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Re: [ontolog-forum] Ontology similarity and accurate communication

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 12 Mar 2008 10:51:59 -0500
Message-id: <p06230902c3fda70789e1@[]>
At 10:44 AM -0400 3/12/08, Patrick Cassidy wrote:
  Thanks for your detailed clarification.  I think we do still have some
   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

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
(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
(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
  *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
  *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


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