Dear Matthew, (01)
Some comments on your comments. (02)
JFS
>> The point I was trying to make is that the *metalevel* terms should be
>> limited to the words used to describe the syntactic units of the logic
>> -- eg, 'relation', 'quantifier', 'variable', 'Boolean operator'. (03)
MW
> As I said repeatedly, a logic, or other formalism for representing an
> ontology should not make any ontological commitments. (04)
I completely agree. But the only meaning that the computer can use
and relate to an application is encoded in the logic. Therefore, any
discussion about what the computer "knows" or can infer must ultimately
be related to the logic. Anything else is informal commentary. (05)
That doesn't mean you have to teach the SMEs how to read predicate
calculus. All four items I mentioned above can be expressed in
ordinary English sentences with no logical or philosophical jargon: (06)
1. Relations: The names of relations should be selected from the
vocabulary used by the experts. (07)
2. Quantifiers: The two words 'some' and 'every' cover the basic
quantifiers of FOL. Mathematics can be defined in terms of logic.
Any mathematical terms you need can be used in the ontology with
just a citation to a textbook or a tutorial on the WWW. (08)
3. Variables: It's common practice in textbooks of math & science
to use variables in the English text: "The force F on an object
is equal to its mass m times its acceleration a." (09)
4. Boolean operators: The English words 'and', 'or', 'not',
'if', and 'then' are among the most common in the language. (010)
You don't need philosophical jargon to specify the ontology. But
I admit that teaching people to think in 4D terms requires a fair
amount of explanation and examples. But that's physics. (011)
JFS
>> But you still have to relate those terms in the upper level ontology
>> to the words that the domain experts or SMEs use to talk about their
>> subject. I agree with Doug Lenat that the mid level and lower level
>> ontology is the most important for applications. (012)
MW
> Actually it is the other way round. The principle purpose of an upper
> ontology is that you relate the terms of domain experts and SMEs to that
> upper ontology together, thereby bringing together similar concepts, and
> distinguishing different uses of the same terms. You can then also apply
> templates from the upper ontology to the domain terms and improve the
> consistency of the ontology at the domain level. (013)
This gets into the issues about how to develop an ontology.
My recommendation seems to be close to yours: start *middle out*
and keep iterating until it covers upper, middle, and lower levels. (014)
One of the philosophers I admire the most is Ludwig Wittgenstein.
He analyzed and critiqued some of the most thorny issues in philosophy,
but he analyzed and explained them in ordinary English (or German). (015)
By the way, I said that I wasn't going to quibble about the details
of your terminology. But the word 'class' creates far more confusion
than it's worth. For example: (016)
HQDM
> kind_of_activity
> A class_of_activity all of whose members are of the same kind. (017)
Much simpler:
kind_of_activity: a one-place relation that is true of every
activity of the same kind. (018)
HQDM
> member_of_ :
> OPTIONAL SET [1:?] OF class_of_class_of_spatio_temporal_extent; (019)
That is an unbelievably complex way to define the basic primitive
of set theory. If you want to use set theory, then just give a
very simple summary with URLs of introductory or review material
on the WWW. For an example, see my tutorial: (020)
http://www.jfsowa.com/logic/math.htm (021)
This short intro has acquired over 176,000 hits, and I keep running
into professors who point their students to it. People who know math
don't need it. The others won't read anything more detailed. I can't
imagine anyone who would prefer the above definition of 'member_of'. (022)
John (023)
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