Re: ONT Intension & Extension
Jon,
Compare Alonzo Church's discussion (below) of the intension and extension of
a concept with the mathematical (Formal Concept Analysis) (Rudolf Wille and
Garrett Birkhoff) definitions of the intent and extent of a formal concept
on the middle of page 30 in the IFF Classification Ontology document
[http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf].
As an illustrious example, see the 19 formal concepts (with explicit intent
and extent) in the concept lattice of the "Living Classification" on pages
74-76 of the same IFF Classification Ontology document.
Robert E. Kent
rekent@ontologos.org
----- Original Message -----
From: "Jon Awbrey" <jawbrey@oakland.edu>
To: "Ontology" <ontology@ieee.org>
Sent: Saturday, January 19, 2002 8:00 PM
Subject: ONT Intension & Extension
>
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> | Intension & Extension
> |
> | The 'intension' of a concept consists
> | of the qualities or properties which
> | go to make up the concept.
> |
> | The 'extension' of a concept consists of the things
> | which fall under the concept; or, according to another
> | definition, the 'extension' of a concept consists of the
> | concepts which are subsumed under it (determine subclasses).
> |
> | This is the old distinction between intension and extension,
> | and coincides approximately with the distinction between
> | a monadic 'propositional function' (q.v.) in intension
> | and a 'class' (q.v.).
> |
> | The words 'intension' and 'extension' are also used in connection
> | with a number of distinctions related or analogous to this one, the
> | adjective 'extensional' being applied to notions or points of view which
> | in some respect confine attention to truth-values of propositions as
opposed
> | to meanings constituting propositions. In the case of (interpreted)
calculi
> | of propositions or propositional functions, the adjective 'intensional'
may
> | mean that account is taken of modality, 'extensional' that all functions
> | of propositions which appear are truth-functions. The extreme of the
> | extensional point of view does away with propositions altogether and
> | retains only truth-values in their place.
> |
> | Alonzo Church, in Runes, pages 147-148.
> |
> | Dagobert Runes (ed.), 'Dictionary of Philosophy',
> | Littlefield, Adams, & Company, Totowa, NJ, 1972.
>
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