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Axiomatic approach to understanding generic resources

From: Jonathan Rees <jar@creativecommons.org>
Date: Sat, 9 May 2009 12:11:30 -0400
Message-ID: <760bcb2a0905090911s3c1609b1n329e4bfaa8325cab@mail.gmail.com>
To: AWWSW TF <public-awwsw@w3.org>
I propose that since words are failing us, as evidenced by the number
of times communication has broken down with everyone unhappy, that we
should consider an axiomatization instead, at least as a detour. That
is, for a little while at least, just give names to the classes and
relationships without trying to define them, and instead talk about
how they might be characterized mathematically, as one might do in
Euclidean geometry. Then, once that's out of the way, we can go back
and figure out what the classes and relationships might actually be
(or, Hayes-like, how we might privately be willing to interpret the
terms).

For example: supposedly there is a three-way relation: X is a
"representation" of generic resource G at time t. Can we say then that
a time-specific resource is one that does not vary according to time -
that is, at every time t, the set A = {X | X is a representation of G
at t} is the same?

Similarly, can we say that a fixed resource is defined by the property
that across all time, a fixed resource has only one "representation"
(for all t1 and t2, if X rep G at t1, then X rep G at t2)?

Can there be more than one fixed resource that has the same
representation (if X rep FR1 and X rep FR2 then FR1 = FR2)?

Is a generic resource defined by its representations (as in Roy's
formalism), or can you have two distinct generic resources that have
the same representations over time ({for all t and X, X rep G1 at t
and X rep G2 at t} -> G1 = G2)?   (Are there "essential
characteristics"  carried not by the representations, but by some
*other* message)?

Does every generic resource have at least one representation at some
time (i.e. for any G is it the case that there exist t and X such that
X is a representation of G at t)?

Moby Dick is a generic resource, right? (Without getting into
definitions for now) Is Moby Dick time specific? Does Moby Dick have
infinitely many representations (e.g., differing in infinitely many
inconsequential ways, or written in infinitely many hypothetical
languages)?

Does there exist a "universal" generic resource, e.g. G such that for
all times t and representations X, X is a representation of G at t?

We can probably come up with a wide variety of similar
cardinality-related questions, and if I knew the answers to them I
think I'd have a much better idea of what's being discussed - I might
even be able to predict what kinds of things might be, or not be,
generic resources, something I've repeatedly failed at so far.

(I use "generic resource" in the sense of
http://www.w3.org/DesignIssues/Generic.html .  I use it in preference
to "information resource" because the latter seems much more difficult
to pin down.)

Jonathan
Received on Saturday, 9 May 2009 16:12:07 GMT

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