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Re: [SKOS] the return of transitive and subproperty (was Re: SKOS comment: change of namespace (ISSUE-117))

From: Bernard Vatant <bernard.vatant@mondeca.com>
Date: Tue, 29 Jul 2008 16:09:53 +0200
Message-ID: <488F24B1.9070706@mondeca.com>
To: Antoine Isaac <aisaac@few.vu.nl>
Cc: "Houghton,Andrew" <houghtoa@oclc.org>, public-swd-wg@w3.org, public-esw-thes@w3.org

Hello all

Since this issue is back on the table, let me put here a (hopefully 
clear) proposal based on both the general "natural understanding" of 
broader and narrower, and its formal mathematical interpretation as 
"strict partial orders".See 
http://en.wikipedia.org/wiki/Partially_ordered_set#Strict_and_non-strict_partial_orders
Seems to me that there are backward compatibility, terminology, hence 
marketing issues here, beyond logical foundationn of the concepts. If 
"broader" and "narrower" do not convey the most intuitive semantics, 
we're bound to endless misunderstandings and have to explain again and 
again why it is specified in such a counter-intuitive way. People will 
buy more easily "closeRelative" defined as a subproperty of "relative" 
than "relative" being defined as a subproperty of "generalRelative", 
with small prints explaining that "relative" means actually "direct 
relative".

Her is my proposal

skos:broader and skos:narrower are the most generic relationships. They 
are irreflexive and transitive (in other words, they define strict 
partial orders).
It's bound to applications to figure how they implement the transitivity 
(asserted vs computed triples).

skos:maximalNarrower  and  skos:minimalBroader  are used to define 
"direct" narrower and broader concepts

A "minimalBroader" of X is indeed mathematically defined as being a 
minimal element, relative to the broader relationship, of the set of all 
broader concepts of X.
http://en.wikipedia.org/wiki/Minimal_element

In other words 
    (X   skos:minimalBroader   Y)
iff 
    (X   skos:broader   Y)
    AND
    {Z | (X   skos:broader   Z) and (Z   skos:broader  Y)} is the empty set

Similar definition for skos:maximalNarrower

By definition :
skos:minimalBroader      rdfs:subPropertyOf       skos:broader
skos:maximalNarrower      rdfs:subPropertyOf       skos:narrower

Although it conveys under different names the same idea as 
skos:broader   rdfs:subPropertyOf    skos:broaderTransitive, I think 
it's easier to swallow because of the names.  :-)

Now something very important, and orthogonal to the terminological 
debate: the sets of minimalBroader and maximalNarrower concepts of a 
given X can only be entailed from the set of broader and narrower 
concepts *in a closed world*. IOW in a well-defined RDF graph (e.g. 
inside a declared Concept Scheme).
Actually the declaration of skos:minimalBroader or skos:maximalNarrower 
does not make much sense in an open world, where they can be easily be 
made inconsistent : one can always insert some concept between X and Y. 
The notion of empty set does not apply to an open world.

So the recommandation could be that those properties should not be 
*declared* in vocabularies, but *computed* as necessary on the basis of 
available assertions at run time, that is, in the closed world of 
assertions available here and now.

Bernard

Antoine Isaac a écrit :
>
> Dear Andrew,
>
>> It also seems to me that there is a problem with this flip/flop of 
>> skos:broader and skos:narrower being transitive.  SKOS now specifies 
>> skos:broader and skos:narrower to be non-transitive, but 
>> skos:broaderTransitive and skos:narrowerTransitive are a sub-property 
>> of skos:broader and skos:narrower respectively.  This implies to me, 
>> not being an RDF/OWL expert, that skos:broaderTransitive and 
>> skos:narrowerTransitive inherit non-transtivity from skos:broader and 
>> skos:narrower respectively, and that just seems funky since you are 
>> saying that the relationship is transitive.
>>
>
> The problem of transitivity "inheritance" (or more precisely 
> non-inheritance) problem has been many times raised, and many mails 
> have been written about it.
> Cf http://lists.w3.org/Archives/Public/public-swd-wg/2008Jun/0102.html
>
> Now, I'm afraid we cannot do otherwise. Whatever being the naming 
> decisions in the end:
> - there is need non-transitive "broader-as-asserted" property 
> (skos:broader)
> - there is a need for a transitive "broader-as-get-me-all-ancestors" 
> (skos:broaderTransitive)
> - there is a need to infer that every asserted direct broader 
> statement shall be interpreted in a way that allows to get a 
> transitive version of the hierarchy (I assume that you too have this 
> requirement)
> And for the third you have no choice but to declare the first property 
> a subproperty of the second. That's just the way OWL is made, even if 
> it may appear counter-intuitive :-(
> The nice thing is that in OWL doing so does not enforce skos:broader 
> to be transitive...
>
> Best,
>
> Antoine
>
>
>
>
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>

-- 

*Bernard Vatant
*Knowledge Engineering
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Received on Tuesday, 29 July 2008 14:10:51 GMT

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