Len, Paola, and Ron, (01)
Marvin Minsky made the point that if you only understand a subject
from one point of view, you don't really understand it. (02)
There is no such thing as a one-size-fits-all textbook, tutorial,
lecture, or course. Each one has a different point of view, and
it's best to read several so that you can see the interconnections. (03)
I recommended the tutorial by Norman Swartz because it covers
a lot of ground in a short space from a point of view that is
logically equivalent to, but slightly different from what is
usually said in most of these email threads. (04)
LY> For example, following explanation: "The extension of a term
> or phrase is understood to be the timeless class of all things
> which properly 'fall under' or are described by that phrase."
> This may be workable for linguist, but not for computer scientists
> or mathematicians (although I am not one of them).
>
> Here is quite different definition of the same term in
> http://en.wikipedia.org/wiki/Extension_(predicate_logic)
> "The extension of a predicate ? a truth-valued function ? is
> the set of tuples of values that, used as arguments, satisfy
> the predicate. Such a set of tuples is a relation." (05)
The definition from the Wikipedia covers only relations. The
definition by Swartz is more general because it covers terms
that represent relations as well as other kinds of things
-- including relations that might be called by other names,
such as properties or predicates. (06)
I also recommend a definition of the distinction between
extension and intension by the logician Alonzo Church.
See Section 2 of his book on the lambda calculus: (07)
http://www.jfsowa.com/logic/alonzo.htm (08)
This is a very different, but highly illuminating insight
into the same distinction. But it is more mathematical.
If you want a gentler introduction to these issues, see
my tutorial on math and logic: (09)
http://www.jfsowa.com/logic/math.htm (010)
LY> I recall several discussions on this forum that attempted to
> connect the terms "intension", "extension", "class", "predicate"
> etc. into coherent framework, but IMO failed to do so for the
> very same reason - lack of interdisciplinary definition that
> would satisfy the need of constructive discussion...
>
> If anyone agrees with me I would suggest to begin with notions
> of "intention" and "extension" as it relates to notions of "model"
> and "theory". (011)
For more about those terms, see my tutorial on math & logic. (012)
PDM> ... each definition can be interpreted differently by different
> people who place it in different context (relating to different
> axioms) ... (013)
That may be true of some words. But for the terms 'intension' and
'extension', all the definitions are equivalent. They are different
ways of expressing the same distinction, and it is important to
realize that the distinction is identical in each case. (014)
For other words used in ontology, there was a series of workshops
during the late 1990s that was sponsored by the NCITS T2 committee.
As a result of that workshop, I put together a glossary of many
of the common terms. It was circulated at the workshops, and many
people made comments and suggested additions and revisions. It
was never officially voted and approved by the committee, but it
is still a useful glossary. I appended it to the end of the
following article: (015)
http://www.jfsowa.com/ontology/ontoshar.htm
Building, Sharing, and Merging Ontologies (016)
RW> If we are not willing to put the effort in, either nothing
> will happen or someone else will. (017)
If you want to start with the glossary in that article, you
have my permission to use it. If anyone is interested in the
discussions of the old X3T2 committee, their archive can be
found on the Stanford web site: (018)
http://www-ksl.stanford.edu/onto-std/ (019)
Reading these old archives brings to mind the French proverb,
"Plus ça change, plus c'est la même chose." The only difference
is that we were younger then, and some of us were still hopeful. (020)
John Sowa (021)
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