John,
There appears to be a point you are making here that has not yet been
covered to the point of exhaustion in our previous discussions, so pardon me
if this comment is repetitive: (01)
[JFS] > Pat,
>
> Domaindependent terminologies are extremely important for
> supporting interoperability. Those terminologies are the
> starting point for ontologies. On that point, there is no
> controversy whatever.
>
[PC] I agree that *domain ontologies* often start with some standardized
domain terminology, but we are talking about interoperability *among* domain
ontologies, and we know from vast experience that no standardized
terminology will be accepted among many different domains. The point I was
making is that the solution to disputes about terminology is to recognize
the difference between a terminology and an ontology  between words and the
concepts that they label. I am sure you are well aware of that, and can't
understand why you are reiterating the obvious. (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 logicbased notation used in computer systems, such as
> SQL, RDF, OWL, UML diagrams, etc.
>
Yes, that has been quite clear for many years, but I am not talking about
*isolated* systems of logical symbols, but ontologies modeling the real
world. What I learned new from the earlier notes is that PatH seems to
regard "time theories" that one would imagine to be models of the realworld
to be in fact just systems of connected symbols whose meanings are not
related to anything outside each set of symbols. That seems to be what he
said, though I am skeptical that that is what he really intended those time
theories to be. That is the only interpretation I can see that would make
his emphatic statement (below) sensible. (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 mathematicalstyle
> definitions.
>
> 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:
>
> 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.
>
> 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.
>
> PC> It seems to me clear from Pat Hayes's comment that interoperability
> > of mathematical theories is a meaningless concept.
>
> 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".
>
Yes, in *mathematical theories* as Pat Hayes states, everything is a
primitive and primitives have no independent meaning. But in an ontology
that models the real world, primitives are important and unavoidable because
the external world is part of the ontology, not just the symbols. (04)
> PC> So perhaps the better term would be "ontology" rather than
> > "theory" to avoid confusion with abstract pure mathematics.
>
> 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 logicbased notation, you have a theory.
>
I agree with the general principle that in a mathematical theorem, all of
the "meaning" (an undefined term in that context) resides in the
relationships of the terms and axioms. The problem is that an ontology is
not *just* a mathematical theorem, though a mathematical theorem is a *part*
of it. To differentiate between an isolated system of symbols and an
ontology that purports to model some aspect of the real world is not just to
substitute one label for another, and I can hardly believe that you don't
grasp that point. As soon as one asserts that some entity in an ontology
is a model of or analogous to some entity in the real world, the set of
symbols is no longer isolated, and there are various consequences, in
particular how the ontologist, database manager, or user chooses to
interpret and use those symbols. The realworld entities that one asserts
are being modeled become *part* of the ontology, and that link in itself
creates a new "theory" that is not purely logical, even though one can still
do logical operations on the parts that are in FOL.
This is the point I was making that started this thread: only the link to
something in common between two theories can cause a logical contradiction.
For ontologies, the things in common are the realworld entities that are
being modeled. If two ontologies model totally different fields with
nothing in common, they cannot be contradictory. Two ontologies that assert
contradictory things about the *same* realworld entity *are* contradictory. (05)
>
> 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.
>
[JFS] > Connecting your computer to the world won't magically make it
> interoperable with anything. (06)
[PC] And resorting to meaningless insulting distortions of my comments won't
make your argument any more cogent. (07)
>[JF] 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.
>
[PC] yes, absolutely, and testing a theory that models the world is the way
scientists decide which of two or more conflicting theories is the closer
approximation to the real world situation. That is one reason why I feel
confident that there will be few logically contradictory ontologies modeling
the real world, if the different ontologists compare notes: they can each be
tested to see which is more accurate. (08)
> And if you try to define your ontology in terms of some collection
> of vague "primitives", the chance of incompatibility is very high. (09)
Actually, as long as we are trying to model the real world, I can't see how
primitives can be avoided. Sure, they are a red herring if you think of an
ontology as nothing more than a set of meaningless symbols  or if you
prefer  symbols whose "meaning" is nothing more than a set of relations to
other symbols. But when links to the real world are created in some
ontology, the meanings of those elements no longer are determined just by
the links within the ontology, but also by the links to, for example,
instances in the real world. I think it likely that the *intended meaning*
(which determines how the elements will be used in an application) will not
change at all when new elements are introduced that are more than a few
inference links distant in the ontology; this is very different from the way
you and PatH (and I presume other mathematicians) view a mathematical
theory. I gave an example of how this external grounding could work, via
internet search. I imagine you could think of many more. (010)
Pat (011)
Patrick Cassidy
MICRA, Inc.
9085613416
cell: 9085654053
cassidy@xxxxxxxxx (012)
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