ONT Re: Intension & Extension
Jon,
----- Original Message -----
From: "Jon Awbrey" <jawbrey@oakland.edu>
To: "Robert E. Kent" <rekent@ontologos.org>
Cc: "Ontology" <ontology@ieee.org>
Sent: Sunday, January 20, 2002 4:48 PM
Subject: Re: Intension & Extension
<snip>
I quote from the text by Ganter and Wille (page 17):
"The basic notions of Formal Concept Analysis are those of a *formal
context* and a *formal concept*. The adjective 'formal' is meant to
emphasize that we are dealing with mathematical notions, which only reflect
some aspects of the meaning of *context* and *concept* in standard
language."
The purpose of my original message to you
[http://suo.ieee.org/email/msg07729.html] was to invite people to consider
how well these mathematical notions represent the intuitive notions
discussed in the passage from Alonzo Church that you quoted. I feel that
these matters should be fully discussed. In that light, consider the
following excerpts from your message and Church's passage.
> For me, an intension is always just a property or a quality.
> When people speak of "the" intension of a concept or a term,
> I usually take them to mean the conjunction of "all" of the
> intensions that it has in the relevant context of discourse,
> which is more properly called the "comprehension", though
Suppose we make the identification:
FCA formal context
= IF classification
= the relevant context of discourse
And we further make the identifications
FCA attribute
= IF type
= an intension is always just a property or a quality
Then
"the" intension of a concept or a term
= the "comprehension" of the concept
= (Church) the qualities or properties which go to make up the concept.
= the conjunction of "all" of the intensions that it has in the relevant
context of discourse
would seem to correspond exactly to the FCA notion of intent of a formal
concept defined as
the intent of a formal concept
(within a formal context)
= all attributes that are shared by all the objects of the formal
concept (its extent)
So, does not the FCA intent seem to fit the intuitive idea of conceptual
intension or comprehension. What do you think?
Robert E. Kent
rekent@ontologos.org