Re: Differences between SKOS and ISO standards : transitivity

Hi Simon,

On Fri, Feb 13, 2009 at 03:40:49PM -0500, Simon Spero wrote:
> On Fri, Feb 13, 2009 at 11:47 AM, Leonard Will
> <L.Will@willpowerinfo.co.uk>wrote:
> 
> I realise that I was not quite rigorous in what I said about transitivity in
> > my message earlier today. To  clarify, as I understand them to be used in
> > the thesaurus community and in ISO standards:
> >
> > The generic relationship BTG is transitive
> >
> > The partitive relationship BTP is transitive
> >
> > The generalised  relationship BT can not be assumed to be transitive,
> > because different occurrences of it may represent a mixture of the above
> > types.
> >

I think the statement above, and Svenonius' interpretation (below) are
perfectly compatible. I think this argument disappears when you
consider how to model Svenonius' interpretation in RDF/OWL. I wrote
about this briefly in [1].

In a nutshell, I believe the following axiom completely expresses
Svenonius' model:

SubPropertyOf( PropertyChain( dcterms:subject skos:broader ) dcterms:subject )

I chose dcterms:subject to represent the "aboutness" relationship, you
could chose whichever property you like, the point is you need *some*
property to represent the link between a SKOS concept and some
document which is "about" that SKOS concept. Once you have that
property, you can assert the above axiom, which entails the
propagation of "aboutness" up a skos:broader tree. This entailment
*does not require* that skos:broader itself be transitive.

For more on property chains, see [2].

Generally speaking, I would avoid using "extension" as Svenonius does
on this list, because it has a different sense from the RDF or OWL
notions of a class or property extension [3]. If you must talk about
"extensions", I suggest you say "the Svenonius extension" to help
disambiguate in discussions here. We can then represent the Svenonius
extension in RDF triples via some property like dcterms:subject,
assert a property chain axiom, and all live in harmony.

Cheers,

Alistair

[1] http://lists.w3.org/Archives/Public/public-esw-thes/2008Jul/0003.html
[2] http://www.w3.org/TR/2008/WD-owl2-new-features-20081202/#F8:_Property_chain_inclusion
[3] http://www.w3.org/TR/2004/REC-rdf-mt-20040210/#RDFSINTERP

> 
> I don't believe that the last  statement is correct.   As Svenonius(2000,
> p.130) explains:
> 
> Subject language terms differ *referentially* from words used in ordinary
> language. The former do not refer to objects in the real world or concepts
> in a mentalistic world but to subjects. As a name of a subject, the term *
> Butterflies* refers not to actual butterflies but rather to the set of all
> indexed documents about butterflies. In a natural language the extension, or
> extensional meaning, of a word is the class of entities denoted by that
> word, such as the class consisting of all butterflies. In a subject language
> the extension of a term is the class of all documents about what the term
> denotes, such as all documents about butterflies.
> 
> The BT relationship is thus transitive, because it operates over the domain
> of documents, not the domain of the items described by those documents.
> 
> This is distinction is absolutely fundamental to understanding any formal
> model of controlled vocabularies and subject analysis.
> 
> As Barbara Tillett states in her endorsement of both the 2000 printing, and
> the new 2009 paperback edition,  "This book provides sound guidance to
> future developers of search engines and retrieval systems. The work is
> original, building on the foundations of information science and
> librarianship of the past 150 years."
> 
> If the distinction is rejected, and the extension of SKOS concepts are
> butterflies, not documents, then it is entirely redundant in the face of OWL
> and its progeny. Otherwise the logical consequences of making this
> distinction are simple and direct .
> 
> a, b : Thing
> A,B : Document , where A is a Document about a, and B is a document about b
> 
> As Leonard says: isa and is_part_of are transitive:
> 
> a isa b, b isa c   |= a isa c
> a is_part_of b, b is_part_of c  |= a is_part_of c
> 
> (The latter rule has been the subject of some disagreement, mostly between
> Alan Cruse and himself. It is now generally accepted within  Lexical
> semantics. See e,g. Croft and Cruse (2004).)
> 
> These underlying relationships entail certain relationships in the domain of
> Indexing systems.
> 
> a is_part_of b   |=  A BTP B  -- if every a is part of a b, then every
> document about a is also about b , because an a part of a b
> A BTP B           |= a is_part_of b
> 
> Note that this implies that A BTP B, B BTP C |= A BTP C  -- the specific
> underlying partative relationship is preserved
> 
> a isa b      |= A BTG B
> A BTG B  |= a isa b
> 
> Note that this implies that A BTG B, B BTG C |= A BTG C
> 
> A BTG B            |= A BT B
> A BTP B             |= A BT B
> 
> (since BTG and BTP are subrelations of BT)
> 
> The inference rule that is in dispute is this one:
> 
> A BT B, B BT C  |= A BT C
> 
> This can be read saying "If all documents about A are also about B, and all
> documents about B are also about C, all documents about A are also about
> C".
> 
> Note that this *does not* allow one to infer A BTG B ( and thus a isa b )
> from A BT B.
> 
> An example may make this clearer.
> 
> An S2000 Steering Wheel may be part of a Honda S2000, a Honda S2000 may be a
> type of car and a Car may be a type of Vehicle.
> 
> These ontological relationships can be expressed as
> 
> S2000_Steering_Wheel is_part_of Honda_S2000
> Honda_S2000 isa Car
> Car isa Vehicle
> 
> >From this we can infer the following relationships between sets of
> documents.
> 
> (1) S2000 Streering Wheel BTP Honda S2000
> (2) Honda S2000 BTG Car
> (3) Car BTG Vehicle
> 
> Using the standard framing, we can express these assertions in English as:
> 
> (A) Every document about a Honda S2000 Steering Wheel  (H2KSW) is
> necessarily also about Honda S2000s, by virtue of the H2KSWl being part of
> an S2000.
> 
> (B) Every document about a Honda S2000 is necessarily also about cars,
> because an S2000 is a kind of car.
> 
> (C) Every document that is about cars is necessarily also about vehicles,
> because cars are a kind of vehicle.
> 
> Now, let us assume that the transitivity property of BT does not hold.
> 
> (D) This requires  that there may be a document *d* that is about S2KSWs but
> is not about cars.
> 
> (E) By (A), we can infer that *d* is about Honda S2000s
> 
> (F) By (B,E), we can infer that *d* is about Cars
> 
> But (D,E) is a contradiction.  RAA.
> 
> Simon
> 
> [Croft and Cruse(2004)]    William Croft and D. A. Cruse. Cognitive
> Linguistics. Cambridge University Press, 2004. ISBN 0521667704,
> 9780521667708.
> 
> [Cruse(1986)]    D. A. Cruse. Lexical semantics. Cambridge textbooks in
> linguistics. Cambridge University Press, Cambridge Cambridgeshire; New York,
> 1986. ISBN 052125678X; 0521276438. D.A. Cruse.; ;24 cm; Includes indexes.;
> Bibliography: p. 295-301.
> 
> [Svenonius(2000)]    Elaine Svenonius. The Intellectual Foundation of
> Information Organization. MIT Press, Cambridge, Mass., 2000. ISBN 0262194333
> (hc : alk. paper). URL http://www.netlibrary.com/AccessProduct.aspx?
> ProductId=39954.
> 
> 
> 
> 
> >
> >

-- 
Alistair Miles
Senior Computing Officer
Image Bioinformatics Research Group
Department of Zoology
The Tinbergen Building
University of Oxford
South Parks Road
Oxford
OX1 3PS
United Kingdom
Web: http://purl.org/net/aliman
Email: alistair.miles@zoo.ox.ac.uk
Tel: +44 (0)1865 281993

Received on Monday, 16 February 2009 18:10:19 UTC