ONT Re: Extension x Comprehension = Information
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JA = Jon Awbrey
RK = Robert Kent
JA: 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.
RK: Consider again the example of the concept lattice
for the Living Classification discussed on page 74
of the IFF Classification Ontology:
RK: http://suo.ieee.org/IFF/versions/20020102/IFFClassificationOntology.pdf
i have been periodically returning to this example.
it has some quirky properties, and you know that
we like that sort thing here in pizarro world.
but i will have to take it kinda slow as the
main for me now is this long overdue duty
to figure out what peirce meant by this
new-fangled invention of "information".
per via, was this a bona fide example? --
i have seen it around and about, but
it looks kind of like the sort of
critter whose bones came out of
some matroid or finite geometry
context that somebody just hung
all of that extra flesh upon?
anyway, give me time, and
of course, i will have to
interweave back and forth
between the bridge and
the brig.
RK: 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*.
i think that i asked this a couple of times, but i still need
to know how you think of concepts, as objects (things mainly
being denoted or talked about, in which case we collapse or
quotient out their multiplicities as much we possibly can,
and think of them like numbers or functions that are named
by a canonical sign or a "normal form"), or as signs (like
the particular expressions that we have to maintain and
to transform in a genuine computation)?
RK: 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.
what does "wave" stand for, and do you have a link to some info on it?
jon awbrey,
pièce sans vu,
chateau d'iff.
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