SUO: Re: ONT Re: Extension x Comprehension = Information
- To: "Jon Awbrey" <jawbrey@oakland.edu>
- Subject: SUO: Re: ONT Re: Extension x Comprehension = Information
- From: "Robert E. Kent" <rekent@ontologos.org>
- Date: Fri, 22 Feb 2002 12:01:08 -0800
- Cc: "SUO" <standard-upper-ontology@ieee.org>
- References: <3C6BD812.AA7F03BD@oakland.edu> <3C6C0DE0.C50D564F@oakland.edu> <3C6C8222.93DA16B@oakland.edu> <3C6D1B7C.991D1897@oakland.edu> <3C6D6759.7123C15A@oakland.edu> <3C6D78B1.2DB9D732@oakland.edu> <3C6D8210.8016A55F@oakland.edu> <3C711F73.A55C82B8@oakland.edu> <3C714441.66C7ED66@oakland.edu> <3C726462.4F82B5A5@oakland.edu> <3C72DBE1.C1D08560@oakland.edu> <3C73FE72.22226E83@oakland.edu> <3C742C7B.7C0E470A@oakland.edu> <3C748CE0.58989AA0@oakland.edu> <3C7533E9.CCB99136@oakland.edu> <3C756DF7.FC6943AE@oakland.edu> <3C75D418.E3B3844A@oakland.edu> <3C769879.97B623EB@oakland.edu>
- Reply-To: "Robert E. Kent" <rekent@ontologos.org>
- Sender: owner-standard-upper-ontology@majordomo.ieee.org
Heavens to Murgatroid Jon, from all of these recent excerpts I am beginning
to believe that CSP was the first Formal Concept Analyst!
(comments below)
----- Original Message -----
From: "Jon Awbrey" <jawbrey@oakland.edu>
To: "Arisbe" <arisbe@stderr.org>; "Gdsemiocom" <gdsemiocom@univ-perp.fr>;
"Ontology" <ontology@ieee.org>
Sent: Friday, February 22, 2002 11:14 AM
Subject: ONT Re: Extension x Comprehension = Information
>
> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
>
> | With me -- the 'Sphere' of a term is all the things we know that
> | it applies to, or the disjunctive sum of the subjects to which
> | it can be predicate in an affirmative subsumptive proposition.
> | The 'content' of a term is all the attributes it tells us,
> | or the conjunctive sum of the predicates to which it can
> | be made subject in a universal necessary proposition.
The IFF Classification Ontology
<http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf> is
in one sense categorical rendition of the basic theorem of Formal Concept
Analysis -- it is a distillation and axiomatization of my Relmics'6 paper
"Distributed Conceptual Structures"
http://www.kub.nl/faculteiten/fww/medewerkers/swart/conference/rmcs2001.html
A central aspect of the basic theorem of FCA is that the instances of a
classification are join-dense, and that the types are meet-dense, in the
corresponding concept lattice. This fact is concentrated on page 35 of the
IFF Classification Ontology. There you see a formula that states that every
formal concept (element in the concept lattice of a classification) is both
the join (disjunctive sum) of the objects (= instances) below it, and the
meet (conjunctive sum) of the attributes (= types) above it.
> | The maxim then which rules explicatory reasoning
> | is that any part of the content of a term can
> | be predicated of any part of its sphere.
By derivation, (the formal concept generated by) any object (part of CSP's
sphere) of a formal concept (CSP's term) is below (the formal concept
generated by) any attribute (part of CSP's content) of a formal concept.
> |
> | CSP, CE 1, page 462.
> |
> | Charles Sanders Peirce,
> |"The Logic of Science, or, Induction and Hypothesis",
> | Lowell Institute Lectures of 1866, pages 357-504 in:
> |
> |'Writings of Charles S. Peirce: A Chronological Edition',
> |'Volume 1, 1857-1866', Peirce Edition Project,
> | Indiana University Press, Bloomington, IN, 1982.
>
> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Robert E. Kent
rekent@ontologos.org