[topicmapmail] Re: generate hierarchical GUIs from all transitive associations

[Tom Myers]

"Conal Tuohy"  wrote:

> ...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: ...
> ...which associations should appear as a hierarchy ... an association type
> is suitable if it is transitive and hence represents some kind of ordering.

Equivalence relations are transitive too...(things greater than the same
thing are greater than each other, right?) A type is a (partial) ordering
and therefore can be displayed as a directed acyclic graph, if it's transitive
_and_ reflexive _and_ anti-symmetric.
   (e.g., http://www.jboden.demon.co.uk/SetTheory/order.html ).
Of course, if you add all the properties as PSIs, then you can add an
inference engine which will display a partially ordered set one way and an
equivalence relation another, but why not have the PSI be what you're
actually interested in? Let "ordered" be a PSI; let transitive/reflexive/
[anti]symmetric come later, along with the code that knows about them and
infers "ordered" from them. Yes? No? Maybe?

Of course maybe it's just that I need more coffee before I can make any
sense at all.

Tom Myers