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Subject: Re: [tm-pubsubj-comment] XTM questions

Lars Marius Garshol wrote:
> * Murray Altheim
> | 
> | Two more things to note regarding scope. First, <scope> is a
> | container for one *or more* topics, which act in combination. So,
> | 
> |    <scope>
> |      <topicRef xlink:href="#england"/>
> |      <topicRef xlink:href="#eighteenth_century"/>
> |    </scope>
> | 
> | means "England" AND "18th Century", not OR. Think of them as
> | coloured filters, additive.

I think any confusion is my own fault here in my use of "AND" and
"OR", in that the context in which a statement is made affects its
interpretation. In colloquial language people (myself included)
often conflate "union" and "intersection", and I'm guilty here.

If one says "'England' and '18th Century'", in natural language it
is not uncommon to consider this the "union" of those two topics, as
in "18th Century England". But if we want to create a scope that
represents "18th Century England", then logically, this is the
*intersection* of the two sets "England" and "18th Century", if
we're talking set theory, which would be an OR relation between
the sets. Confused?

> Note that XTM 1.0 says both that whether it's AND or OR is undefined
> (1, and that it is OR (3.3.1). states that the *interpretation* of scope is not constrained
by XTM 1.0. This is as it should be. But that's very different than
*how scope operates within XTM*. states that the scope is
considered as a "set of topics", not as individual topics within a
<scope> element. The scope's topics are not meant to be decomposed, as
they operate as a set.

3.3.1 states that the union of the topics is considered as the scope.
I believe this was meant to state the same thing as, as my
memory of this was that we weren't talking set theory in 3.3.1 but in
the colloquial sense of the topics' union, subject-wise, e.g., "18th
Century England". I don't know who originally wrote this section; it
might have been me (maybe we should blame Tommy Franks).

IOW, it is the union of the subjects "semantically", or the
intersection of any sets they describe. I think the problem is that
we don't really describe any of this in terms of set theory, yet we
borrow its parlance now and then. This is similar to the type vs. class
discussion in that the language derives from what direction the
statement is being made.

> The new specification says that it is AND, but so far that is only the
> resolution proposed by the authors of the specification and the
> committee hasn't settled the issue.
> See <URL: http://www.ontopia.net/omnigator/models/topic_complete.jsp?tm=tm-standards.xtm&id=term-scope-def >

If multiple topic refs within <scope> do not act additively, we
made a mistake in XTM 1.0 and should have only allowed one topic
reference, such that "England" and "18th Century" would have been
then been associated together as a single topic and that topic
used to scope the base name. I think the *intent* is that they
do act additively, as the union of their subjects, the intersection
of their sets, however it is best described.

I hope that if the specification authors mean that the set of topics
within a scope act additively (i.e, the union of their subjects, or
the intersection of their sets), that the committee will decide this
issue in their favour.

It's sometimes exceedingly difficult to be precise in natural
language, despite one's attempts at careful writing and editing.
And writing specifications that use natural language as technical
descriptions is prone to an error now and then. It's only a minor
comfort to know that these kinds of errors plague many a discussion
on logic, by even the most expert logicians, and I don't even play
one on TV. One solution would be to resort to mathematical rather
than natural language, avoiding any ambiguities.

*sigh* I'll avoid using capitalized AND and OR in the future, unless
I'm typing into a search engine...


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

    Hunt the Boeing! And test your perceptions!

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