Mr. McCabe,
No, I have not seen that described as a problem in
some practical implemented ontology-dependent system. Perhaps you can
provide us with a reference to paper(s) on this issue? I assume you
are talking about what others call “physical grounding” of ontology
symbols?
Pat
Patrick Cassidy
MICRA, Inc.
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From:
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[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Francis
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Sent: Sunday, January 11, 2009 12:01 PM
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Subject: Re: [ontolog-forum] FW: Next steps in using ontologies as
standards
Pat
May I assume, based on your responses to this somewhat
repetitive thread, that you might recognize that a major issue for Ontology
engineering is the symbol binding problem?
Frank
On Jan 11, 2009, at 8:18 AM, Pat Hayes wrote:
On Jan 11, 2009, at 12:59 AM, Patrick Cassidy wrote:
Just
short responses to two points. I think we have almost bottomed out here
on differences that can be fruitfully discussed further in anticipation of
learning something.
I agree; but this conversation has been useful, in that it
has revealed (for me) the key point of our disagreement.
(1) [PC] >> Is it possible that learning *some*
new things always requires creating new primitives? Possibly, but
that is the question that I have suggested can be investigated
To investigate that
is the business of cognitive psychology, not ontology engineering. I'm just not
interested in this question, and I don't think it is germane to this forum.
I strongly disagree, and feel
that the question of how many primitives are required to express the
meanings of an unlimited number of domain terms is one of the most basic
questions, beyond the definition of the basic logic, that can be asked
about how an ontology can be structured so as to achieve broad
interoperability, and I think it would be inherently interesting to
anyone who deals in representation of concepts.
I think the question is unanswerable, if posed with
precision (see below for exegesis) and therefore completely unimportant.
But ‘de gustibus non disputandum’ and if this is not
a matter of interest to you, your opinion is noted, and there is no point in
discussing that further. It also has the very practical virtue of
providing a tactic that can focus collaborative construction of a common
foundation ontology on the minimum number of basic ontology elements that will
serve the purpose of translating among multiple ontologies.
I think that to even discuss notions of 'primitiveness' is
to divert useful effort into pointless and ultimately meaningless debate about
nothing.
If you don’t believe that there are such things as
primitives, then I can see this point as being questionable to you, but I feel
strongly that the linguistic evidence of the dictionary defining vocabularies
is strongly suggestive of such primitives, and if you don’t think that
linguistic descriptions are sufficiently related to ontological expressions,
then again we just differ and this is still a question that has to be resolved
by experiment. If you think it’s a waste of time, don’t
participate.
Of course, I will not. But the point of the debate here is
surely how the community should focus effort, not just you and I.
(2) [PC] >> Well, knowledge
is certainly open-ended, but if new concepts (or terms labeling those concepts)
are always composed from some combination of pre-existing concepts
[PH] >> Again, what ARE you
talking about? What is this 'composed from some combination'? What kind of
composition operations do you have in mind here? How does these concept
combinators relate to logical ontologies? None of this makes sense to me.
Every time you (a) create an element in an ontology (type or
relation) and (b) the axioms expressing the intended meaning of that element
(to a level of detail sufficient for your intended purpose) contain only terms
already pre-existing in the ontology (no two or more newly created elements
depend mutually one each other for their axiomatic description); and (c) one
asserts that the intended meaning of that ontology element is adequately
captured by the axioms, without appealing to known instances of the type,
or to a linguistic description that is not also expressed by the axioms, then
that type or relation is, in the sense I am discussing, “expressed by”
or “described by” or “specified in terms of” the
pre-existing ontology elements, i.e. it is not a “primitive” in the
sense I am using it for an ontology element.
OK, though I would observe that to use language like
'combine' or 'construct' for this is misleading. But allow me to point out some
problems with this. First, you have phrased it in terms of creating a new
concept, so the distinction between new and old is a given; but in practice,
things are not this simple. As others have pointed out, if we are simply
presented with a complex logical theory, such as the equation F=M.A, one can
decide that any one of these is less 'primitive' than the others, using the
above criterion, just by re-ordering the set {F, M, A}. And this is typical:
first-order theories don't typically have the onion-peel layered structure that
your criteria relies upon. Second, your notion here is extremely fragile. For
example, it can be changed simply by re-casting an ontology in slightly
different terms, or by adding a single axiom. If one were to track the
development history of an ontology, even in its initial informal stages, the
classification of concepts as primitive or non-primitive would be varying
wildly as new facts were noted by the participants. Third, it begs the central
issue which is illustrated by the time catalog: there isn't a single ontology
to create new elements into. Right from the start, even for the most 'basic'
concepts such as space, time and objecthood, there are alternatives, all
equally valid and all having their active proponents and devotees, and all
mutually incompatible. Your criteria, as stated here, simply cannot deal with
this basic fact. And fourth, its too weak. For example, if I take the OWL wine
ontology and add a single new wine to it, asserting only that it is a member of
the class RhoneValleyWhiteWines and different from all the previously described
members of this class, then according to the above, I have not added a
new primitive. Which seems to me to be simply wrong, a clear bug in the
criterion as given.
In the case of relations, a proper description requires that
every newly created relation have some logical inference as part of its
description.
As stated, that does not make sense, but I think I see what
you mean. .
Relations that inherit logical inferences from parent relations
do not require additional inferences specified.
This operation of ontological description does not, in my view,
require a “necessary and sufficient” definition in order to qualify
as “non-primitive” .
As 'primitive' is a term of art which you have introduced,
and has no established psychological or ontological or logical meaning, you are
free to define it any way you like. We are not here talking about matters of
fact.
It only has to express the intended meaning axiomatically so
that a person who understands the axioms can understand the intended meaning
without a textual gloss, and without pointing to instances of a type or
instances of usage of a relation – and the axiomatic specification should
be sufficiently detailed so that ambiguities that might occur to another
ontologist as being relevant to the same application are absent. This may
still leave, in some sense. some “primitive” component unspecified
logically (as with a natural kinds), but if the axiomatic description is
sufficient to distinguish each element from all the others, and is useful for
the intended purpose of the domain ontology, then it can be said, in the sense
I am using, to be “described by” or “specified by” or
“expressed by” a combination of pre-existing ontology elements
– it is not a “primitive” element.
When you say “Those
various temporal theories can all be expressed in terms of three
concepts: time-point, time-interval and duration.” , what do you mean by
that? Is being “expressed in terms of” used only for
necessary and sufficient definitions?
No, I mean only that each theory uses only those three
terms, or can be reformulated using only those (or in some cases only two of
them.) Of course, since the theories have different axioms, they assign
somewhat different meanings to them.
On Jan 10, 2009, at 12:40 AM, Patrick Cassidy wrote:
... I confess it has been an
assumption of mine that, from the point of view of a “primitive”
concept being indivisible into smaller primitive concepts (crudely analogous to
an atom, in its role as a component of molecules), that a finite inventory of
such primitive-atoms (if such exists) would be unique.
Ignoring the finer to-and-fro
points of the argument for a moment, this seems to capture the basic
place where we differ. You have a central vision - I can't use a more precise
term - of concepts being 'formed' out of other concepts. by some process of
combination, a kind of conceptual chemistry; and then there must be a
collection of elements, a kind of concept periodic table. This analogy seems to
drive a lot of your intuitions in this debate. But I don't share this
intuition, and indeed I can't make philosophical sense of it: it seems to me to
simply rest on a mistake, one that Fodor has also critiqued very acutely.
Concepts simply aren't made up of combinations of other concepts in this way.
They are all "atomic". (Well, virtually all: all the
'natural kind' concepts, as opposed to artificial combinations such as
"French women between the ages of 25 and 50".) Just look at a
first-order theory: all the names in it are on an equal
footing; none are more 'primitive' than another, and they have no internal
conceptual structure which would permit their being decomposed into something
simpler or more elemental. The chemistry atom/molecule analogy is just
misleading. Peirce made the same mistake, and others since then (mostly
psychologists) have done so, but it seems to me that its long past time to bury
this idea of concepts having 'structure'. They don't divide into smaller
things, so they are all "primitive"; which is just another way of
saying that "primitive" isn't a useful notion here.
I have never seen this point
raised, and it may be significant, but right now I can’t think of any way
a set of indivisible primitives could be anything but unique.
But surely the time catalog is a
clear case of this non-uniqueness. I fail to understand how you cannot see
this, it seems so obvious. What would you reduce all of it to?
Limited imagination, perhaps.
Now I have noticed
that there are mathematical objects that have very non-intuitive properties,
and perhaps a mathematician can provide some examples of how a set of primitive
concepts (not divisible into component primitive concepts) might be able to be
formulated in more than one way. I am genuinely curious about this
suggestion.
There are many, many ways to model
space, for example, all of them different and none of them reducible to the
others.
(2) are primitives finite in number?
[PC] >> , though the modules can also have other ontology
elements in them. It is not clear to me that we can have a *stable*
set of modules to serve the purpose of interoperability unless we have some
confidence that all or most of the terms needed to express the meanings of
domain terms are there at the start.
[PH] > Seems clear to me that
if we impose this condition as a requirement, we have shot ourselves in the
foot. And why should the set of concepts be "stable" ? Isn't it more
realistic to assume that new concepts will always be being constructed, that
knowledge is always open-ended?
Well, knowledge is certainly
open-ended, but if new concepts (or terms labeling those concepts) are always
composed from some combination of pre-existing concepts
Again, what ARE you talking about?
What is this 'composed from some combination'? What kind of composition
operations do you have in mind here? How does these concept combinators relate
to logical ontologies? None of this makes sense to me.
, then the number of primitives
need not increase as knowledge increases. This may depend on what you
mean by ‘knowledge’. With a set of basic concepts we can
predict an infinite number of things that *might* exist in the real
world, but I think of knowledge as knowing what actually does exist and what
doesn’t. Learning about the laws of physics (and chemistry and
biology) that exist in our real world allows us to know some of the things that
can’t exist. That’s knowledge, in my lexicon, but it
doesn’t necessarily require new primitives.
?? Really? So when you first
learned about, say, the distinction between temperature and heat (an example I
recall especially vividly from my own education), you already had all the
necessary mental apparatus to describe thermodynamics? The learning was just
juggling the same basic stock of ideas in a new way? It sure didn't feel like
that to me: it felt like learning something entirely new, something I had never
previously thought. Similarly the first time I came across the notion of entropy,
it was a wholly new idea, not reducible to anything previously known. I was
able to use it to understand things that had been previously mysterious. My
inventory of mental concepts had grown.
It continues to grow. Not long ago
I learned the idea of "duende", a word that cannot be translated into
English.
Is it possible that learning *some* new things always
requires creating new primitives? Possibly, but that is the
question that I have suggested can be investigated
To investigate that is the
business of cognitive psychology, not ontology engineering. I'm just not
interested in this question, and I don't think it is germane to this forum.
by the process of creating a plausible set of ontology elements
based on primitives (as best we can discern them) and then seeing how quickly
that inventory in the FO must increase to allow the elements in each new
additional domain ontology to be expressed in terms of the primitive
set. If there is a finite set, then from the increase in required primitives
for each new block of domain concepts, it will be possible to assign a
probability that the total inventory will reach an asymptote at infinity.
The alternative is that no limit is indicated, and the number of primitives
behaves, say, like the number of prime numbers as the number of integers
increase. I do not know for sure which is more ‘realistic’,
but my suspicion lies with the finite number, based on evidence from linguistic
usage, such as the Longman defining vocabulary and the relatively small number
(2000 – 5000) in AMESLAN sign language dictionaries. There are
other suggestive kinds of evidence from language, but what needs to be
determined experimentally is whether the finite defining vocabularies in
languages are in fact analogous (at least on the point of the number of
primitives) to the task of creating ontology elements as combinations of other
ontology elements.
Again: what do you mean here? What
kind of combinations are you talking about? How are they expressed?
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