[topicmapmail] generate hierarchical GUIs from all transitive associations

[Conal Tuohy]

Mark wrote:

> A major mathematical tool/approach that TM can heavily
> leverage is Set
> Theory, as you know (just getting us on the same page). Topic
> Map solutions
> must deal with set theory because, in my opinion TMs ARE
> sets.

In the earlier thread about class-subclass and class-instance relations, I
was also inspired to dig out my old algebra text books. It seems to me
useful to categorise associations in terms of the properties of binary
relations, such as symmetry, anti-symmetry, transitivity, reflexivity, etc.
Transitivity at least is recognised in the XTM spec with a PSI:
http://www.topicmaps.com/xtm/1.0/template.xtm#assoc-prop-transitive - it's
possible to annotate any association topic as having this property, and then
use this knowledge e.g. in your UI: the issue that came up earlier, of
selecting which associations should appear as a hierarchy in a UI,
breadcrumbs, etc, can then be dealt with automatically: an association type
is suitable if it is transitive and hence represents some kind of ordering.
The class-subclass relation is just one such relation, and a UI could
present several "genealogies" for a given topic; one for each such relation.
This is quite a common technique e.g. see the "related categories" list on a
page like http://directory.google.com/Top/Computers/Software/Internet/

Holger Rath presents this kind of idea in "Topic Map Fundamentals for
Knowledge Representation", chapter 14 of "XML Topic Maps", Addison-Wesley,
2002.

Cheers

Con