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Thursday, December 15, 2005

 

 The BCNGroup Beadgames

 

 

Challenge Problem  à

 

 

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?