On Tuesday, February 16, 2010 9:12 PM, Patrick Cassidy wrote:
> Chris,
> Thanks for the comment below. It's a relief to see that at least some of
> the participants in this list do not share the misinterpretations of what
> I have been saying about the FO. Try as I might to be unambiguous,
> bizarre distortions of my comments seem to provoke irate replies.
It is not a big secret that i am in close sympathy with Pat's position. And
i have terrible feelings of guilt: being currently unable to assist him in
realizing the truth, validity and value of standard ontology and semantics.
I couldn't track the Forum activity but only occasionally, being assigned
with a megaproject, http://en.wikipedia.org/wiki/Megaproject, involving the
building of a semantic interoperability platform for an Intelligent
Community combining three key types of intelligence: individual, collective,
and computational. http://en.wikipedia.org/wiki/Intelligent_city.
Judging on what i managed to digest, I have to agree with Pat, the level of
criticism of such an unexampled innovation is rather dull and dispiriting.
Allow me to repeat the same hint:
"While the Forum is hotly discussing if the Foundation Ontology and Semantic
Interoperability are valid concepts, the EU set up the Semantic
Interoperability Center Europe, http://www.semic.eu/semic/.
Moreover, the European Interoperability Framework, how administrations,
businesses and citizens intercommunicate with each other within the EU and
across Member States borders, has been ratified by the European Parliament.
The innovative thought is supposed to lead the action."
Azamat Abdoullaev
PS: we are ready for a long-term cooperation with the ontology/semantics/web
consultants able to advise about the Semantic Interoperability Platform for
Intelligent Eco-City. For more details, suggest an offline communication.
----- Original Message -----
From: "Patrick Cassidy" <pat@xxxxxxxxx>
To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Tuesday, February 16, 2010 9:12 PM
Subject: Re: [ontolog-forum] Foundation ontology, CYC, and Mapping (01)
> Chris,
> Thanks for the comment below. It's a relief to see that at least some of
> the participants in this list do not share the misinterpretations of what
> I have been saying about the FO. Try as I might to be unambiguous,
> bizarre distortions of my comments seem to provoke irate replies.
>
>> On Feb 15, 2010, at 4:28 PM, Rob Freeman wrote:
>> > Pat,
>> >
>> > What is clear is that:
>> >
>> > 1) You keep repeating your belief that a single complete
>> > axiomatization (with useful coverage?) is possible.
>> >
>> > 2) You admit you don't know how to prove it is possible.
>> >
>> > 3) You ignore/don't understand that other people have proven it is
>> impossible.
>> >
>> > "A complete and consistent logic complex enough to include arithmetic
>> > was shown by Kurt Goedel to be impossible..."
>>
>
> Chris Menzel replied (amid a delightful exposition of what Goedel said):
>>
>> As for charge #3 that you direct at Pat above, Pat has never claimed
>> that a FO would include a complete, consistent, recursive
>> axiomatization of arithmetic. You should be more careful about
>> lecturing others about what they don't understanding.
>>
> Right. I am not concerned with the foundations of mathematics, I leave
> that to others far more qualified than I. I am concerned with the
> quickest and most direct route to general and accurate semantic
> interoperability. The FO proposal in brief can be summarized:
> (1) there are some ontology elements whose intended meanings cannot be
> expressed solely as an FOL combination of other ontology elements. I call
> these "primitives". Anyone else can call them anything they please.
> (2) for any given group of domain ontologies, there will be some set of
> such primitives that will be sufficient to logically specify by FOL
> combination the intended meanings of the non-primitive elements of those
> ontologies. These meanings will not necessarily be complete descriptions
> of the intended real-world referents; they will be sufficient to perform
> the computations desired for
> (3) To *accurately* translate logical assertions among those domain
> ontologies, the most parsimonious tactic (and probably the fastest) would
> be to identify the primitives in common among those domain ontologies,
> include them in an FO, and use them to create translations of assertions
> between the domain ontologies. Those translations will use "bridging
> axioms" to convert assertions from the form in one ontology to the form in
> another ontology.
> (4) To minimize the changes in the FO as new domain ontologies are linked
> to (mapped to or logically expressed by) the FO, it is advisable to try to
> identify as many of the possible primitives as can be identified, at the
> earliest stages of testing of the FO. This should reduce the number of
> new primitives that need to be created as new domain ontologies are linked
> to the FO. Since the test has never been done, we do not know whether or
> how quickly the need for new primitives will drops for each new domain.
> That can only be determined by testing the FO process. It is possible
> that new primitives will need to be continually added; even so, this
> method appears (to me) to be the most effective to achieve the maximum and
> most accurate semantic interoperability that is possible at any given
> time.
> (5) As possible inventories of primitives that should be included in a
> *starting* FO, to aim for the broadest coverage as quickly as possible, I
> suggest using the senses associated with the Longman dictionary defining
> vocabulary - 2148 words, and probably over 4000 senses. Longman has been
> tested for its ability to linguistically define all other words in the
> dictionary, but whether there could be a similar small inventory of
> primitive ontology elements that can combine to specify *all* other
> ontology elements is unknown and may be impossible. The more relevant
> question is whether a set of primitive ontology elements can be found that
> will not need *significant* supplementation as new domains are linked to
> the FO; if little supplementation is needed, the FO should be stable
> enough for most practical tasks requiring semantic interoperability. This
> question can only be answered by testing multiple domain ontologies versus
> some common FO.
> Other possible sources of essential primitives could be the 3000 most
> frequent Chinese characters (covering 98.9% of modern text) and the 2000
> most common signs of AMESLAN. But these symbols have not been tested as a
> "defining vocabulary".
> (6) The fastest method to test the FO hypothesis is to create a consortium
> of multiple diverse groups of ontology developers and potential users (and
> relevant standards groups), to conduct a carefully organized study to
> agree on an FO and test its utility in practical applications, and test
> its ability to support accurate semantic interoperability.
>
> NOTE that there is nothing in here about a "complete" theory of anything,
> just the most practical and expeditious method to address a practical
> problem. The goal is the fastest and best possible solution to semantic
> interoperability for any given set of ontologies. Theoretical
> completeness of the inventory of primitives is unnecessary, though it is
> an asymptote worthwhile trying to approximate.
>
>
> There is more detail about this approach to semantic interoperability in
> the presentation:
> http://www.micra.com/COSMO/TheFoundationOntologyForInteroperability.ppt
>
> There are doubtless questions that one may have that are not answered even
> in that document; I will be happy to answer any such as best I can, and
> then add the answers to the ppt.
>
> If one does not consider broad semantic interoperability to be of
> significant practical utility, or doubts that an FO can contribute to that
> goal, so be it. I think the problem is serious, and that all serious
> proposals to address the problem should be considered seriously. I am of
> course, happy to hear well-considered technical concerns. But what I have
> heard so far in objection in many cases are based on misinterpretations of
> what I have been saying. If anything sounds wrong, do look at the ppt
> presentation, and if there still seems to be a problem, do let me know.
>
> Pat
>
>
>
>
>
>
>
> 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 Christopher Menzel
>> Sent: Tuesday, February 16, 2010 12:50 PM
>> To: [ontolog-forum]
>> Subject: Re: [ontolog-forum] Foundation ontology, CYC, and Mapping
>>
>> On Feb 15, 2010, at 4:28 PM, Rob Freeman wrote:
>> > Pat,
>> >
>> > What is clear is that:
>> >
>> > 1) You keep repeating your belief that a single complete
>> > axiomatization (with useful coverage?) is possible.
>> >
>> > 2) You admit you don't know how to prove it is possible.
>> >
>> > 3) You ignore/don't understand that other people have proven it is
>> impossible.
>> >
>> > "A complete and consistent logic complex enough to include arithmetic
>> > was shown by Kurt Goedel to be impossible..."
>>
>> Better, in characterizing Gödel's theorem, to talk about theories
>> rather than logics. Also better to emphasize simplicity rather than
>> complexity, as one needs only a very modest bit of arithmetic to prove
>> incompleteness in general. That modest bit is usually called Q. Q
>> contains three axioms for the successor function, two of which also
>> axiomatize 0:
>>
>> 1. ∀x(0 ≠ sx) -- "0 is not the successor of any number."
>> 2. ∀x(x ≠ 0 → ∃y(x = sy)) -- "Every nonzero number has a predecessor"
>> 3. ∀xy(sx = sy → x = y) -- "The successor function is 1-1"
>>
>> In addition, Q provides the obvious axioms for addition and
>> multiplication:
>>
>> 4. ∀x(x + 0 = x)
>> 5. ∀xy(x + sy = s(x + y))
>> 6. ∀x(x • 0 = 0)
>> 7. ∀xy(x • sy = s(x • y))
>>
>> Finally, it is absolutely critical in a characterization of the theorem
>> to mention recursive axiomatizability (basically, the property a theory
>> has when it is possible (i.e., you can write a program) to list its
>> theorems), since there are in fact complete, consistent (but not
>> recursively axiomatizable) theories that include that modest bit of
>> arithmetic (a trivial example being simply being the theory consisting
>> of all true sentences in the language of arithmetic). So, specifically,
>> what Gödel showed was:
>>
>> (*) No consistent, complete theory that includes Q is
>> recursively axiomatizable.
>>
>> And, actually, Gödel didn't prove exactly (*) in his famous 1931 paper,
>> he proved something weaker, although (*) itself can be proved using
>> only the foundations that he laid in that paper (and was done so by
>> Rosser in 1936).
>>
>> As for charge #3 that you direct at Pat above, Pat has never claimed
>> that a FO would include a complete, consistent, recursive
>> axiomatization of arithmetic. You should be more careful about
>> lecturing others about what they don't understanding.
>>
>> > I'm also finding references to a guy named Thoralf Skolem. Anyone
>> else
>> > heard of him?
>>
>> Of course. He's a prominent figure in the history of mathematical
>> logic in the early 20th century, particularly well known for his work
>> in model theory.
>>
>> > "In the 1922 lecture the Löwenheim-Skolem theorem was applied to a
>> > formalization of set theory. The result was a relativization of the
>> > notion of set, later known as the Skolem paradox: If the axiomatic
>> > system (e.g. as presented by Zermelo) is consistent, i.e. if it is at
>> > all satisfiable, then it must be satisfiable within a countable
>> > ``Denkbereich'' (domain). But does this not contradict Cantor's
>> > theorem of the uncountable, the existence of a never-ending sequence
>> > of transfinite powers? The ``paradox'' of Skolem is no contradiction.
>>
>> Indeed not. It is a theorem about the expressive limitations of first-
>> order logic.
>>
>> > Roughly speaking it asserts that there is no complete axiomatization
>> > of mathematics,
>>
>> Actually, the Löwenheim-Skolem theorem doesn't say that at all. It
>> says that a theory with infinite models has a countable model. In and
>> of itself, that does not imply incompleteness. (If it did, Löwenheim
>> and Skolem would be credited with discovering arithmetical
>> incompleteness in the early 1920s.)
>>
>> > and that certain concepts must be interpreted relative to
>> > a given axiomatization and its models and thus have no ``absolute''
>> > meaning."
>>
>> That's in fact a highly controversial (some would even argue decisively
>> refutable) philosophical interpretation of the the L-S theorem.
>> Regardless of your philosophical view of the theorem, the idea that the
>> notion of set is "relative" to an axiomatization is certainly not a
>> *mathematical* consequence of it.
>>
>> > "Towards the end of the 1929 paper Skolem expressed some doubts about
>> > the complete axiomatizability of mathematical concepts. His
>> scepticism
>> > was based on the set-theoretic relativism which follows from the
>> > Löwenheim-Skolem theorem. In 1929 he could give only some partial
>> > results, but in a paper from 1934 (and a previous one from 1933)
>> > ``Über die Nichtcharacterisierbarkeit der Zahlenreihe mittels endlich
>> > oder abzählbar unendlich vieler Aussagen mit ausschliesslich
>> > Zahlenvariablen'' he could prove that there is no finite or countably
>> > infinite set of sentences in the language of Peano arithmetic which
>> > characterizes the natural numbers. Today, this follows as a simple
>> > consequence of Gödel's completeness theorem. The technique used by
>> > Skolem was a more direct model-theoretic construction. And this
>> > technique, suitably refined to the so-called ``ultraproduct''
>> > construction, has been an important tool in recent work on model
>> > theory."
>> >
>> > http://www.hf.uio.no/ifikk/filosofi/njpl/vol1no2/skobio/node1.html
>> >
>> > By the way, my alternative is to work directly with observations of
>> > different kinds, perhaps indexed by labels, and implement
>> > interoperability based on overlaps between sets of these, as the task
>> > demands.
>>
>> Your alternative to *what*? The above is just a description of certain
>> historical developments in mathematical logic. It doesn't make sense
>> to talk about an "alternative" to it, especially one that involves
>> contemporary notions out of ontological engineering like
>> interoperability.
>>
>> Chris Menzel
>>
>>
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