Pat, (01)
The major differences between us result from several related
assumptions about how a formal system can be related to the
world. Following are the points I would emphasize: (02)
1. The immense size and complexity of the universe and its
continuous variability in time and space make it impossible
for any discrete, finite set of labels (words or predicates)
to have a perfect, one-to-one mapping to all aspects of the
universe or even to some small chunk we are familiar with. (03)
2. Human systems for perception, action, and mental imagery
enable us to interact with the world more accurately than
we can characterize it in discrete words or predicates.
A simple example is tying a shoestring. Another example
is the high-speed interactions of basketball players who
can successfully get the ball through the hoop despite the
active interference of the opposing team. (04)
3. Therefore, anything we can express in a discrete string of
symbols (in logic or natural language) will inevitably be
an approximation to some limited part of the universe for
the purpose of fulfilling some particular narrow goal. (05)
4. Natural languages have evolved under those constraints for
thousands of years, and they have proved to be amazingly
successful and flexible in adapting to an open-ended variety
of situations while enabling us to communicate enough of our
thoughts with sufficient accuracy to achieve specific goals. (06)
5. In the past few centuries, mathematics has developed from
a level that could be mastered by a single individual to a
rapidly expanding family of extremely powerful systems that
support the even more rapidly expanding branches of science
and engineering. But it is so rich that no single person
or even a single math department at a university can master
in its totality. (07)
6. By contrast, formal logic is still a relatively compact
subject (especially if some of the complexities, such as
set theory are considered part of mathematics). And that
subset whose semantics is completely defined by a model
theory along the lines of Tarski or Kripke is even smaller. (08)
7. Montague tried to expand that core to accommodate natural
languages, but even many logicians were skeptical (e.g.,
Peter Geach, who called it "Hollywood semantics"). After
40 years of development, no NLP system can translate one
article from a typical newspaper to any version of logic
(except for a short stylized paragraph, such as a weather
report on a calm day). Even pioneers in the field such as
Hans Kamp have admitted that "something more is necessary." (09)
I believe that these observations have strong implications for
the development of logics and ontologies that can support the goals
of interoperable systems, the Semantic Web, and many related problems. (010)
Point #5 about mathematics is significant: any large engineering
project, such as designing a bridge or an airplane, has an enormous
number of related subproblems that require specially tailored
formalisms based on distinct branches of science with very different
mathematical techniques. There is no such thing as a single, unified
ontology that can support every aspect of just one such project under
the management of a single prime contractor. It is inconceivable
that a single unified ontology could be developed for just one
large company, much less for an entire industry, and certainly not
for all the major industrial companies in any large country. (011)
Points #4 and #7 about natural languages imply that we are not
likely to solve the problem of NL understanding with a single
logic and ontology. Even if we were to edict a single logic and
ontology for some important domain, say medicine, it is extremely
unlikely that we could teach all the formal definitions to all
the practitioners (physicians, nurses, pharmacists, technicians,
programmers, administrators, etc.). We might be able to teach
them to use a fixed vocabulary, but each person will continue
to use and interpret those words as though they were part of
their ordinary natural language. (012)
My conclusion is that we will continue to have an open-ended
family of specialized terminologies and ontologies for a long
time to come. The links among those ontologies will not be
supported by a detailed formal ontology. (013)
At best, the upper levels will be a type hierarchy with multiple
inheritance and with very few formal axioms. The two major
relations that would be used are subtype and partOf. At the
lower levels would be an open-ended family of specialized modules
with detailed axioms specialized for particular kinds of problems. (014)
Some comments: (015)
PH> The number of people who can drive a car greatly exceeds the
> number who can build a car. Nevertheless, were it not for the
> latter, the former would have nothing to drive. (016)
Absolutely true. But note that the people who drive those cars
have almost no knowledge about how those cars are constructed.
The same will be true of the people who write semantic tags on
web pages or select them from a menu. (017)
JFS>> What group of "we" are you talking about and for what purpose? (018)
PH> People doing semantics of the formal languages used to write
> ontologies. (019)
But what training will the people who write those ontologies get?
You scoffed at my list of Google counts, but just note the numbers
15,400,000 for "ontology", 785,000 for "model theory", and only
34,000 for both "ontology" and "model theory". I seriously doubt
that the people who will be hired to write those ontologies by
businesses will have any more logical training than those who did
"systems analysis". They will just put up a different shingle
on their front door (or home page). (020)
And even if by the rarest of good fortune you could recruit super
intelligent logicians to define those ontologies, the people who use
them will interpret the terms with their old background knowledge. (021)
JFS>> An academic publication that uses model theory to analyze the
>> foundations of OWL or SQL has little or no influence on the
>> people who use those languages for any practical application. (022)
PH> That has not been my experience with RDF, OWL and SPARQL
> development. (023)
The developers include many good logicians. But if those languages
become successful (i.e., much more widely used than the Google counts
currently indicate), the overwhelming numbers of ontologies will be
written by the great unwashed. (024)
PH> [The developers] find themselves obliged to pay close attention
> to one another. I know, because I was often the guy who had to do
> the mutual translations of terminology. (025)
Great. So how are we going to make your services available to the
millions of people who write/use those ontologies if and when those
languages become widely used? (026)
JFS>> That kind of very precise talk is done by the academics who
>> publish papers about model theory. (027)
PH> It is done, perhaps implicitly, by anyone who uses mathematics
> to talk about the real world. Which is a lot of people. (028)
Wait. Practicing mathematicians, as Chris M. concurred, do not care
about the foundations of math or logic. They don't use models in
Tarski's sense, but in George Box's sense: "All models are wrong,
but some are useful." (029)
PH> In fact, this concern with vagueness or blurriness of boundaries
> is itself a purely academic issue, verging at all times on the
> philosophical. (030)
Practicing DB analysts are extremely sensitive to those issues,
which constantly plague their systems. For a good source of examples
and anecdotes, see the book _Data and Reality_ by Bill Kent, who was
not an academic, but a DB guy who had to work with actual data.
He discussed "philosophical" problems like the oil company that had
different departments with different definitions of 'oil well'. (031)
PH> ... the people who know most about boundary-line issues are,
> of course, the people who specialize in this topic, which includes
> surveyors, lawyers (of a certain specialization), cartographers
> and others. I've worked with some of these people, and its quite
> possible to ontologize their expertise, just as it with other experts. (032)
I was using the term 'borderline' in a metaphorical sense, which
includes physical borders as a special case. But since you mention
lawyers, essentially every case they address is a metaphorically
borderline problem -- primarily because the ones that are not on
the border are settled out of court. (033)
PH> Previously we were talking about individuation criteria (this
> cabbage vs. that cabbage), now you are talking about how to
> distinguish among genera (cabbage vs. broccoli). (034)
Chris is the one who brought up cabbages. And I pointed out that
there are no clear identity criteria for distinguishing a cabbage.
You need such criteria if you want to count cabbages or oil wells. (035)
PH> My own view on questions like this is, consult an expert:
> for Brassica Oleracea, a botanist or gardener, and so on. (036)
The oil company had no shortage of experts on oil wells, but different
experts looked at the same question from different points of view. (037)
JFS>> Even for the 3% who know model theory, the task of ensuring
>> that those models reflect reality won't get done by itself. (038)
PH> What is this 'task' that you keep worrying about? (039)
Please read Bill Kent's book or George Box's book or many others
written by people who map reality to actual databases. (040)
JFS>> That means that their usage [ontology users] will be
>> unrelated to the formal definitions. (041)
PH> ...it does not mean this. It means only that they may fall into
> the mistake of 'reading more into' the RDFS than it can in fact
> carry. And this is quite common, and is widely recognized as a
> practical issue, and down-to-dirty-earth user guides warn against it. (042)
Such warnings are as effective as Sarah Palin's "abstinence only"
approach to sex education. (043)
JFS>> just look at Carnap's famous "Logische Aufbau der Welt". (044)
PH> I know it very well, with great affection: this is the book that
> I read as an undergraduate and which made me decide to go looking
> for AI (rather than mathematics!) at a time when there was no such
> subject yet. It is a masterpiece, and should be required reading
> for all ontology-builders. Early, and of course incomplete, and
> easy now to critique in details; but the very first attempt at
> what we would now call a comprehensive upper ontology. (045)
I agree that Carnap's book is a classic of its kind. But just look
at all the hand waving at every difficult problem. I blame that book
for leading Doug Lenat (directly or indirectly) to an attempt to carry
out the details. The entire AI field (and the US taxpayers) learned
a lot from that exercise: it doesn't work. And pouring more millions
into the same approach on a larger scale won't make it work. (046)
John (047)
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