SUO: Re: ONT Re: Extension x Comprehension = Information

["Robert E. Kent" <rekent@ontologos.org>]

Jon,

Consider again the example of the concept lattice for the Living
Classification discussed on page 74 of the IFF Classification Ontology
http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf. The
universe of objects {Leech Bream, ... , Maize} has cardinality 8. So the
power set has cardinality 256. Thus there are 256 potential extents.
However, the nature of closure for the Galois connection between the
derivation operators for the concept lattice restrict this to only the 19
extents listed in the Living example. Now in a real world example even this
restriction may not be manageable -- one may not be able to fully represent
the concept lattice for a particular classification. In the  IFF
Classification Ontology there is a practical solution axiomatized on page 41
called a *collective concept*. This was the central data structure (there
called a conceptual frame) used in the implementation of the conceptual
browser in the Intel-sponsered WAVE system that I directed several years
ago. It allows one to recursively build up an approximation to any concept
lattice, starting from primitive data and using the lattice operations.

Robert E. Kent
rekent@ontologos.org

----- Original Message -----
From: "Jon Awbrey" <jawbrey@oakland.edu>
To: "Arisbe" <arisbe@stderr.org>; "Gdsemiocom" <gdsemiocom@univ-perp.fr>;
"Ontology" <ontology@ieee.org>
Sent: Tuesday, February 19, 2002 3:12 PM
Subject: ONT Re: Extension x Comprehension = Information

> Our focus at present is on the extra measure of constraint,
> in other words, the information, that comes between Set(X),
> the full lattice of all possible subsets of our universe X,
> and Nat(X), the more constrained, determined, or informed
> lattice of "natural kinds" that we commonly acknowledge in
> our more practical outlooks on this universe of discourse.