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

[Conal Tuohy]

Tom Myers wrote:

> Equivalence relations are transitive too...

true ... very true.

> (things greater than the same
> thing are greater than each other, right?)

Hmmm... I think you're right - you DO need more coffee ;-)

> 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 ).

You're right: anti-symmetry is necessary to rule out equivalence. But an
irreflexive relation would also be good. e.g. > is irreflexive.

> 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?

I suppose so, though different kinds of orderings might be handled
differently in a GUI? I like the idea of using these well-known relational
properties because there are only a few of them, and they form a logical
basis for a whole lot of different types of relations.

Cheers

Con