Re: [topicmaps-comment] Mapping Topics to Cyc: How To Handle Scope?

[Murray Altheim <m.altheim@open.ac.uk>]

Lars Marius Garshol wrote:

> * Lars Marius Garshol
> | 
> | BTW, here's a reference table to the terminology:
> | 
> |   +---------------------+--------------+-------+
> |   | Deprecated          | Intersection | Union |
> |   +---------------------+--------------+-------+
> |   | Sub-optimal         | Or           | And   |
> |   +---------------------+--------------+-------+
> |   | Currently preferred | Any          | All   |
> |   +---------------------+--------------+-------+
> 
> This is wrong, of course. It should be:
> 
>   +---------------------+--------------+-------+
>   | Deprecated          | Intersection | Union |
>   +---------------------+--------------+-------+
>   | Sub-optimal         | And          | Or    |
>   +---------------------+--------------+-------+
>   | Currently preferred | All          | Any   |
>   +---------------------+--------------+-------+
> 
> So the second and third rows were wrong.


You guys had me confused, but I think I've discovered where my
confusion originated. I agree with the corrected table, and
I think the original error may have came about because we can
look at this two ways, so perhaps an ambiguity of language has
been the barrier.

There's (a) the union or intersection of the topics *as a scope*,
then there's (b) the union or intersection of the *set of topics*
bound by such a scope. We (or at least I) seem to have been
confusing the two.

In the case of (a) I believe we're talking about the "semantic union"
of the topics included in the scope, but in (b) we're talking about
the logical (ie., set) intersection. But because "semantic union" is
a bit on the intuitive side, the latter is perhaps the better definion.
To borrow one of Jon Awbrey's Venn diagrams:

o-----------------------------------o
| X                                 |
|              o     o              |
|             / \   / \             |
|            /   \ /   \            |
|           /     o     \           |
|          /     / \     \          |
|         /     /   \     \         |
|        /     /     \     \        |
|       /     o   P   o     \       |
|      /     /         \     \      |
|     o     o           o     o     |
|      \     \         /     /      |
|       \  Q  \       /  R  /       |
|        \     \     /     /        |
|         \     \   /     /         |
|          \     \ /     /          |
|           \     .     /           |
|            \   / \   /            |
|             \ /   \ /             |
|              o     o              |
|                                   |
o-----------------------------------o

Using a simplification of my earlier example, if Q is the set of
topics considered as the scope of US Presidents and R is the set
of topics whose temporal scope is "after 1977", then the intersection
P is the set of topics including "Jimmy Carter".

I hope this finally clears things up (it did for me).

Murray

......................................................................
Murray Altheim                  <http://kmi.open.ac.uk/people/murray/>
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK

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