Hi All, (01)
Felt the need to poke my nose in on this one, and I'm sure I'll regret it. (02)
I think it *is* possible to have a small set of primitives (I've heard them
called "ontic categories"), provided everyone using them has the same
ground-rules (I've heard Chris Partridge call these "metaphysical choices").
Without an agreement on those metaphysical choices, there cannot be an
agreed set of primitives that are realistically usable. Here are some
(purely fictitious) examples: (03)
* I decide first-order ontologies are plain nonsense, dreamt up by
flat-earther computer scientists in a vain attempt to retro-fit the real
world to their ideas about inference (obviously, I would never do such a
thing). Let's call this metaphysical choice "world of warcraft". I want my
ontology to be higher-order, let's call this "hairy-arsed engineer". The
computer scientist grunts twice from beneath his beard to indicate he wishes
the primitive "class" to be first order. Immediately here, we have a problem
- the extent of what I call "class" is different to what he calls "class";
mine can have classes as members, his can't. My higher-order class can't be
used by the flat-earthers, as they might have to wait an infinite amount of
time for their computer (probably called "Gandalf") to come up with an
answer. I can't use their class, as it's too restrictive. OWL tried to get
round this by having different language conformance classes - full, DL, etc.
But...if one person uses OWL:Class in the full sense and another in the lite
sense, they have a different extent, and so really shouldn't use the same
OWL keyword, if we're going to be pedantic (i.e. extensional, see next
point). (04)
* If I decide to be an extensional fundamentalist (a la Partridge / West
flavour of ontology), and someone else decides intensional is the way, then
again we have a problem. My classes are defined by the extent of their
members. And, I need to ground my thinking in physical reality, so I have
these things called individuals (or elements in BORO) which have
spatio-temporal extent. The extent of the intensional classes will be
different to that of the extensional ones - I'd have one class with two
names "Equiangular Triangles" and "Equilateral Triangles", they'd have two
classes. Similarly, if they bother to have individuals, the intensional
folks might have more than one referring to the same spatio-temporal extent.
This would be a no-no to an extensional Jihadi like Chris Partridge. Again,
we're unable to re-use each other's primitives. (05)
There are plenty of other choices too - modal logic vs possible worlds, 3D
vs 4D, etc. (06)
So, in my view, you can't have a common set of ontic categories unless you
all agree on the ground-rules (metaphysical choices). If you really want to
go down the road of developing a common set of primitives, you need to get
an understanding of what everyone's ground-rules are, and how they all
differ. Philosophers and logicians must have lots of ways to categorise this
kind of stuff. Let's face it, what else have they got to do with their time
? They've had 3000 years to work on all this, albeit 2999 of them seem to
have been spent arguing the existence/non-existence of God/gods. (07)
So, I think the idea of one set of primitives to rule them all is
impractical at least, and probably impossible. Based just on the range of
opinion on ontolog alone, you can bloody well forget it. If you're talking
about going beyond ontic categories, to produce what is sometimes called an
"upper ontology" then the problem becomes an order of magnitude worse. (08)
There. I think I've insulted just about everyone. A fine evening's work, I
think. (09)
No computer scientists were harmed in the making of this e-mail. (010)
Cheers
--
Ian (011)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Azamat
Sent: 30 May 2009 18:46
To: [ontolog-forum]
Cc: John F. Sowa
Subject: Re: [ontolog-forum] Guo's word senses and Foundational Ontologies (012)
John, (013)
I believe you got the real meanings of the statement: " Not Statistics but
Ontology should rule the world." We debated many times that a full
signification of any word, or term, consists in its denotation (definition,
primary meaning) and connotation (all the properties and relations
associated with the term). For concepts, it is intension and extension. Then (014)
'Statistics' connotes data, senseless correlations, and all sorts of
number-crunching machines, data processing tools and search engines, as
Google and now wolfram alfa.
By contrast, 'Ontology' connotes the real world with real things, substance
and essence, meaningful correlations, and all sorts of meaning processing
machines, intelligent tools and semantic search engines (no examples yet).
I sympathise with your associations: "When it comes to ontology, I am
willing to admit that there might be a perfect ontology somewhere in the
infinite lattice of all possible theories. .." They HAVE but rather distant
connotation to the context of my message.
We must be fundamental but pragmatic, and vice versa. (015)
Bottom line: Truth and Meaning, not statistical nonsense, should rule the
world. (016)
Azamat (017)
----- Original Message -----
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Saturday, May 30, 2009 7:20 PM
Subject: Re: [ontolog-forum] Guo's word senses and Foundational Ontologies (018)
> Pat, John B, Azamat, and Frank,
>
> The notes in this thread have wandered all over the map in their
> range of topics. I'd like to comment on all of them in one note,
> because taken together they raise an important range of issues
> that any ontology (or AI in general) must deal with.
>
> First, I'd like to recommend Pat's slides for a good summary
> of an approach to ontology based on primitives:
> http://www.micra.com/COSMO/TheFoundationOntologyForInteroperability.ppt
>
> Although I like the slides as a summary of the approach, I still
> have serious concerns about their assumptions:
>
> 1. If you have N ontologies, the number of mappings from each to each
> is N^2. But if you have a single universal ontology, you could
> reduce the total to 2N mappings of the universal ontology to and
> from each of the others.
>
> 2. Many linguists, such as Anna Wierzbicka and others, have proposed
> or discovered a universal set of primitives that underlie all the
> world's languages. Practical applications of primitives include
> Ogden's Basic English and the LDOCE list of defining terms.
>
> 3. Therefore, a universal ontology based on a set of primitives
> derived from the linguistic R & D would be sufficient to define
> all the humanly conceivable concepts, and it would gain the
> advantage of reducing the possible mappings from N^2 to 2N.
>
> The first assumption is true *only* for the formally defined systems
> of mathematics, logic, and computer science in which each term has
> precisely one meaning. Even a slight variation in the meaning of a
> single term can introduce inconsistencies that cause total collapse.
>
> Another criticism of #1 is illustrated by the universal intermediate
> languages (ILs) often used in multi-language compilers, such as the Gnu
> compilers. Those languages can be compiled to a common form because
> they were *designed* to be compiled to a precisely defined machine code.
> The IL is just a generic machine code that is somewhat more systematic
> and regular than most popular computers.
>
> But a serious problem arises when trying to use the IL in a universal
> translator between source languages, say FORTRAN -> IL -> C++, or
> FORTRAN 90 -> IL -> FORTRAN IV.
>
> That kind of translation can be done for some simple expressions,
> but serious difficulties arise in trying to support features of
> C++ that are not present in FORTRAN or features that are similar,
> but not identical in the two languages.
>
> Even an expression like A+B creates problems because of all the
> variations of data types in each of the languages. For a simple
> add of two integers, problems arise because of different ways
> of handling overflow exceptions in the two languages. An exact
> translation of A+B to another language would have to supplement
> the code with a library of error handling routines that would
> accommodate all the variations in exception handling that are
> different in the two languages.
>
> Because of these issues, *nobody* uses the IL of the Gnu compilers
> to do translations of any Gnu language to any of the others.
> It is just not practical.
>
> When you move from math & comp. sci. to natural languages, you have
> to contend with the open ended range of meanings of *every* word
> in the language. Before getting into the primitives, I'd like to
> mention the following paper about primitives, which Pat cited:
>
> http://www.une.edu.au/bcss/linguistics/nsm/pdfs/bad-arguments5.pdf
>
> This is a good paper, which presents a strong defense of primitives
> in NLs, especially the kinds of primitives proposed by Wierzbicka.
> I highly recommend it as a survey of the field and the various
> issues that have been raised. But I'd like to point out several
> points that the author, Cliff Goddard, does not make:
>
> 1. He admits that nobody has yet discovered an ideal set of
> primitives. He notes that Wierzbicka's primitives are as
> good as any and better than most, but he does not suggest
> that the research has reached a final or even a stable
> universal set.
>
> 2. Goddard, Wierzbicka, Ogden, LDOCE, and others *never* claim
> their primitives are as precisely defined as a mathematical
> theory or a programming language. In fact, their examples
> show that their primitives are just as "squishy" -- i.e.,
> just as vague and fuzzy as any words in any of the languages
> they are trying to define.
>
> 3. In various examples, Wierzbicka shows how similar words in
> different languages (such as English and Russian) expand
> into different definitions in terms of the primitives. Each
> of those definitions typically takes one or more sentences
> composed of primitives -- anywhere from a dozen to several
> dozen words. If you expand a Russian text into primitives,
> the size expands by at least an order of magnitude, and it
> is extremely difficult or impossible to determine how to
> compress it into a smaller number of English words.
>
> For these reasons, machine translation systems that expand one
> language into a universal Interlingua have not been successful.
> Many attempts have been made, but all of projects have been
> canceled before any practical MT systems were produced. For
> ontology, there is even less experience: nobody has even
> attempted to build a universal Interlingua that is suitable
> for translating one ontology to another.
>
> For a survey of the issues about an Interlingua for MT, see the
> following chapter from a book by John Hutchins:
>
> http://www.hutchinsweb.me.uk/IntroMT-6.pdf
>
> In the summary at the end, Hutchins says "the 'conceptual meaning'
> representations required for interlingua-based systems demand a
> complexity of semantic analysis beyond the limitations of current
> linguistic theory. It is generally agreed that transfer-based
> approaches are at present the best foundations for advances in MT."
>
> In short, all attempts to develop a universal Interlingua for MT
> have *failed*. Linguists have retreated to the pairwise transfer
> approach, which requires N^2 translators for N languages.
>
> Doug Lenat>> The problems... are (a) there is no small set, and
> >> (b) it's almost impossible to nail down the meaning of most
> >> interesting terms, because of the inherent ambiguity in whatever
> >> set of terms are "primitive."
>
> PC> This remark seems to be directed at "primitive terms" used in
> > language. The kind of semantic primitives in an ontology are not
> > ambiguous, of course, so Lenat here is talking about human language.
>
> The reason why a small set was adequate for Wierzbicka and others
> is that they could take advantage of vagueness to cover a large range
> of "microsenses" with a small number of primitives.
>
> If you demand absolute precision, you need a distinct primitive
> for each microsense, and Lenat's estimate of 15,000 primitives is
> probably too small. (His previous estimates about the number of
> concepts and axioms needed for Cyc have always been too small.)
>
> PC> My suggestion was that, rather than guess, we actually conduct
> > a proper study to determine whether there is a finite inventory
> > of conceptual primitives and if so what the number is.
>
> I have no objection to that as a long-term research project. It
> might produce something useful. But I wouldn't expect it to solve
> the translation problems for a long, long time.
>
> JB> I also wonder about the work being done at Renaissance Technology
> > with the use of the Chern-Simons algorithms used to extract patterns
> > from stream data.
>
> Thanks for that reference. It illustrates the advantage of statistical
> methods and clever algorithms for certain kinds of problems. Those
> algorithms are complementary to ontology-based approaches, and it's
> important to have methods for taking advantage of multiple paradigms.
>
> AA> An academic geometer, James Simon, first had coauthored a
> > geometrical theory to be used for a quantum gravity string theory,
> > then left the academia to establish a hedge fund, Renaissance
> > Technologies Corporation, managing now up to $ 20 b, being 80
> > years old, and recently titled as "the smartest billionaire."
> > Statistics is still ruling the world...
> >
> > Not Statistics but Ontology should rule the world.
>
> I don't believe that the world should have a single ruling monarch
> or dictator. All previous attempts to establish one have been
> unpleasant or worse. Some religious leaders claim that God should
> rule the world. But in practice, that means that some finite
> mortals who claim to know the infinite mind end up as dictators.
>
> When it comes to ontology, I am willing to admit that there might
> be a perfect ontology somewhere in the infinite lattice of all
> possible theories. But I seriously doubt that our finite minds
> and machines will be able to discover it any time soon.
>
> FK> Thinking is too fast and too rich in paths of associations
> > to be satisfied by snapshots of net shaped representations.
>
> I would agree that any snapshot of human thinking, no matter what
> shape it's mapped into, is likely to be superseded by a better one
> fairly quickly. Just look at all the daily patches that Microsoft
> ships out for their software systems.
>
> We might find fixed and frozen snapshots that are useful for
> narrowly defined problems (such as an ontology for units of measure,
> for example). But a universal ontology of everything doesn't exist
> today, and all the large attempts (such as Cyc) are undergoing
> continuous revision and extension.
>
> In summary, any foundation for ontology should accommodate continuous
> revision and update. That is why I have recommended a hierarchy of
> ontologies, not a single, fixed standard. Let the users decide which,
> if any, are appropriate for their problems.
>
> John Sowa
>
>
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