Dear All, (01)
Extracting something simple
Joe is seeking something simple, and I think that we now have it. (02)
The argument is as follows:
1) There is a magnitude_of_quantity (Q3) that is expressed as "1.3 kg". This
is an equivalence class. (03)
2) My_book is classified as a member of "1.3 kg". (04)
3) There is a set of mass instances of magnitude_of_quantity, which we can
call "mass as a class of magnitude". This set is a member of
kind_of_quantity (as class of magnitude - Q4). (05)
4) Any quantity of matter is a member of exactly one member of "mass as a
class of magnitude". Therefore there is a function from quantity of matter
to "mass as a class of magnitude". We can call this function "hasMass". (06)
5) The relationship between my_book and "1.3 kg" is an evaluation of this
function. So in OWL serialised as N3, we have: (07)
:My_book :hasMass [ :expressedAs [ number: "1.3"; reference:
"kilogram" ] ] . (08)
In this representation:
- The instance of magnitude_of_quantity is anonymous. It is merely necessary
to specify the quantity_value that expresses it.
- The instance of quantity_value is anonymous. It is merely necessary to
specify its number and reference. (09)
What do we need in the standard ontology?
This example replies upon:
Q3 - magnitude of quantity - an equivalence class;
Q4 - kind of quantity (as class of magnitude) - a set of instances of
magnitude of quantity of the same kind;
mass - as a member of Q4 and a subclass of Q3. (010)
The definitions of Q3 and Q4 are rooted in the VIM, and therefore we have
largely met our objective. We can declare that we have won, and go home. (011)
The example also relies upon the function "hasMass". I suggest that this
function is out of scope because: (012)
1) It is a derived concept, which is there for implementation purposes only.
The statement about the mass of the book can be made without using this
function as: (013)
:My_book a [ :expressedAs [ number: "1.3"; reference: "kilogram" ] ] . (014)
This is a true statement, but not useful in an implementation. A query "what
is my_book classified as?" is going to return a lot of rubbish. (015)
2) The function "hasMass" is one of a family of functions such as "has mass
when empty", "has mass when full of oil", "has mass when full of water",
etc.. The standardisation of these functions is clearly outside our scope. (016)
(Ed says that the discussion of mass does not generalise. We need to work on
this. I think that it does, but only for the quantity mass is a function
"hasQuantity" widely useful. The function hasLength exists, but it is only
useful for lines. Instead we use "has height", "has waist measurement", etc..) (017)
What have we missed?
We have not specified what is the particular quantity (Q1) or its kind (Q2).
There are different views about this, so lets tackle this later. (018)
The concepts "mass when empty", "mass when full of oil" are all member of
the box in the straw man UML diagram denoted "generic quantity". These are
sometimes conveniently regarded as functions, but this is not the only
approach. Again, lets tackle this later. (019)
At 16:05 25/09/2009 -0400, you wrote:
>PH> ... but we ought to provide some axioms relating our notions
> > to appropriate higher-level categories, if only in order to provide
> > a guide to those whose task it is to write such axioms. Can people
> > use 'mass' as a function on physical objects, for example?
>"Mass" can be interpreted as a function applied to a physical object.
>An algorithm that evaluates this function is a weighing procedure.
>Joseph B. Collins, Ph.D.
>Code 5583, Adv. Info. Tech.
>Naval Research Laboratory
>Washington, DC 20375
>(202) 767-1122 (fax)
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