[xtm-wg] Association Type "Scope", for popularizing?

[Andrius Kulikauskas <ms@ms.lt>]

Hi,
     I'm getting ready for the TopicMaps.Org meeting, so I'm reading the
TopicMaps standard.
     The following quote is from the introduction: 

"A topic map defines a multidimensional topic space — a space in which
the locations are topics, and in which the distances between topics are
measurable in terms of the number of intervening topics which must be
visited in order to get from one topic to another, and the kinds of
relationships that define the path from one topic to another, if any,
through the intervening topics, if any."

     That brings to my mind the letter I wrote here on 7/30/00 about
Structural Constraints are Extensions of Equality.  The idea that
"distances between topics are measurable in terms of the number of
intervening topics" is an "extension of equality" of the kind that I
associate with Nondirected Networks.  
     Furthermore, Nondirected Networks bring to mind "atlases" -
"networks restructured with hierarchies".  Indeed, I think it is fair to
characterize topic maps as a network of topics (by means of
associations) on top of which there is a hierarchy of topics (by means
of scope).
     So, from this point of view, TopicMaps are not structurally
neutral.  I think that structurally they are atlases, and are intended
primarily for that use.
     In a sense, it is possible to code anything in terms of TopicMaps. 
However, to do this involves abandoning the hierarchical notion of
Scope, or having a structurally confusing situation where the
associations may be used to code a hierarchy of topics, and there is
also a Scope hierarchy of topics that is coded completely differently.
     Am I reading too much into the introduction?  But I think not.  I
think TopicMaps are designed for a specific way of extending equality
("the number of intervening topics").  Although, here is another quote,
from Chapter 1:

"To link topics together in such a way as to enable navigation between
them. This capability can be used for virtual document assembly, and for
creating thesaurus-like interfaces to corpora, knowledge bases, etc."

Here two topics are similar not if they are close or far apart, but if
they are on common cycles.  This brings to my mind Directed Networks
with Cycles Allowed, a "tour" - "network restructured with sequence".
      There are other ways of extending equality, as I wrote.  Each
involves its own structural point of view.:

CLOSED SEQUENCE
visualization: chronicle (sequence restructured with hierarchy)
for: reasoning
Thoughts are equal to the extent that:
they belong to subsequences that are interchangeable.

OPEN SEQUENCE
visualization: canon (sequence restructured with network)
for: priorities
Thoughts are equal to the extent that:
they extend the preceding thoughts in the same way.
Example from UML: Sequence diagrams.

TREE, HIERARCHY
visualization: catalog (hierarchy restructured with network)
for: relevance
Thoughts are equal to the extent that:
they belong to the same, but not different topics.
Example from OO: Design by contract.

DIRECTED NETWORK, NO CYCLES ALLOWED
visualization: evolution (hierarchy restructured with sequence)
for: requirements
Thoughts are equal to the extent that:
the thoughts they require are the same.
Example from UML: Activity diagrams.

DIRECTED NETWORK, CYCLES ALLOWED
visualization: tour (network restructured with sequence)
for: attention
Thoughts are equal to the extent that:
they occur on the same cycles.
Example from UML: State diagrams.

NONDIRECTED NETWORK
visualization: atlas (network restructured with hierarchy)
for: adjacency, relatedness
Thoughts are equal to the extent that:
they are adjacent to each other.
Example from OO: Package diagrams, CRC cards*, Refactoring, Extending
Use Cases, Abstract classes. 

      I added some examples from OO (Object Technology) and the UML
(Unified Modeling Language).  They are from "Organizing Thoughts into
Sequences, Hierarchies and Networks" by Andrius Kulikauskas and Saulius
Maskeliunas.

http://www.ms.lt/ms/projects/structurekinds/paper052499.html

      I wonder how the conceptual elegance of "TopicMaps" modeling
language can be expressed in terms of the "UML" modeling language, which
I think is a politicially remarkable hodge podge of structure.  It will
be impressive (and helpful for me) to see.
      I think - I hope - TopicMaps are all of the above structures, but
then - especially in popularizing them, bringing them to the widest use,
I think it would be good to emphasize the structural neutrality.
      In a popularization of TopicMaps - meant for use with the widest
variety of structures - would it be possible to have SCOPE be treated as
just a particular kind of ASSOCIATION TYPE?

Andrius Kulikauskas
Director
Minciu Sodas
http://www.ms.lt
ms@ms.lt


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