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Re: [ontolog-forum] Foundations for Ontology

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 30 Sep 2011 02:23:00 -0400
Message-id: <4E856044.3020900@xxxxxxxxxxx>
On 9/30/2011 12:52 AM, Rob Freeman wrote:
> I'm not sure what you mean by "statistical vectors". I use vectors of
> word contexts. I think interpretations of these vectors must be
> subjective, but are perfectly precise.    (01)

The distinction I was trying to make is between a symbolic knowledge
representation, which can be translated to and from a natural language,
and a string of numbers derived by some algorithm that cannot be
meaningfully translated to an intelligible phrase of sentence.    (02)

For example, any statement in any version of logic can be translated
to a meaningful English sentence.  That sentence might miss some of
the nuances of the formal notation, but it is intelligible as an
approximation to what the statement asserts.    (03)

Formalisms that cannot be translated to English in a meaningful way
are the weights on the nodes of a neural network.  You can explain
how those weights were computed, but it is not possible to derive
a sentence or phrase that could be used as an explanation of what
any particular node "means".    (04)

Another example is a vector that counts the co-occurrences of words
in various documents.  You can point to any particular number and
say that it states the number of times word A and word B occurred
in the same document.  But that doesn't have any kind of intuitive
meaning that you can state as an English sentence.    (05)

Then if you take those vectors and apply the SVD algorithms to
reduce the dimensionality, you get a string of numbers whose
meaning is totally opaque.  All you can say is that the vector
represents "something" that is related to the meaning of the word.    (06)

> I grant you quantum variables imply a certain randomness. Though I
> think that randomness is actually just subjectivity too.    (07)

This has nothing to do with subjectivity.  As another example,
look at the definition of any word in any dictionary designed
for humans.  The lexicographers tried to be as unbiased as they
could be, and for most purposes, they succeeded.    (08)

But their definitions are meaningful to people, and a translation
of those definitions to some version of logic could be mapped
back to an English statement that was a good approximation to
the original.    (09)

> In that sense your infinite lattice of theories is also random. It is
> random in the sense that you can't universally identify any one theory
> with "truth".    (010)

But the full lattice exhibits all possible theories, some of which
are true, some false, and most irrelevant to your application, but
perhaps very relevant so someone else's.  Any one of them could
be translated to a collection of English sentences.    (011)

To clarify some of thee issues, I added another slide to the
presentation that started this thread.  See below.    (012)

_______________________________________________________________________    (013)

Source:  Slide 12 of http://www.jfsowa.com/talks/ontofound.pdf    (014)

Statistical Methods    (015)

During the 1990s, the stagnation of traditional AI methods and
larger faster computers led to many new statistical methods.    (016)

Statistical methods for information retrieval, learning, data
mining, parsing, and machine translation were promising.    (017)

Various kinds of neural networks also showed some promise.    (018)

But none of those methods could compete with Cyc in reasoning
or compete with Laura in learning language.    (019)

Relating human language to the world and to computer systems
still requires some kind of symbolic representation.    (020)

In his _Society of Mind_ and _Emotion Engine_, Marvin Minsky
recommended systems of heterogeneous interacting agents.    (021)

Perhaps evidence from psycholinguistics and neuroscience can
suggest ways of designing and connecting such agents.    (022)

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