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Re: owl:allValuesFrom and rdfs:domain

From: Sampo Syreeni <decoy@iki.fi>
Date: Thu, 18 Dec 2003 18:42:10 +0200 (EET)
To: Bernard Vatant <bernard.vatant@mondeca.com>
Cc: www-rdf-logic@w3.org
Message-ID: <Pine.SOL.4.58.0312181741070.18596@kruuna.Helsinki.FI>

On 2003-12-18, Bernard Vatant uttered:

><owl:Class rdf:ID="BlueThing">
>  <owl:equivalentClass>
>    <owl:Restriction>
>      <owl:onProperty rdf:resource="#color" />
>      <owl:allValuesFrom rdf:resource="#ShadeOfBlue" />
>    </owl:Restriction>
>  </owl:equivalentClass>
></owl:Class>
>
><owl:ObjectProperty rdf:ID="color">
>  <rdfs:domain rdf:resource="#VisibleThing"/>
></owl:ObjectProperty>
>
>What can be asserted between the classes BlueThing and VisibleThing?

Nothing, really. Under these definitions we only know that colored things
are visible and that a subset of them is also blue. Nothing is said about
things which do not have a color, so in this case things can come in all
combinations of visible/invisible and blue/complement(blue).

>There is more tricky.
>
><owl:Class rdf:ID="InvisibleThing">
>  <owl:complementOf>
>    <owl:Class rdf:about="#VisibleObject"/>
>  </owl:complementOf>
></owl:Class>
>
>Does the following triple hold?
>
>InvisibleThing  rdfs:subClassOf  BlueThing

Yes. Invisible is the complement of visible, and complements are disjoint,
so invisible things cannot be visible. Since all things with a color are
visible, invisible things cannot have a color. When a thing has no color,
all of its colors are a shade of blue, so all invisible things are blue
things.

This only seems weird because BlueThing is underspecified. All of the
colors being shades of blue isn't a sufficient condition for something
being a blue thing if there are things which do not have a color. Since
this is possible, our objects can be one of three (not two) types: blue,
some other color, or invisible. When we define blue things, we'll have to
exclude things with no color in addition to things with the wrong color.
Your definition of blue things (and the TexasThings example) assumes that
things come in just two varieties, and bumps into weirdness when we take a
complement of one of them. This is essentially a form of the fallacy of
the excluded middle.
-- 
Sampo Syreeni, aka decoy - mailto:decoy@iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
Received on Thursday, 18 December 2003 11:42:18 GMT

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