Re: [SKOS]: [ISSUE 44] BroaderNarrowerSemantics

Hi Alistair,

It seems we're getting somewhere.
I of course always favored the B statement ;-) because it allows "local" 
enforcement of the other statements (that is, via subproperties which 
have the concerned axiom) to co-exist seamlessly once all the graphs are 
gathered.

Cheers,

Antoine
> 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:
>
> :cows skos:broader :mammals.
> :mammals skos:broader :animals.
> :cows skos:broader :animals.
>
> 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 A. skos:broader is transitive
>  Option B. skos:broader is not transitive
>  Option C. skos:broader is antitransitive
>  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. 
>
> :violin skos:broader :stringedinstruments.
> :stringedinstruments skos:broader :musicalinstruments.
> :violin skos:broader :sopranoinstruments.
> :sopranoinstruments skos:broader :musicalinstruments.
>
> (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 
>> (my:transitiveBroader rdf:type
>> owl:TransitiveProperty)
>>
>> This way, for the concepts involved in transitiveBroader 
>> statements, there will be some "locally transitive" broader.
>> If we have (ex:A,my:transitiveBroader,ex:B),
>> (ex:B,my:transitiveBroader,ex:C) then we'll have
>> (ex:A,my:transitiveBroader,ex:C) and hence (ex:A,skos:broader,ex:C)
>>
>> 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 
>>>       
>> skos:broader as 
>>     
>>> 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 Thursday, 13 December 2007 23:28:26 UTC