[topicmapmail] Re: Consistency and Formal Model

[Bernard Vatant]

Sam

Following your judicious remarks about the slides,
and after some remarks from Patrice too,
I've made some modifications, starting from:
http://www.universimmedia.com/topicmaps/hypergraph/hgtm2.htm

Points to highlight, BTW answering some of your questions:

-- A vertex or an edge are represented like a "node", because they can be linked by an
arbitrary number of incidences.
But incidences are not to be seen as "nodes", they are "labeled arcs" *linking* a vertex
to an edge - and not "linked to" a vertex and an edge. Patrice pointed at that error too
in the first version. It's corrected in the prose too.

I've put the lines on each side of the label the same color as the label, to be more
explicit about the fact that they belong to the incidence/arc (they are the two "ends" of
it, if you like). Sometimes the label hides an "angle" in the arc, for graphical
representation reasons, but don't get misled by that ...

So there are in the hypergraph really no other element type than vertex, edge and
incidence. No "hidden arcs".

-- I've added some maths in the first slide, to try to explain more that the structure is
completely formal, and the figure just a representation, and link the two through the
example.

-- I've put names on every other object on all the figures, so it would me more easy to
speak about them - and that meets hopefully your requirement of distinction by other means
than colors.

 ... to be continued. Keep feedback going.

Bernard