[xtm-wg] Re: Summary of PM discussion

[<guy.a.lukes@frb.gov>]

* Sam Hunting
>I guess I see things, well, more "multidimensionally". My (CURRENT)
>preference is for the following:
>
>   - graph model (the underlying formalism)
>   - UML notation (what the model is expressed in)
>   - infoset-style prose description

I think this is the right top-down approach for a well understood problem.
The discussion has congealed around the three basic metaphors for modeling
information (paths, containers, and positions).  The graph model, based on
a connected intersection of paths, provides a high level abstraction for
the integration of any structure.  Its abstraction is its greatest strength
and its greatest weakness.

The class diagrams of UML and their inheritance and aggregation concepts
are a formalization of the container metaphor.  While they don't provide
the global integration of a graph, they provide a more intuitive
abstraction of the more detailed components (objects) of the system.  This
is very useful to someone designing the structure of an XTM engine.

Finally, the property-set uses the metaphor of a multi-dimensional position
in space to describe the specific characteristics of a system. These
characteristics provide the fine grain detail required to determine in an
intuitive way, when two things are equal or when something is valid.  This
makes it particularly useful to the user of an XTM engine.  However, unless
it is grounded on an appropriate set of abstractions, things can get very
messy.

Each level is grounded on the level above it.  Unfortunately, whether it is
the right grounding can only be determined by looking at the detail of what
it supports.

Each starting point can be expanded to cover all possibilities.  UML is
much more than class diagrams, groves have containment and can describe
graphs, the mathematics of graph theory can describe partial-orders and
multi-dimensional spaces.  But when you start to mix and stretch metaphors,
it can take a lot of effort to understand what is going on.

Guy


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