ONT Re: Intension & Extension
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RK = Robert Kent
RK: 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:
RK: http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf
RK: 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.
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Robert,
I have been looking at the Living Classification Lattice that
you mentioned, and I have a couple of questions just to start:
o-------o-------o-------o-------o--------o-----o------o--------o--------o---------o
| | needs | lives | lives | needs | di | mono | motile | limbed | suckles |
| | water | in | on | chloro | cot | cot | | | young |
| | | water | land | phyll | | | | | |
o-------o-------o-------o-------o--------o-----o------o--------o--------o---------o
| leech | 1 | 1 | | | | | 1 | | |
| bream | 1 | 1 | | | | | 1 | 1 | |
| frog | 1 | 1 | 1 | | | | 1 | 1 | |
| dog | 1 | | 1 | | | | 1 | 1 | 1 |
| hemiz | 1 | 1 | | 1 | | 1 | | | |
| reed | 1 | 1 | 1 | 1 | | 1 | | | |
| bean | 1 | | 1 | 1 | 1 | | | | |
| maize | 1 | | 1 | 1 | | 1 | | | |
o-------o-------o-------o-------o--------o-----o------o--------o--------o---------o
FE = Formal Extent
FI = Formal Intent
1. Are you using "object" and "instance" as synonyms?
2. Can you explain to me in what sense it makes sense to you to say
that {bream, frog} is the FE of the fo.co. "bream", or similarly,
that {maize, reed} is the FE of the fo.co. "maize", as generators?
I mean, you can say whatever you like, formally speaking, but I am
asking this in the light of a supposed analogy to ordinary extension.
And now I can finally sleep ...
Jon Awbrey
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