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At 10:44 AM -0400 3/12/08, Patrick Cassidy wrote:
John,
Thanks for your detailed clarification. I think we do
still have some
disagreements.
First, I agree with your comments about the difference
between dictionary
and mathematical definitions. I also believe that many of the
definitions
used in Longman would not be adequate to specify the meanings of terms
to
the required level of detail. But my own tests suggest that the
same set of
words would do that job, possibly needing a little additional
supplementation (as in the case of 'dimension' mentioned earlier).
But I do
not believe that the meanings of terms as specified in an ontology
follow
the mathematical method of creating mathematical concepts.
Just quickly, for the record, neither do I. I wish we could
simply stop talking of definitions altogether: definitions have no
place in an ontology, and the term only serves to confuse the
discussion.
In most cases,
we can only specify necessary conditions for membership in a type.
There is
simply no way to reduce the meanings to some very small set of
primitives.
I don't know what the number is, but I feel that the number of
necessary
primitives is an intensely important question to answer if we are ever
to
put the study of computational ontology on a scientific basis.
I must be misreading you. The above seems to contradict itself.
Do you believe in a number of primitives, or not?
You (and
others) may well not agree with this. I think that the
difference between
us may hinge very much on the degree of accuracy that we consider
necessary
for interoperability. I am focused on the needs of
mission-critical
applications where the machines will be making important decisions
automatically - where very high accuracy is required. I am not
sure what
applications you have worked on for which analogical reasoning is
adequate.
It has been used in military planning with some success.
Searching for information, where people
are presented with a list of
possibly relevant documents and they make the final relevance
judgment, does
not require high accuracy - though higher accuracy is better.
> PC> My point is that it is an important enough issue to
warrant
> > the effort required to discover that number -- a
project adequately
> > funded to support at least 50 people half time for a
couple of
> years.
>
> But I don't believe that there is any number to be
"discovered".
> If somebody set out to do the project with 10 primitives,
they
> could probably succeed. But then somebody else could add
one more
> axiom and reduce the number of primitives to 9. And
somebody else
> would add 8 more axioms and reduce the number of primitives to
1.
>
> If you completed such a project, it would be pointless, since
it
> wouldn't prove anything.
>
Well, if we found that 6000 basic concept representations
are necessary
and adequate to specify the meanings of
the 100,000+ terms in WordNet, it
would prove that those who believe there
is no such thing as a 'Conceptual
Defining Vocabulary' are wrong, and may be pursuing alternatives that
are
less effective at achieving interoperability. It would also provide a
means
of enabling accurate interoperability among a very diverse set of
ontology-based applications. If it turns out that that number can be
reduced
by further analysis to 4000, so much the better.
Since you think that 10 primitives may be enough, it is now
worthwhile
asking just what the criterion is for a concept representation to
be
considered one of the 'primitives' suitable for inclusion in the
foundation
ontology (PatH asked that a few posts ago, but it is very relevant to
your
comment that we might need only 10 primitives).
For the present, I use a *tentative* set of criteria
(below) to decide
whether a type or relation is 'primitive' in the sense of not being
able to
be adequately specified by pre-existing ontology elements. If
anyone else
who thinks that finding a list of
primitives is worthwhile believes that
these criteria should be modified, I will be very interested in
such
thoughts.
****************************************************************************
**********************************
What is a primitive concept?
A concept that cannot have its meaning specified
The problem here is that you havn't said what this means with
enough precision to allow us to apply this in practice.
solely by use of
preexisting elements in the foundation ontology is a primitive
concept, and
should be included in the foundation ontology. These criteria
assume that
the meaning of every type is specified by describing necessary
conditions
for being an instance of that type.
But not ANY necessary conditions, right? That would be
ridiculously weak. What you mean is, ENOUGH conditions to be in some
sense 'reasonable', to be enough to be able to say that one has pinned
down the meaning well enough for... for what? For the purposes at
hand? For all forseeable extensions or applications of the concept?
But that would be too strong...
When this is not possible (cases 3
and
4 ), there are other considerations. This also assumes that
every relation
has logical consequences specified for the case when that relation
holds.
(1) if the meanings of two or more new concepts to be represented can
only
be specified by reference to each other, and none can be specified
without
reference to one of the others, all of these would have to be added to
the
foundation ontology as new primitives.
(2) if the only way to distinguish a new concept from others is to
declare
that it is disjoint with other concepts, that new concept will be
a
primitive.
(3) if the meaning of a new type (class) cannot be specified by
necessary
conditions for membership, but must be explained by pointing to
real-world
instances, then that concept may also be a primitive. (But see
*3 below for
further discussion)
(4) if a type does not have any uninherited necessary conditions, but
is
specified solely as a union of some set of subtypes, it is not
necessarily
primitive and is not required as a part of the foundation ontology.
It may
nevertheless be convenient to include it in the foundation ontology,
to
allow assertions that efficiently refer to all of the subtypes.
See *3
below.
(5) a relation that is not a subrelation of another relation, and is
not the
logical consequence of some other relation(s) is a
primitive.
(6) if two relations necessarily imply each other, and neither is
a
subrelation of another relation, those relations are both
primitives.
==================
*3 These kinds of primitive can present special problems.
To specify a meaning of some type A by pointing to
instances or subtypes
is to specify the meaning by using sufficient conditions, not
necessary
conditions
*3a . If a type is specified as a union of subtypes, and
each of the
subtypes is specified by necessary conditions, then the meaning of
type A is
also by implication specified by necessary conditions, as being an
inclusive
disjunction of the necessary conditions of the subtypes, and this
is
acceptable.
*3b If a type is specified by an exhaustive list of
instances, then it is
adequately specified and acceptable as a primitive.
*3c If a type is specified by pointing to only some, but
not all
instances, then it is problematic, since the logic will not be able
to
relate it to other concept representations. It may be accepted,
but effort
should be made to specify the meaning in more detail. At a low
(leaf node)
level (a 1958 Ford Edsel), such primitives may be useful and
harmless. At a
high level, if highly abstract concepts (such as continuant and
occurrent)
are specified only as the union of some set of subtypes, the meaning
will
depend only on the subtypes. Though logically acceptable, the
ability of
the human developers to understand the intended meanings of types
defined
that way can be seriously diminished.
****************************************************************************
***********
Back to John and the 10 primitives.
What ten primitive concepts do you think will be adequate to
specify the
meanings of other concepts by necessary conditions? If there are
13
relations in the interval calculus alone, does this not suggest a
much
larger number of primitives?
Those can be reduced to the total ordering of the endpoints,
which arguably is a single concept. Or if one prefers, they can all be
defined in terms of 'meets', see
http://citeseer.ist.psu.edu/context/6330/0
PatH
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