Re: SUO: RE: RE: "Abstract" and "dimensionality" - Re: SUMO axiomatization
Folks,
Can you relate the issues about physical existence and observers to
either of the two starter documents? This discussion started off with a
title referring to SUMO but doesn't currently specify any term or axiom in
the current document along with a proposed change as far as I can see.
John's original message had a helpful pointer but more helpful in order
of increasing helpfulness would be
1. A suggestion for which theories from the reference to add
2. ...which theories to add along with some justification and examples as
to how they are useful, and why they belong at the upper level
3. ...and what implications those theories have and changes they
necessitate in the existing document
4. a proposal for specific changes and additions (provided as KIF) in the
current document.
Adam
At 10:57 AM 1/7/2002 +0100, West, Matthew R SITI-ITPSIE wrote:
>Dear Graham,
>
>See comments below.
>
>
>Matthew West
>Principal Consultant
>Shell Information Technology International Limited
>Shell Centre, London SE1 7NA, United Kingdom
>
>Tel: +44 20 7934 4490 Other Tel: +44 7796 336538
>Email: matthew.r.west@is.shell.com
>Internet: <http://www.shell.com/>http://www.shell.com
>>-----Original Message-----
>>From: Horn, Graham [mailto:graham.horn@aihw.gov.au]
>>Sent: 03 January 2002 00:10
>>To: West, Matthew R SITI-ITPSIE; standard-upper-ontology@ieee.org
>>Subject: RE: RE: "Abstract" and "dimensionality" - Re: SUMO axiomatization
>>
>>Matthew,
>> . Thanks for your response. Further comments
>> interspersed below, prefaced GH> .
>>
>>
>>Cheers Graham Horn
>>National Data Standards Unit
>>Australian Institute of Health and Welfare
>>=================================
>>Phone: 02.6244.1094
>>Fax: 02.6244.1199
>>E-mail:
>><mailto:graham.horn@aihw.gov.au>Graham.Horn@aihw.gov.au
>>Knowledgebase:
>><mailto:graham.horn@aihw.gov.au>www.aihw.gov.au/knowledgebase/
>>
>>-----Original Message-----
>>From: West, Matthew R SITI-ITPSIE [mailto:Matthew.R.West@is.shell.com]
>>Sent: Wednesday, 2 January 2002 20:07
>>To: standard-upper-ontology@ieee.org
>>Subject: SUO: RE: "Abstract" and "dimensionality" - Re: SUMO axiomatization
>>
>>Dear Graham,
>>
>>See comments below.
>>
>>
>>Matthew West
>>Principal Consultant
>>Shell Information Technology International Limited
>>Shell Centre, London SE1 7NA, United Kingdom
>>
>>Tel: +44 20 7934 4490 Other Tel: +44 7796 336538
>>E-mail: matthew.r.west@is.shell.com
>>Internet: <http://www.shell.com/>http://www.shell.com
>>>-----Original Message-----
>>>From: Horn, Graham [mailto:graham.horn@aihw.gov.au]
>>>Sent: 02 January 2002 07:19
>>>To: 'John F. Sowa'; kif@philebus.tamu.edu
>>>Cc: standard-upper-ontology@ieee.org
>>>Subject: SUO: "Abstract" and "dimensionality" - Re: SUMO axiomatization
>>>
>>>John et al,
>>> . I have had considerable problems with trying to
>>> tie down the nature of pure structure, theory, etc. I tried to apply
>>> the term "concept" to this, but was ruled out of order on the basis
>>> that a concept had to have been conceived by someone, and by
>>> implication, at a given point in time. The latest draft of ISO/IEC
>>> 111793 accordingly defines "Concept" as
>>>
>>>· "a unit of thought constituted through abstraction based on
>>>characteristics common to a set of objects".
>>>
>>>MW: An interesting string of words, but I'm not sure they say very much.
>>>
>>>GH> Agreed. You may rest assured I was not involved in the
>>>formulation of such a clause.
>>>
>>> . I fear the same attitude may be taken to "Abstract",
>>> since someone had to perform the (mental) task of "drawing away" the
>>> pattern or structure from the original observation or thought.
>>>
>>>MW: That is just a matter of definition.
>>>
>>>GH> Not quite. I was just following the traditional pattern of
>>>depending on etymology for elucidating word meanings. The reason for
>>>such a practice is that it follows the logical facilitation of
>>>maximising scientific rigour of analysability and repeatability.
>>>
>>>MW2: Not on the whole something I would recommend. Interesting as an
>>>historical exercise for sure, but I find usage is the only reliable
>>>indicator of meaning.
>>>
>>> MW: There are patterns (what I would call classes) that sit out there
>>> in all their infinite glory waiting to be noticed - e.g. Kepler's laws
>>> of planetary motion. Someone notices them, and forms an instance of a
>>> pattern in their brain (another class) that represents them. This might
>>> get written down and copied (another pattern with (perhaps) several
>>> instances, etc.
>>>
>>>GH> I'd prefer to say someone observes some apparent pattern they can
>>>attribute to a mathematical model they conceive or have come across.
>>>
>>>MW2: In practice this is OK, but if abstract things are timeless, they
>>>have to "exist" (not in a physical sense) independent of observers.
>>>
>>> MW: From this what you can say is that a concept (if it must be
>>> something someone has thought) is a pattern for which there is a
>>> representation class of which there is at least one instance in
>>> someone's brain at some time.
>>>
>>>GH> Fine.
>>>
>>>MW: By the way, personally I might want to argue that you can have
>>>concepts about individuals too, although you can always fit them into
>>>the above definition as singleton sets.
>>>
>>>GH> Agreed.
>>>
>>>GH> This doesn't seem to get me very much further below.
>>>
>>>MW2: I will try to elaborate then.
>>>
>>> . Personally, I feel there is something in the nature of
>>> pure structure or pattern that can exist independently of whether it
>>> exists in physical reality, and also independently of whether any
>>> intelligent being has conceived of or observed it.
>>>
>>>MW2: This is just the point I am making above, but this is abstract
>>>existence, not physical existence (in space and time).
>>>
>>> . By way of explanation, I would suggest that both
>>> Newton's law of gravity and Kepler's laws of planetary motion are not
>>> precisely accurate, and so do not exist in physical reality, but are
>>> rather mere approximations of physical reality. Yet, I would suggest
>>> that they are both timeless and without location or mass
>>> ("zero-dimensional" in the physical sense), and hence existed
>>> infinitely before either Newton or Kepler were born, and will continue
>>> to do so after all records and other traces of them have been obliterated.
>>>
>>>MW2: Quite.
>>>
>>> . The problem is I don't know what term I can use to
>>> apply to such pure structures or patterns that one can abstract or conceive.
>>>
>>>MW2: At the most general level, I use the term "class" for all of these.
>>>Patterns have individuals in some possible world that are instances of
>>>the pattern.
>>>
>>> . Neither does "information" cover this. One can observe
>>> and document the spread of information, whether be it physical, such as
>>> through the spread of genes, etc., or purely conceptual, such as with
>>> nemes, by means of, say, semaphore communication.
>>>
>>>MW2: Some classes are the patterns that we recognise as information. An
>>>instance is something physical (like the image on this screen) that is a
>>>member of that class. Information classes are classes that are used to
>>>represent (other) things.
>>>
>>> . The reason I ask this question is that there are times
>>> when I wish to consider these "zero-dimensional" patterns / structures.
>>>
>>>MW2: This can be done with the approach I have outlined here.
>>>
>>> . Incidentally, t have a related problem about the nature
>>> of "dimensionality". I wish to apply the term beyond the traditional
>>> physics scope of mass, length and time, into far more abstract areas.
>>> This is because it can be extremely useful in information management
>>> and information based sciences to apply to a far broader range of
>>> concepts. Statisticians psychologists and pharmacists do this when they
>>> are looking to ascertain which factors are relevant, and which
>>> irrelevant, for particular avenues of research and endeavour. The
>>> concept of "dimensionality", along with others like "mutual
>>> exclusivity" or "orthogonality" also come into play here, and can
>>> greatly facilitate conceptual design and analysis.
>>>
>>>MW2: It is certainly useful to understand which (sets of) classes are
>>>mutually exclusive, and also which can be combined (to give greater
>>>expressiveness). For me this is just part of the analysis.
>>>
>>> . Can anyone suggest a rigorous definition that covers
>>> this broader scope?
>>>
>>>MW2: Class: A thing that has members, a pattern that some thing may
>>>conform to.
>>>
>>>MW2: Concept: A class that represents some thing independent of the
>>>means of expressing it e.g. in a particular language, or in a particular
>>>form e.g. written, spoken.
>>>
>>>
>>>Cheers Graham Horn
>>>National Data Standards Unit
>>>Australian Institute of Health and Welfare
>>>================================================
>>>Phone: 02.6244.1094
>>>Fax: 02.6244.1199
>>>E-mail:
>>><mailto:graham.horn@aihw.gov.au>Graham.Horn@aihw.gov.au
>>>Knowledgebase: www.aihw.gov.au/knowledgebase/
>>>
>>>-----Original Message-----
>>>From: John F. Sowa [<mailto:sowa@bestweb.net>mailto:sowa@bestweb.net]
>>>Sent: Wednesday, 2 January 2002 14:28
>>>To: kif@philebus.tamu.edu
>>>Cc: standard-upper-ontology@ieee.org
>>>Subject: SUO: Re: KIF: Re: SUMO axiomatization
>>>
>>>Chris,
>>>
>>>I would include all mathematical structures under the category Abstract
>>>in my ontology. In fact, everything under that category is of the
>>>same nature as Abstract; i.e., it is the category of every kind of
>>>form that can be defined without contradiction.
>>>
>>>The subtype Schema includes all the "static" structures, and the
>>>subtype Script includes all the "dynamic" structures -- i.e., all
>>>those that have a time-like succession of forms. As Nicola keeps
>>>insisting, the category of abstractions is outside of space & time.
>>>That is true, but you can have mathematical theories that include
>>>a dimension labelled t, which just happens to be very time-like.
>>>
>>>"Christopher A. Welty" wrote:
>>>
>>>CW> Thanks for pointing this out, John. It brings up an interesting
>>> > point for me - (sorry if this was discussed already during my
>>> > SUO-absence) - do people find this to be "upper level"? Certainly if
>>> > graphs is considered upper level, then this library demonstrates that
>>> > there are over a hundred other things at the same "level".
>>>
>>>At 1:55 PM -0500 12/22/01, John F. Sowa wrote:
>>>
>>>JFS>There is a collection of over a hundred mathematical theories
>>> > >(fully axiomatized) that were developed to run under IMPS
>>> > >(Interactive Mathematical Proof System). The theorem-proving
>>> > >programs that use these axioms run on most versions of LISP and
>>> > >are available from Mitre as software that has been made freely
>>> > >available. Following is the home page:
>>> > >
>>> > > <http://imps.mcmaster.ca/>http://imps.mcmaster.ca/
>>> > >
>>> > >The theories include graphs, groups, fields, automata,
>>> > >and several versions of geometry, arithmetic, etc.
>>>
>>>The category of all abstractions has forms for everything that exists
>>>and everything that might exist without contradiction in any kind of
>>>universe. So it is even richer than the category Physical, which only
>>>includes those kinds of things that are physically possible in our
>>>universe.
>>>
>>>All those theories can be organized in a lattice, according to
>>>the partial ordering defined by implication; i.e., if every axiom
>>>of theory A is a theorem of theory B, then A is more general than B.
>>>
>>>But not all mathematical theories are in the upper level. Chess,
>>>for example, is a mathematical theory, but it would be farther down
>>>the hierarchy.
>>>
>>>And I would also include the mathematical forms of virtual reality
>>>under the category of abstractions. For examples, see the following
>>>web site, which has a couple of frames from a recent movie. It took
>>>90 minutes of time on a supercomputer to do all the computations for
>>>each frame:
>>>
>>>
>>><http://a330.g.akamai.net/7/330/2540/e15dfb847b2b87/www.e-insite.net/ednmag/contents/images/185947f6.pdf>http://a330.g.akamai.net/7/330/2540/e15dfb847b2b87/www.e-insite.net/ednmag/contents/images/185947f6.pdf
>>>
>>>
>>>All the computer is doing is generating lots of colored polygons.
>>>Those polygons would be fairly far down the hierarchy, but they're
>>>still abstract.
>>>
>>>John
>>
>>Adam Pease
>>Teknowledge
>>(650) 424-0500 x571