Pat, (01)
Domain-dependent terminologies are extremely important for
supporting interoperability. Those terminologies are the
starting point for ontologies. On that point, there is no
controversy whatever. (02)
What Pat H. and I have been trying to explain is that meaning in
any system of logic is determined by patterns of relationships
stated in rules or axioms. That is true of any version of logic
or any logic-based notation used in computer systems, such as
SQL, RDF, OWL, UML diagrams, etc. (03)
It's also true when you're talking about tables, chairs, and cats
or when you're talking about numbers and sets. If you're trying
to do ontology for computers, you are doing mathematics. A computer
is a mathematical machine, and you can't escape mathematical-style
definitions. (04)
PC> Pat Hayes has very emphatically denied that any different
> mathematical theories (seemingly contradictory or not) can be
> related to each other in any way: (05)
PH>> Each theory nails down ONE set of concepts. And they are ALL
>> 'primitive' in that theory, and they are not primitive or non-
>> primitive in any other theory, because they aren't in any other
>> theory AT ALL. (06)
That is not what Pat H. said. He was trying to say that the source
of meaning in any theory stated in logic is in the axioms, not in
the choice of labels for naming the relations, functions, and types. (07)
PC> It seems to me clear from Pat Hayes's comment that interoperability
> of mathematical theories is a meaningless concept. (08)
No. Pat H. was saying that the word 'primitive' is a red herring.
The meaning comes from the patterns of interrelationships in the
axioms. It does not come from some choice of terms as "primitive". (09)
PC> So perhaps the better term would be "ontology" rather than
> "theory" to avoid confusion with abstract pure mathematics. (010)
You can't make a problem go away by relabeling it. The word
'theory' is a supertype of 'ontology' because every ontology is
stated in some form of logic, and every collection of statements
in logic is a theory. As soon as you represent your ontology in
some logic-based notation, you have a theory. (011)
PC> But there is still a very big difference, in that when used in
> a practical application, the models interact with the real world
> - through the interpretations of ontologists, programmers, or
> database developers, and potentially by direct operations such
> a sensor or robotic actions or internet access, as well as user
> input. (012)
Connecting your computer to the world won't magically make it
interoperable with anything. It just introduces one more danger:
the likelihood that the ontology implemented in the computer
programs is inconsistent with the world -- i.e., it says something
false about the world. (013)
And if you try to define your ontology in terms of some collection
of vague "primitives", the chance of incompatibility is very high. (014)
John (015)
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