On Jan 21, 2009, at 11:02 AM, Patrick Cassidy wrote: John,
Yes, you have completely misunderstood my proposal, and your description
of it shows why.
I have not suggested creating a terminology by using words as
representatives of primitive concepts, and at no time have I *ever* confused
words or other terms with the concepts that they label, nor with the logical
representations of the concepts that they label. I have suggested creating
a common foundation **ontology** that *includes* logical representations of
the concepts that are also represented by the Longman defining vocabulary.
The meanings of those logically represented concepts will be as unambiguous
as any logical representation can be, and their **computational behavior**
does not in any way depend on the human language used in the documentation,
nor on any errors in interpretation of that usage by humans who rely only on
the documentation.
Of course not: but whether or not that computational behavior is (considered by human users to be) correct will almost certainly depend upon this. Any nuanced division/partition of a general concept
considered significant by any member of the consortium can also be included
(using a different label for each representation of a different meaning),
and the logical specification of each nuance of meaning will be different
from any other logical representation in the ontology. The labels used for
the logical specifications are ***irrelevant***, except insofar as they can
help (or mislead) *human* readers in understanding the intended meanings and
computational behavior of the logical specifications; but the real meanings
are determined only by the logical specifications themselves.
I see what you mean, and your point here is of course well-known in KR circles, even in textbooks; but you need to be very careful at this point, when talking of "real meanings". If we assume that there are concepts AT ALL (never mind how they are encoded into English words), then whether any set of FOL axioms can fully capture those concepts is never certain. In some cases it clearly cannot. For example, take a country such as Wales, my homeland. The Welsh name for Wales is "Cymri". Now, you and I know that 'Cymri' denotes Wales, but no amount of first-order axiomatization is ever going to pin down the meaning of the name 'Cymri' so that it denotes Wales. And this is not because there are many different notions of Wales (geographical, historical, cultural, etc.), but because of Herbrand's theorem, which states that if any set of FOL axioms is satisfiable, then it has a model made entirely of symbols. So it is literally impossible to write enough FOL axioms to pin down "real meanings" when those real (intended) meanings are found in the physical world.
The labels
can be gensyms (or can be replaced by pictures if the pictures could be used
as entity label in reasoning), without affecting the meaning of the logical
specifications.
Without affecting the logical meaning, yes. But that leaves open the central question of how those logical meanings relate to the "real meanings" or "intended meanings" or whatever we call the pre-theoretic intuitions which guide the construction of the axioms in the first place. This is ***not*** a terminology, nor is it any attempt to fix on a controlled terminology. The relations of the logical specifications to human-language words are entirely dependent on the preferred usage in different communities, and is a subject for natural language understanding programs. The ontology itself is independent of language. The focus on conceptual primitives is not a *requirement* for creating an effective foundation ontology that is useful for translating among multiple ontologies (or databases), but is a tactic that can help focus the initial effort and minimize the size of the ontology that is the initial goal. As it gains in usage, the foundation ontology and all of the other ontologies in the resulting lattice of theories can be expanded or modified. That observation is true for every formal ontology. There
are no primitives. There are just equations (or other
kinds of formulas) that relate the terms. The words in
one theory and its successors are frequently the same
or similar. But the equations that relate them are
very different.
As Pat Hayes pointed out, all of his time theories can be "expressed by" (Pat Hayes's phrase) axioms containing only three classes, time point, time interval, and duration. That is ***exactly** the same sense in which I have said that a very large number of complex concepts (such as, but not restricted to, concepts defined by necessary and sufficient conditions) or theories can be represented as combinations of the primitive concepts.
Really? Then I have not been understanding you at all. And I fail to see quite how this squares with what you say above. Bear in mind that these various theories, while they all use the same concept names, are mutually incompatible. So to make them into a single coherent ontology, they have to be distinguished, using your guidelines, so that there will be timepoint-simple, timepoint-linearorder, timepoint-glasscontinuum, etc. ., and similarly for the various order relations. The three 'primitive' concepts will generate perhaps ( I havn't checked in detail) 15 or so alternatives.
I agree that one could do this, but I fail to see the purpose. It seems to me both more honest and more useful to say that we have a number of alternative ontologies here, all describing the same small group of basic ideas or concepts, but describing them differently. Then there are indeed a small number of 'primitive' concepts, but multiple ontologies of them. Rather then one ontology with many alternative 'primitive' concepts, all very similar but subtly different, and all bearing the same rather diffuse relationship to the normal English words or intuitive ideas. When I think of time-intervals, it does not seem to be that I switch concepts when ignoring whether they are open or closed. Rather, a time-interval is what it is, and I can think about it in various ways. I am
using a different terminology than Pat Hayes, but I am expressing
**exactly** the same idea. I go a little further, in suggesting that there
is likely a lot of benefit in identifying those basic concepts, not just for
the time theories, but for all the other theories and concepts in domain
ontologies that can be expressed by axioms using the basic concept
representations. It is useful to distinguish the theories and complex
concepts that can be expressed by the basic concepts from the basic concepts
themselves, so as to minimize the number of concepts that can be included in
the first version of the FO.
If you think there are no such things as basic concepts that can be
distinguished from theories that are expressed by those basic concepts,
please argue the point with Pat Hayes, he has been saying the same thing
(using different words) for years. He also seems to have persistently
misinterpreted what I have been suggesting - except that we may disagree on
the number of the basic concepts, not their existence - but I'm not sure of
that, because he hasn't yet acknowledged that the basic concepts he uses to
express his time theories are the same sort of thing as my "primitives"
Well, I now do not feel that I have any idea what you have been talking about. But I certainly don't think that the time concepts in the 'catalog' are particularly "primitive", or that other concepts can be described in terms of them. They are useful and ubiquitous, but that doesn't give them any special status other than being, well, useful and ubiquitous. But if I look at a chunk of, say, Cyc, and see timeinterval concepts and many other concepts all related together by axioms, I don't see any useful or coherent way in which these time concepts stand out as in any way more 'primitive' than any others. , and
he hasn't yet suggested an alternative term to label that class of things
(the class that contains representations of the concepts TimePoint,
TimeInterval, and Duration, but not the theories expressed by using those
concepts).
That sentence simply does not make sense. What kind of 'representations' are there when there are no theories (axioms) to relate the names together? The set {timeinterval, timepoint, before} is just a set of three character strings. None of that says that the different time theories, or any other logically
inconsistent set of alternative theories, can be made **logically
consistent** by finding these basic concept representations, nor can they be
"reduced" to each other.
Then what is the significance of this word "primitive" that you keep insisting upon? The relations of the theories can be discovered by
inspecting their different representations that use the same set of basic
concepts. Logically inconsistent theories will be part of a lattice of
theories. Just how much of the lattice should be maintained by the
consortium is for the consortium to decide. What we don't know now, but
can discover by the consortium process, is just how large a group of
logically consistent ontology elements can be agreed on, whether they are
considered "basic" or not. Learning this is something I feel certain will
help advance the art and science of ontology. I think that knowing the
extent of agreement on the basic concepts will be better than not knowing,
even if there are some people who are not interested, and even if it turns
out that the number of "primitives" is actually unlimited.
This all presupposes what I have always thought to be false, that there actually is a set of 'primitive' concepts to be found. I challenge you to find anything I have written in past 20 years which suggest that I accept this notion. Other, of course, than in the reductio sense in which all the concepts in a FOL ontology are "primitive". There probably are some genuine differences in our opinions on the issues we
have been discussing but they have been horribly confused by the
misinterpretations that you and Pat Hayes have been putting on the things I
have been saying.
Well, let me try to gain some clarity by stating some propositions with which we might agree or disagree. I will put in my current understanding of your and my positions as we go along.
1. Ontologies are first-order theories. (C, H) 2. Ontologies can be organized in a Sowa-ian lattice of theories (C, H) 3. There is, or could be, or should be, a single basic ontology on which all users will agree (C, ~H) 4. Ontological disagreements can be decided, in a large professional group, by voting. (C, ~H) 5. There is a meaningful relationship of being more primitive than, which holds between concepts in a (large enough) ontology (C, ~H) 6. The set of all 'most primitive' concepts in a meaningfully large ontology can be usefully related to Longman's dictionary (C, ~H) 7. Disagreements about the correctness of theories can often be understood as disagreements about content, and hence can be usefully resolved by allowing multiple versions of the concepts involved, thereby restoring formal consistency. (C, ?H)
where the '?' means that while I agree this can often be done, I don't think it is a useful strategy. At best, it will produce a consistent ontology which nobody wants to use.
Overall, I wouldn't say that this amounted to a full agreement between us.
PatH PatC Patrick Cassidy MICRA, Inc. 908-561-3416 cell: 908-565-4053 cassidy@xxxxxxxxx-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
Sent: Tuesday, January 20, 2009 2:35 AM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Next steps in using ontologies as
standards
Pat,
I know *exactly* what you are trying to do, and your comments
show that you haven't seriously examined the definitions in
Longman's dictionary, which you keep citing as a paradigm.
PC> It is clear that you have completely misinterpreted the
proposal I have been making.
I'll summarize your proposal:
1. Find a set of primitive concepts that are common to all
natural languages. These would be similar to the defining
vocabulary of Longman's dictionary for students who are
learning English as a second language.
2. Use those primitives to define a much larger vocabulary of
terms and thereby relate them by means of those primitives.
This idea is not bad for writing a dictionary that is intended
to be used by students who *already* learned the concepts in
their native country and just need to learn the English words
for them. Just look at a typical definition:
energy. The power which does work and drives machines:
atomic/electrical energy | the energy of the sun.
If the students had already learned the concept, this kind
of definition would enable them to relate the English word
'energy' to their previous knowledge. But for an ontology,
this definition is worthless. In physics, the words 'energy',
'work', and 'power' express three different, but related
concepts that are defined by different formulas. For an
ontology, the above definition would be worse than useless
-- because it happens to be false. Almost every definition
in that dictionary is either false or hopelessly vague.
PC> The whole point of creating an FO by a large consortium
is precisely to be certain that the views representing many
different interests and ways to express knowledge are taken
into account...
A consortium or committee is good for evaluating proposals,
but they can't solve the unsolvable. Just look at the way
the Newtonian concepts of space, time, mass, and energy
evolved in the progression to relativity and quantum mechanics.
Those words are used in all three theories (and many other
variations). But those words are *not* defined in terms of
primitives. They are related to one another by various
equations. Furthermore, the equations in the three theories
are not only different; they are contradictory. There is
nothing that remotely resembles defining primitives.
That observation is true for every formal ontology. There
are no primitives. There are just equations (or other
kinds of formulas) that relate the terms. The words in
one theory and its successors are frequently the same
or similar. But the equations that relate them are
very different.
There's a fundamental reason why it's impossible to use any
subset of natural language vocabulary as ontological primitives:
NL words are intended to be used in a open-ended number of ways,
but ontological terms are absolutely precise within the scope
of a particular theory.
That distinction creates an inherent conflict:
1. There are common ideas expressed in the basic vocabularies
of many different languages, as many people such as Len Talmy
and Anna Wierzbicka have shown. But the corresponding words
are vague, with many different *microsenses* that vary from
one "language game" to another.
2. Formal ontologies and scientific theories require sharply
defined terms that denote values that can be measured
precisely. Those terms are defined only within a formal
theory (or language game), and any paraphrase in the words
of #1 is at best a vague approximation.
The Longman's defining terms (or anything similar, such as
Wierzbicka's primitives) are inherently vague. They cannot
be used to define ontological terms that must have a precise,
formally defined sense.
John
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