Re: subsumption of properties?
Timothy Redmond <[email protected]> Mon, 11 Nov 2013 09:36:23 -0800
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On 11/11/2013 08:52 AM, Michael DeBellis wrote:
> I've been using Protege for a while now and one thing I'm still not
> clear on is when and why do you subclass a property? All the other
> capabilities make perfect sense but I've never come across a system
> where you make sublcasses of properties or relations before. Can
> someone give a brief couple of sentences that explains this or point
> me to the appropriate place in the documentation?
A simple example comes from the pizza ontology wherein hasTopping and
hasBase are sub-object-properties of hasIngredient.
Informally, p is a sub object property of q if for any pair of
indiivduals, x and y, if p maps x to y then q maps x to y. This can be
formalized by introducing the notion of an interpretation of a language
which is done for owl 2 here:
http://www.w3.org/TR/2012/REC-owl2-direct-semantics-20121211/
The formal definition of subObjectProperty is given here (the first
entry at the top of table 6):
http://www.w3.org/TR/2012/REC-owl2-direct-semantics-20121211/#Object_Property_Expression_Axioms
Data sub properties are similar. r is a sub data property of s if for
any individual, x, and any data value, d, if r maps x to d then s maps x
to d.
>
> One thing that would help is understanding the formal definition of
> what it means to say one property is a subclass of another. Looking at
> properties as relations it seems to me a necessary requirement for
> property X to be a subclass of property Y is that the domain and
> range of X must be subsets of the domain and range of Y. But that
> doesn't seem like a sufficient definition,
This is a necessary but not a sufficient condition.
-Timothy
> I think I could create examples where that was true but it doesn't
> seem appropriate to have the two properties be sub-properties.
>
> Michael DeBellis
>
>
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<div class="moz-cite-prefix">On 11/11/2013 08:52 AM, Michael
DeBellis wrote:<br>
</div>
<blockquote
cite="mid:[email protected]"
type="cite">
<div style="color:#000; background-color:#fff; font-family:times
new roman, new york, times, serif;font-size:12pt">
<div>I've been using Protege for a while now and one thing I'm
still not clear on is when and why do you subclass a
property? All the other capabilities make perfect sense but
I've never come across a system where you make sublcasses of
properties or relations before. Can someone give a brief
couple of sentences that explains this or point me to the
appropriate place in the documentation? <br>
</div>
</div>
</blockquote>
<br>
<br>
A simple example comes from the pizza ontology wherein hasTopping
and hasBase are sub-object-properties of hasIngredient.<br>
<br>
Informally, p is a sub object property of q if for any pair of
indiivduals, x and y, if p maps x to y then q maps x to y. This can
be formalized by introducing the notion of an interpretation of a
language which is done for owl 2 here:<br>
<br>
<pre> <a class="moz-txt-link-freetext" href="http://www.w3.org/TR/2012/REC-owl2-direct-semantics-20121211/">http://www.w3.org/TR/2012/REC-owl2-direct-semantics-20121211/</a>
</pre>
<br>
The formal definition of subObjectProperty is given here (the first
entry at the top of table 6):<br>
<br>
<pre> <a class="moz-txt-link-freetext" href="http://www.w3.org/TR/2012/REC-owl2-direct-semantics-20121211/#Object_Property_Expression_Axioms">http://www.w3.org/TR/2012/REC-owl2-direct-semantics-20121211/#Object_Property_Expression_Axioms</a>
</pre>
<br>
Data sub properties are similar. r is a sub data property of s if
for any individual, x, and any data value, d, if r maps x to d then
s maps x to d. <br>
<br>
<br>
<blockquote
cite="mid:[email protected]"
type="cite">
<div style="color:#000; background-color:#fff; font-family:times
new roman, new york, times, serif;font-size:12pt">
<div style="color: rgb(0, 0, 0); font-size: 16px; font-family:
times new roman,new york,times,serif; background-color:
transparent; font-style: normal;"><br>
<span></span></div>
<div style="color: rgb(0, 0, 0); font-size: 16px; font-family:
times new roman,new york,times,serif; background-color:
transparent; font-style: normal;"><span>One thing that would
help is understanding the formal definition of what it means
to say one property is a subclass of another. Looking at
properties as relations it seems to me a necessary
requirement for property X to be a subclass of property Y
is that the domain and range of X must be subsets of the
domain and range of Y. But that doesn't seem like a
sufficient definition,</span></div>
</div>
</blockquote>
<br>
This is a necessary but not a sufficient condition.<br>
<br>
<br>
-Timothy<br>
<br>
<blockquote
cite="mid:[email protected]"
type="cite">
<div style="color:#000; background-color:#fff; font-family:times
new roman, new york, times, serif;font-size:12pt">
<div style="color: rgb(0, 0, 0); font-size: 16px; font-family:
times new roman,new york,times,serif; background-color:
transparent; font-style: normal;"><span> I think I could
create examples where that was true but it doesn't seem
appropriate to have the two properties be sub-properties.</span></div>
<div style="color: rgb(0, 0, 0); font-size: 16px; font-family:
times new roman,new york,times,serif; background-color:
transparent; font-style: normal;"><br>
<span></span></div>
<div style="color: rgb(0, 0, 0); font-size: 16px; font-family:
times new roman,new york,times,serif; background-color:
transparent; font-style: normal;"><span>Michael DeBellis</span></div>
</div>
<br>
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<br>
<pre wrap="">_______________________________________________
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</pre>
</blockquote>
<br>
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