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Re: (Round 2) Proposed Extensions to OWL

From: Sandro Hawke <sandro@w3.org>
Date: Fri, 27 Jun 2003 07:41:03 -0400
Message-Id: <200306271141.h5RBf3P7014343@roke.hawke.org>
To: "Roger L. Costello" <costello@mitre.org>
cc: www-rdf-interest@w3.org


> Do you agree that this is the relationship between the two
> anonymous resources?  Or is the relationship something else?  /Roger

I would model it like this:

   There is one PhysicalQuantity here which has two measures (which
   are Measures); the two measures have different units and scalar
   quantities.


SUMO [0] says [1]:

  If number is an instance of real number, then "number inch(s)" is
  equal to ""number*" meter(s)".  

  (=>
      (instance ?NUMBER RealNumber)
      (equal
            (MeasureFn ?NUMBER Inch)
            (MeasureFn
                  (MultiplicationFn ?NUMBER 0.0254)
                  Meter)))

This uses "MeasureFn" to map from two arguments (or as you put it "the
"concatentation" of two things in RDF, which only allows one argument)
to the things which are in fact equal.  MeasureFn is defined [2] as:

  This BinaryFunction maps a RealNumber and a UnitOfMeasure to that
  Number of units. It is used for expressing ConstantQuantities. For
  example, the concept of three meters is represented as (MeasureFn 3
  Meter).  

In RDF you'd have to have to write "(MeasureFn 3 Meter)" as something
more like

    <x:LengthMeasure>
      <x:measure rdf:parseType="Resource">
         <x:number rdf:datatype="xsd:int">3</x:number>
	 <x:units rdf:resource="x:meter"/>
      <x:MeasureFn>
    </rdf:LengthMeasure>

Of course the class "LengthMeasure" could be replaced by anything in
the class tree, like PhysicalQuantity, Quantity, or Resource (aka
Description). 

Back to your example.    Given:

    <x:LengthMeasure rdf:about="#m1">
      <x:measure rdf:parseType="Resource">
         <x:number rdf:datatype="xsd:float">1.0</x:number>
	 <x:units rdf:resource="x:in"/>
      <x:MeasureFn>
    </rdf:LengthMeasure>

    <x:LengthMeasure rdf:about="#m2">
      <x:measure rdf:parseType="Resource">
         <x:number rdf:datatype="xsd:float">2.54</x:number>
	 <x:units rdf:resource="x:cm"/>
      <x:MeasureFn>
    </rdf:LengthMeasure>

and the suitable axioms (as given in [1] and [2]), we should be able
to prove:

    <x:Description rdf:about="#m2">
       <owl:sameAs rdf:resource="#m2" />
    <rdf:Description>

which is as it should be.

In n3 we might write:

   [x:measure [ x:number 1.0; x:units x:in ]]
   =  
   [x:measure [ x:number 2.54; x:units x:cm ]]

which should follow from the SUMO PhysicalQuantity axioms.

(I don't actually know much about SUMO.  The links I've used look less
official than [3] but somewhat clearer.  My "x" namespace doesn't
match SUMO because SUMO includes n-ary predicates and function terms.)

       -- sandro  (doing penance for reinventing too many wheels)


[0] http://ontology.teknowledge.com/
[1] http://virtual.cvut.cz/kifb/en/concepts/_inch.html
[2] http://virtual.cvut.cz/kifb/en/concepts/_measure_fn.html
[3] http://ontology.teknowledge.com:8080/rsigma/SKB.jsp?req=SC&skb=SUMO&id=449

================================================================
> Thanks for your comments yesterday.  We are making progress 
> (by discarding things that are not true).
> 
> Let's take a very close look at these anonymous resources again:
> 
> Resource #1:
> 
>        <rdf:Description>
>            <rdf:value>1.0</rdf:value>
>            <units>inch</units>
>        </rdf:Description>
> 
> Resource #2:
> 
>        <rdf:Description>
>            <rdf:value>2.54</rdf:value>
>            <units>centimeter</units>
>        </rdf:Description>
>       
> What do we know about these two anonymous resources?
> 
> 1. They do not represent the same resource.
> 
> 2. There is a relationship between
> 
>         concat(rdf:value, units) in resource #1, and
>         concat(rdf:value, units) in resource #2.
> 
>     "There is a relationship between the concatenation of the
>      value of the rdf:value property with the value of the units
>      property in resource #1, and a similar concatenation of
>      values in resource #2."
> 
>     The relationship is:
> 
>        1.0 inch = 2.54 centimeter
> 
Received on Friday, 27 June 2003 07:41:06 GMT

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