Broader, collections and the difference between SKOS and OWL

[I'm currently working on a more formal model, but I wanted to post an  
outline to get some feedback (and to keep me away from LaTeX related  
avoidance behavior :) .

The key point is that SKOS Concepts do not correspond directly to  
concepts/classes but instead more closely resemble Subject Terms.  If  
this distinction is taken into  account, and the relationship between  
the SKOS Concept and its associated class is explicitly modeled, many  
outstanding issues with SKOS become much easier to resolve cleanly.

  ]

1: Svenonius on Subject Terms.

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.  
(Svenonius 2000, p. 130)

2: SKOS Concepts are Svenonian Subject Terms, not concepts.

3: The extension of a SKOS Concept is the set of all documents which  
have that SKOS Concept as a subject; compare with the definition of an  
rdfs class in RDF Semantics (Hayes 2004)

4: Concept schemes are defined in the context of a specific domain  
(which may be general).  Relationships need not be valid outside that  
domain (Turbine/Fan/Blades ISO; Parrots BT Pets in a pet shop  
thesaurus).

5: Relationships between SKOS Concepts are relationships between  
Subject Terms, not Classes.   These relationships entail a different  
set of relationships between the  Classes associated with those  
Subject Terms.

6: Every hierarchical relationships between Subject Terms in  
Controlled Vocabularies must be transitive by definition. The  
relationships they entail between underly classes need not be.   
Transitivity across different subtypes of hierarchical relationships  
is only valid at the level of their least common subsumer.

[ A hierarchical relationship] is assigned to a pair of terms when the  
scope of one of the terms totally includes (is broader than) the scope  
of the other. (Dextre Clarke 2001, p. 42)

There seems to be no particular logical reason why the part-whole  
relationship should not be generally applicable. It only has to meet  
the test of always being true, just as with the other hierarchical  
relationships. (Milstead 2001, p.60)

This test of total inclusion is a rigid property of hierarchical  
relationships.   Given that associative relationships are defined  
negatively as relationships which are neither hierarchical nor  
equivalence, and  that the standards specify that relationships that  
are not truely broader are associative, an intransitive skos:broader  
cannot be disjoint with skos:related.

  7:   A  skos:broader B  means: every document  ( within the domain  
of the concept scheme) about A must also be about B.    Thus:

Wheels BT Cars   == Every document   about wheels is also a document  
about cars.
Cars BT Vehicles == Every document about cars is also a document about  
vehicles.
| 
----------------------------------------------------------------------------------------------------------------
  Wheels BT Vehicles == Every document about wheels is also a document  
about vehicles

It is incorrect to infer any relationship between the class of Wheels  
and the class of Vehicles given only a plain broader/BT assertion

8:   A BTG B means:  every document about A must also be about B  
because the class of As is a subclass of the class of Bs.

Cars BTG Vehicles == Every document about cars is also about vehicles,  
because a car is-a vehicle.
Convertibles BTG Cars == Every document about convertibles is also  
about cars, because  a convertible is a car
| 
----------------------------------------------------------------------------------------------------------------------------------------------------
  Convertibles BTG Vehicles == Every document about convertibles is  
also about vehicles, because a convertible is a vehicle

9: A BTP B means:  every document about A must also be about B,  
because every A is in some sense part of a B.

Fingers BTP Hands == Every document about fingers  is also about  
Hands, because every finger is part of a hand.
Hands BTP People == Every document about hands  is also about People,  
because every hand is  part of a person.
| 
----------------------------------------------------------------------------------------------------------------------------------------------------
Fingers BTP People == Every document about fingers is also about  
People, because every finger is part of a person.

10:  The exact relationship between the classes of two SKOS Concepts  
that are BTP depends on the nature of  partitive relationship.  Some  
subtypes of BTP may allow a more precise transitive semantics for the  
related Classes.

11:   A BTI B means:  every document about the individual A is also  
about B, because A is an instance of  B.    BTI is subset of BTG;   
thus transitivity is maintained for the underlying classes

My S2000 BTI Convertibles == Every document about my S2000 is also  
about Convertibles, because my S2000 is-a convertible
Convertibles BTG Cars == Every document about convertibles is also  
about cars, because  a convertible is-a car
| 
----------------------------------------------------------------------------------------------------------------------------------------------------
My S2000 BTI Cars == Every document about my S2000 is also about cars,  
because my S2000 is-a car

12: SKOS Collections correspond to arrays, and to what Svenonius  
termed  "perspective hierarchies".    These types of hierarchies are  
useful for representing classificatory structures; it might be  
possible to infer  quasi-facets , or specific properties.

More to come

Simon


References
Hayes, Patrick (2004). RDF Semantics. Recommendation. World Wide Web  
Consortium.
URL: http://www.w3.org/TR/2004/REC-rdf-mt-20040210/

Milstead, Jessica L. (2001). “Standards for Relationships between Sub  
ject Indexing Terms”. In: Relationships in the Organization of  
Knowledge. Ed. by Carol A Bean and Rebecca Green. Information science  
and knowledge management. Dordrecht: Kluwer Academic Publishers. Pp.  
53–66. ISBN: 0792368134.

Svenonius, Elaine (2000). The Intellectual Foundation of Information  
Organization. Cambridge, Mass.: MIT Press. ISBN: 0262194333 (hc : alk.  
paper).
URL: http://www.netlibrary.com/AccessProduct.aspx?ProductId=39954.