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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Cc: "'arun@xxxxxxxxxxxx'" <arun@xxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 01 Feb 2008 19:33:03 -0500
Message-id: <47A3BA3F.80101@xxxxxxxxxxx>
Pat,    (01)

I think that there are some important points on which we either
agree or are not too far apart:    (02)

  1. Any reasoning system (human, animal, or computer) must store
     its knowledge in some internal form that is not likely to be
     identical to a natural language.    (03)

  2. An enormous amount of human knowledge is implicit in forms
     that are probably closer to the forms used by the perceptual
     and motor mechanisms.  Examples include imagery, sounds,
     smells, tastes, feelings, muscular habits (e.g. tying a shoe
     string), and possibly others.    (04)

  3. Language understanding and reasoning about anything related
     to #2 probably involve "mental models" that are more likely
     to be geometric (at least for spatial phenomena) than NL-like
     or logic-like.    (05)

  4. The internal form of language-derived information is likely
     to have items that correspond to words and other symbols
     linked to other items in some way, but probably not in
     linear strings that have a one-to-one correspondence to
     sentences in a natural language.    (06)

  5. But there are likely to be many intermediate or mixed-mode
     representations.  Examples include singing and dancing, in
     which words and actions are linked to sounds and rhythms.
     Observation:  most people can remember words more accurately
     when they are attached to melodies and recall melodies more
     easily when they have associated words.  Tables and diagrams
     are mixed-mode representations that make it easier to recall
     and understand complex relationships among word-like items.    (07)

  6. Mathematical notations (including logic) have syntax and
     symbols that are related to mechanisms that are used for
     NL (point #4), but they may also be linked to geometrical
     models (point #3).  In fact, different people may differ in
     how their verbal or geometrical mechanisms are linked to the
     mathematical symbols and syntax.  (Note that people differ
     in their ability to do mental math or understand spoken math.)    (08)

Given these points, I would agree that language understanding
requires the spoken or written forms to be related to something
internal.  What I was objecting to is the word 'extraction'.
I would prefer the more neutral and more general word 'mapping'.    (09)

I also object to any suggestion that a propositional form that
might be expressed in some mathematical notation (point #7)
is involved in human understanding of a sentence.  Mapping a
sentence to a geometrical "mental model" probably goes from
something in point #4 to something in point #3 or #5 rather
than anything that resembles point #6.  However, professional
mathematicians probably acquire much more direct connections
from #6 to #3 than novices.    (010)

When I talk about using analogical methods for language processing,
I am thinking of methods for mapping external language to the
internal forms of #4 and #3 and bypassing point #6.    (011)

Some comments on your comments:    (012)

PH> People gain knowledge from many sources, and use it in many
 > ways to help them understand language. Most of the common sense
 > knowledge we all have of the everyday physical world is learned
 > without the use of language at all, during the first 5 or 6 years
 > of life; yet it is used during language comprehension in ways we
 > have probably not fully understood yet.    (013)

I agree.  Most of that prelinguistic knowledge is in some sort of
"mental models" (to give a name to the as-yet-unspecified form).
It's more likely geometrical, and a mapping to a logical form
may be more of a distraction than an aid.    (014)

PH> Cyc is obliged to make many more distinctions than are found
 > in any dictionary, but also ignores many dictionary distinctions
 > based for example on historical or lexicographical distinctions.    (015)

I agree.  But many of those distinctions may be easier to resolve
by a mapping to a geometrical form than to any version of logic.
For example, some books on prepositions illustrate the distinctions
for spatial prepositions with diagrams.  Given analogical reasoning
methods that can deal with images (which Arun and I are considering),
the mappings for words like 'in', 'on', or 'above' may be easier to
resolve in terms of a geometrical model than a propositional form.    (016)

PH> No dictionary will make the continuant/occurrent contrast.    (017)

I don't think it should.  In my KR book, I made the claim that it
depends on your point of view.  Even a diamond could be considered
a process if you examine it at the atomic level or over a period
of billions of years.    (018)

PH> As problem-solving is not itself conducted in natural language,
 > this intermediate knowledge must be somehow represented in a
 > formalism which can be input to the problem-solving machinery.    (019)

I was thinking of some kinds of purely verbal problems that would
involve word-based analogies (point #4) as well as some that involve
geometrical models (point #3).  Neither of them would require a
"formalism" such as Cyc's.    (020)

JFS>> But I do claim that we will *never* do [language understanding]
 >> if we must first construct a knowledge base or ontology that
 >> remotely resembles Cyc.    (021)

PH> Well, you are entitled to your opinion, but I see no evidence
 > for it.  And after all, we have now first constructed such a
 > knowledge base, so apparently it can be done.    (022)

We have all learned a great deal from Cyc.  One point that the
HALO exercise demonstrated (which many of us suspected for years)
is that despite its millions of axioms, Cyc is still too shallow
for the kind of detailed reasoning required for understanding a
typical textbook.  Even though Cyc started with much more built-in
knowledge, it had no advantage over the other two systems.    (023)

Following are my suspicions, which I cannot, as yet, prove:    (024)

  1. Cyc has not yet demonstrated an effective method for automatic
     knowledge acquisition from text.    (025)

  2. There is no evidence that anything in Cyc, as it is now, could
     significantly aid the process of acquiring knowledge by reading
     a book or the web.    (026)

  3. Any system that does solve that problem could catch up with
     Cyc in 6 months and go far beyond it in 12 months.    (027)

John    (028)

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