SUO: Re: JA v/s JD on Peirce, Hillman, FCA, etc...
"Robert E. Kent" a écrit :
> (comments below -- mostly a FYI)
[snip]
> The SUO starter document called the IFF (Informationm Flow Framework)
> represents many basic notions of Set Theory, Order Theory and Formal
[snip]
> the IFF Core Ontology
> <http://suo.ieee.org/IFF/versions/20020102/IFFCoreOntology.pdf> and the IFF
97 pages!
> Classification Ontology
> <http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf>.
78 pages!
> These are located in the upper metalevel. Eventually, there will also be a
> representation for the small naotions, and these will be located in the
> lower metalevel. Let us use the abbrevations: IFF-CORE for the IFF Core
> Ontology and IFF-CLS for the IFF Classification Ontology. In particular, the
> notions that you discuss below are all represented and axiomatized in the IFF.
Should I mention:
http://suo.ieee.org/IFF/versions/20020102/IFFBasicKIFOntology.pdf
17 pages!
and
http://suo.ieee.org/IFF/versions/20020102/IFFCategoryTheoryOntology.pdf
53 pages!
I do have these at the 2002-01-02 revision levels.
Sorry for not using the !#&$concept names but I prefer to have a *human*
readable text, readable without having to browse thru the 245+ pages
(and I forgot the IFFFoundationOntology.htm which is not PDF)
> > I found what I deem a remarkably concise and usefull set of definitions
> > related to FCA in pages 3 and 4 of "What is a concept?",
> > from Chris Hillman: http://www.math.washington.edu/~hillman/papers.html
> > and this prompted me to make some critical comments to JA's message:
>
> [snip]
>
> > According to Hillman what makes a subset a proper concept is the fact that
> it
> > is closed under <||> if taken from X and closed under |><| if taken from
> Y.
> > (duality allows to halve the amount of demonstrations, see Hillman's)
> >
> > Where: |> A = {y : (x ,y) in R for all x in A}
> > <| B = {x : (x ,y) in R for all y in B}
> > <||> A = {x : (x ,y) in R for all y in |> A}
> > |><| B = {y : (x ,y) in R for all x in <| B}
> >
> > So we can beef up our ontology structure with a set of 'concepts' which
> > will be names for subsets of X which happen to be extensions of proper
> > concepts. That is, from now on, the ontology will be build upon
> > X, Y, R c XxY, N, pow(X), C c N x pow(X) where:
> > - N is a set of Names for the concepts
> > - pow(X) is the power set of the "things" set X
> > - C is a mapping from names to "proper concepts" subsets of X
Hillman makes it two pages, I reduced it to one, and *you* cut it down
to one half-page and still retain the meat of it.
I am not myself in the business of building an ontology and I just wanted to
make some points about the inherent difficulties of what you are attempting
while still having a reasonably formalised setting to avoid ambiguities.
These points are mainly:
1) Ontology building is an ever ongoing process,
no nirvana to be reached some day.
2) During the process the structure of the lattice of concepts will
undergo drastic changes for wich some decisions rely on pure
opportunity and even the order of entry of various data items.
So there is no "best" ontology building way nor any kind of
canonical representation to be preferred at any point in time.
3) Part of the knowledge we collect cannot be stored in the ontology
lest we run the risk of "freezing" woefully wrong information just
because it happened to have been entered too early.
See beyond the definitions in my previous message.
Best.
-- Jean-Luc Delatre
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From the moment I picked your book up until I laid it down
I was convulsed with laughter. Someday I intend reading it.
-Groucho Marx
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