I think that David Leal makes a good point that certain specific measures
will be used as though they were instances (individuals). However, they
can also be represented as the values of specific functions, as he also
suggests. (01)
What I think this indicates is that we should have a class (type) in the
ontology that represents 'particular quantities' as described by Ed
Barkmeyer:
[EB] > Q1 = a measurable aspect of a particular physical thing, e.g., the
> height of the Eiffel Tower, the length of stick A, the weight of a
> specific pack of cigarettes, as distinct from the weight of the next
> pack of cigarettes in the same carton. (Q1 = 'particular quantity',
> a subtype of 'property instance' = trope)
> (02)
This will provide a 'return value' type for the function. But I am not
sure that it will be necessary to have any subtypes for that type other than
the functions that are defined for specific needs. To represent the
individual values (the tropes), a general 5-ary function 'The' may serve,
such as: (03)
(isanInstanceOf Function The)
Arguments:
1 <AttributeType>
2 'of'
3 <Entity>
4 'atTime'
5 <TimeInterval>
'The' with its arguments:
(The <AttributeType> of <Entity> atTime <TimeInterval>) (04)
This function could be used with individuals or variables in the
argument positions: (05)
More specific functions would be subtypes:
(= HeightFun (The Height of <Object> atTime <TimeInterval>))
(isaSubtypeOf HeightFun ParticularQuantity) (06)
. . . and if desired, even more specifically:
(= HeightOfComoFun (The Height of LakeComo atTime <TimeInterval>))
(isaSubtypeOf HeightOfComoFun HeightFun) (07)
Then when these individual values need to be referenced, they can be
referenced as individuals:
(hasValue HeightOfComoFun(D20090807) (meters 23))
(this is not an equality because the 'ParticularQuantity' "
HeightOfComoFun(D20090807)" is not the same thing as the generic measure
(meters 23) (which I will call an instance of 'QuantitativeAttributeValue')
.
To get the QuantitativeAttributeValue (meters 23) directly it should also
by possible to define a unary function, e.g. 'ValueOf' which returns an
instance of measure value for any given ParticularQuantity - which I believe
is what Ed Barkmeyer's 'Q3' is intended to be: (08)
[EB] > Q3 = the measurement/abstraction of a Q1 that is comparable to the
measurement of another Q1 that is of the same Q2, e.g., an "amount of
length", that abstraction of the height of the Eiffel Tower that can be
compared to the distance between the Eiffel Tower and the Arc de Triomphe.
The Q3 is what is the same about the weight of the two identical packages of
cigarettes. It is what is being compared when we say "the distance to the
Arc is longer", "stick B is shorter than stick A". (Q3 = 'specific
quantity'?) (Each Q3 is an "equivalence class of Q1s", e.g., of all length
measurements that are the same. Each Q3 is also an "equivalence class of
quantity values", except that the abstraction exists without the values.) (09)
Then ValueOf argument is <particularQuantity> and return value would be an
instance of 'QuantitativeAttributeValue'.
The actual value that we use in mathematical equations would then be
obtained as
(= ValueOf(HeightOfComoFun(D20090807)) (meters 23)) (010)
Where
(<>
(= ValueOf(HeightOfComoFun(?Time)) ?val)
(hasValue HeightOfComoFun(?Time) ?val) (011)
. . . and, to represent mathematical/scientific generalizations, this
kind of entity can be used in a mathematical equation:
dTheValueOf(HeightOfComoFun)/dt = f(t)
. . . where f(t) can express whatever dependence that property has on
time.
[I do not have a recommendation as to the best way to represent an equation
in an ontology; this may not always be necessary, since the mathematical
calculations are likely to be done by programs that only use the ontology
representation for input and output of data, rather than calculating by
logical inference in the ontology language] (012)
Two questions:
(1) is there a simpler way to do this?
And (2) Is there any problem using such a representation? (013)
Pat (014)
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx (015)
> -----Original Message-----
> From: uom-ontology-std-bounces@xxxxxxxxxxxxxxxx [mailto:uom-ontology-
> std-bounces@xxxxxxxxxxxxxxxx] On Behalf Of David Leal
> Sent: Friday, August 07, 2009 6:23 AM
> To: uom-ontology-std
> Subject: Re: [uom-ontology-std] retitled - tropes in the ontology
>
> Dear All,
>
> An ontology for quantities and units needs to have a clear relationship
> with
> an ontology that defines what is measured. We can decide to concentrate
> on
> the former, but we need to do some work on the latter in order to
> define the
> scope boundary.
>
> A requirement
> -------------
> An ontology for what is measured needs to encompass the following
> statements:
> - The level of Lake Como in period 1990 to 2000 is cyclical with a
> period of
> one year.
> - The level of Lake Como in 1993 has a maximum value of 6 metres above
> chart
> datum.
> - The level of Lake Como on 23rd February 1993 is 5 metres above chart
> datum.
>
> This suggests that:
> 1) the_level_of_Lake_Como_in_period_1990_to_2000 needs to be recognised
> as
> an object, because it has the classification "cyclical" and the
> property
> "period";
> 2) level_of_Lake_Como_in_period_1993 is a similar type of object, and a
> part
> (in some sense) of the object
> the_level_of_Lake_Como_in_period_1990_to_2000;
> 3) level_of_Lake_Como_in_period_1993 has values qualified as maximum,
> minimum, mean, etc.;
> 3) level_of_Lake_Como_on_23rd_February_1993 is another part, which is
> sufficiently short in the chosen engineering context to be regarded as
> an
> instant and therefore have an unqualified value.
>
> A "practical engineering mathematics" approach
> ----------------------------------------------
> With a practical engineering mathematics approach, there are no
> mysteries
> here - height_of_lake_Como_about_chart_datum is a function with domain
> Lake_Como and range Length. That Lake_Como is not a class does not
> worry a
> "practical engineering mathematician" - it is a thing with
> mereotopology,
> mereotopology is just another algebraic structure, and algebraic
> structures
> are what most functions in mathematics have as their domain. Length is
> near
> enough a manifold, which is another algebraic structure.
>
> If height_of_lake_Como_above_chart_datum_in_period_1990_to_2000 is a
> subfunction defined by a constraint upon the domain. The
> height_of_Lake_Como_above_chart_datum_on_23rd_February_1993 is the
> evaluation the function at a point in its domain.
>
> Our task
> --------
> Perhaps this is to produce an ontology, or perhaps alternative
> ontologies,
> each of which formalises what "practical engineering mathematicians" do.
> We
> can then define which parts of these ontologies are within scope.
>
> Best regards,
> David
>
> At 19:03 06/08/2009 -0400, you wrote:
> >I wrote:
> >> Q1 = a measurable aspect of a particular physical thing, e.g., the
> >> height of the Eiffel Tower, the length of stick A, the weight of a
> >> specific pack of cigarettes, as distinct from the weight of the next
> >> pack of cigarettes in the same carton. (Q1 = 'particular quantity',
> a
> >> subtype of 'property instance' = trope)
> >>
> >>
> >I should make clear that I agree with Pat that this concept is
> probably
> >not useful in the ontology. It just has to be in the list of terms
> and
> >definitions so that we don't confuse it with any useful concept, and
> >don't get accused of ignoring it. We want to make and document the
> >decision to include it or exclude it.
> >
> >And I aver that it is definitely an important concept to the VIM, but
> >that is because much of the VIM is about making measurements of the
> >'tropes' -- measuring individuals and characterizing the individual
> results.
> >
> >-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."
>
> ============================================================
> 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
> ============================================================
>
>
>
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