Thursday, December 15, 2005
Communications on lattice of theories
John’s response to [309] is
Paul,
The word
"infinite" literally means without boundaries
-- i.e., unlimited.
> Rather than "infinite number of models", if we were
to
> say "unlimited number of models" would this be in
line
> with what you want to say?
Use any word you please -- infinite,
unlimited, open-ended.
They're synonyms.
John
John
Of
course, and I understand your saying that unlimited or infinite is the same
concept
but,
also of course, if is not the same concept in mathematics. This is a very old distinction between
actual and potential infinity. Again,
there are practical implications to how one feels about this concept(s).
But
here the point I am pressing has to do with "when" the
"number" or the "model" is made available.
If
the very large number, or the situational model for "this" event (ie
an event "now"), is produced in response to real time structure of
those things that are making up the event; we may have the creation of the very
large number or the situational model "now".
The
core issue is not abduction, but induction; and by induction I mean also the
concept in biological morphology...
metabolic induction, selectionism, etc.
As
you know, an infinite set, say of integers, has as members all possible
positive integers (defined with Peano axioms to be the set of symbols having a
first element and having the property that any element in the set has a
successor element.)
What
I am having in mind is some set of basic ontological construction that are in
the spirit of SUMO (or in the spirit of the Foundational Model of Anatomy as
discussed at
http://sigpubs.biostr.washington.edu/archive/00000135/
so
that ontologies developed according to the standard would be able to be compliant
without the imposition of specific machine inference mechanisms. The standard would also be independent of
the data encoding, and the formal specification of knowledge representation (as
in RDF).
The
formal theory, however would be laid out in an understandable curriculum, one
that would be acceptable to non-computer scientists in universities.
Your,
and Tarski’s, lattice of models must be part of that theory, but there are
aspects of the use of lattice theory that we have not been able to talk
about.
This
"ontological resource" could be conceptual in nature and abstract, in
the sense of an abstract upper ontology, so that domain and utility ontology
might have the freedom to develop in a flexible fashion.
It
would even be possible, using this resource, that a situational ontology (and
associated inference rules and deductive machinery) might come into existence
quickly to deal with some surprising situation. This "emergent" ontology would have the resources in
the set of "common" concepts in the central hub of a hub type
ontology construction.
The
term "controlled vocabulary" is often used. Perhaps we should be talking about a high level (abstract)
"controlled conceptual specification" having the abstract properties
of SUMO, or the Part 1 of the ISO 15926 ontology.
There
might be two or three developed so that individuals could select which one they
wanted to use, and some reconciliation of terminology differences between
controlled vocabulary technology (such as SchemaLogic's) instantiated. The various communities could then
adaptively evolve their specific domain and utility ontologies (with or without
logics).
Comments?