From: Miles, AJ \(Alistair\) <A.J.Miles@rl.ac.uk>
Date: Wed, 12 Dec 2007 19:04:22 -0000
Message-ID: <677CE4DD24B12C4B9FA138534E29FB1D03B3FAB7@exchange11.fed.cclrc.ac.uk>
To: "Antoine Isaac" <aisaac@few.vu.nl>, "Reul, Q. H." <q.reul@abdn.ac.uk>

```
Hi all,

I've just learned that, although it's perfectly clear what a "transitive" property is, it's not so clear what an "intransitive" property is.

In my previous discussion, I assumed that a "transitive" property :p is one for whom the graph (example 1)

:a :p :b.
:b :p :c.

entails

:a :p :c.

This is the standard notion of a transitive property, e.g. as used in OWL.

I also assumed that an "intransitive" property :q is one for whom the graph (example 2)

:a :q :b.
:b :q :c.
:a :q :c.

is inconsistent (i.e. cannot be true).

So I assumed, for example, if someone interpreted skos:broader as an "intransitive" property, they would find the following graph inconsistent:

However, I just read [1], which says there are in fact several different notions of "intransitivity".

According to [1], a binary relation is sometimes called "intransitive" to indicate that it is not transitive. This is different from the way I've used "intransitive" previously.

Alternatively, a binary relation R can be called "intransitive" or "antitransitive" when for all {a, b, c} ( (aRb and bRc) implies not aRc ). This is closer to the sense I've previously used. I.e. if the property :q above is "antitransitive", then the graph (example 2) would be inconsistent.

However, note that by this definition of "antitransitivity", the graph (example 3)

:a :q :b.
:b :q :c.
:c :q :d.
:a :q :d.

is perfectly consistent, even if :q is "antitransitive". This is why [1] says that the notion of "antitransitivity" is not very useful.

Previously, I had understood "intransitive" to mean that there are no "short cuts". I.e. If I can get from a to d via b and c, there is no "shorter" way to get from a to d more "directly". In other words, any two nodes are connected by exactly one path. However, I realise now that this is a completely different notion from either of the definitions of "intransitive" given at [1].

So it would appear there are four possible options for skos:broader regarding "transitivity" ...

Option B. skos:broader is not transitive
Option D. there are no alternative paths in skos:broader

Option A supports the entailment in example 1 above.

Option B is the weakest statement. It does not support the entailment in example 1, nor does it make examples 2 or 3 inconsistent.

Option C makes example 2 inconsistent, but example 3 is consistent.

Option D makes examples 2 and 3 both inconsistent.

Note that option D also makes graphs of the form

:a :q :b.
:b :q :d.
:a :q :c.
:c :q :d.

inconsistent. This is a pattern found in some KOS, e.g.

(I made this up, but I've seen similar patterns somewhere else, I can't remember where exactly.)

Anyway, clear as mud :)

None of this answers the important question, which is: what should the "standard" interpretation of skos:broader be?

Cheers,

Al.

[1] <http://en.wikipedia.org/wiki/Intransitivity>

--
Alistair Miles
Research Associate
Science and Technology Facilities Council
Rutherford Appleton Laboratory
Harwell Science and Innovation Campus
Didcot
Oxfordshire OX11 0QX
United Kingdom
Web: http://purl.org/net/aliman
Email: a.j.miles@rl.ac.uk
Tel: +44 (0)1235 445440

> -----Original Message-----
> From: Antoine Isaac [mailto:aisaac@few.vu.nl]
> Sent: 26 November 2007 18:09
> To: Reul, Q. H.
> Cc: public-swd-wg@w3.org; public-esw-thes@w3.org; Miles, AJ (Alistair)
> Subject: Re: [SKOS]: [ISSUE 44] BroaderNarrowerSemantics
>
> Hello Quentin, Alistair
>
> The way I would treat "transitive broader" would be to 1.
> create a specialization of skos:broader (let's say,
> my:transitiveBroader) 2. declare it transitive
> owl:TransitiveProperty)
>
> This way, for the concepts involved in transitiveBroader
> statements, there will be some "locally transitive" broader.
>
> Notice that in my mind this is very different from
> interpreting skos:broader as transitive, which would be
> skos:broader rdf:type owl:TransitiveProperty And notice also
> that I *really object* to saying that, as Alistair writes it
> in the reference [1]
>
> > Interpreting skos:broader as a Transitive Property would be
> consistent
> > with the SKOS semantics. Alternatively, interpreting
> > an Intransitive Property would also be consistent with the
> SKOS semantics.
>
> If we have one case somewhere where skos:broader is not
> transitive, then *nobody on semantic web can assert that it
> is transitive*. Just consider the following case:
> - John has a thesaurus for which broader is not transitive
> - Mary has a thesaurus for which broader is transitive and,
> "interpreting skos:braoder as transitive", puts the infamous
> triple skos:broader rdf:type owl:TransitiveProperty in here
> knowledge base.
> Then whenever a Semantic Web tool loads Mary's knowledge base
> at the same time as John's one, it would propagate unintended
> skos:broader statements (between the concepts of John's
> thesaurus) With respect to this kind of problem, only the
> "locally transitive"
> specialization pattern I've proposed is safe.
>
> Cheers,
>
> Antoine
>
> [1] http://www.w3.org/2006/07/SWD/wiki/SKOS/Reference
>
> > Hi all,
> >
> > I think [ISSUE 44] might have been resolved at the f2f in
> Amsterdam a
> > few months ago as I think to remember that we would allow people to
> > use skos:broader/skos:narrower as both transitive and intransitive.
> >
> > However, I believe that these semantic relations should be made
> > transitive. For each skos:ConceptScheme, there might have
> one or more
> > top concept and there might have several subconcepts available for
> > each of them.
> >
> > Example:
> > skos:ConceptScheme W
> > W skos:hasTopConcept X
> > X skos:narrower Y
> > Y skos:narrower Z
> >
> > The user might want to know that Z skos:broader X. Or would simple
> > graph operation be enough to find all the sub- or super- concepts?
> >
> > Furthermore, we have defined a skos:Concept rdf:type owl:Class and
> > hence skos:broader and skos:narrower could be used to describe
> > owl:Class in ontologies. I'm not sure that we want
> > skos:semanticRelation to be applied between owl:Class.
> >
> > I'm sorry if any of these issues have already been covered.
> >
> > Regards,
> >
> > Quentin
> >
> > [ISSUE 44] http://www.w3.org/2006/07/SWD/track/issues/44
> >
> > ******************************************
> > * Quentin H. Reul                        *
> > * PhD Research Student                   *
> > * Department of Computing Science        *
> > * University of Aberdeen, King's College *
> > * Room 238 in the Meston Building        *
> > * ABERDEEN AB24 3UE                      *
> > * Phone: +44 (0)1224 27 4485             *
> > * http://www.csd.abdn.ac.uk/~qreul       *
> > ******************************************
> >
> >
> >
> >
> >
>
>
>
```
Received on Wednesday, 12 December 2007 19:13:22 GMT

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