expressed as: (51.181102, inch) (08)
Best regards,
David (09)
At 12:12 21/09/2009 +0200, you wrote:
>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_progre
>ss-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 (010)
============================================================
David Leal
CAESAR Systems Limited
registered office: 29 Somertrees Avenue, Lee, London SE12 0BS
registered in England no. 2422371
tel: +44 (0)20 8857 1095
mob: +44 (0)77 0702 6926
e-mail: david.leal@xxxxxxxxxxxxxxxxxxx
web site: http://www.caesarsystems.co.uk
============================================================ (011)
_________________________________________________________________
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 (012)
|