SUO: Re: IFF LOT glossary
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SUO Work Gang,
Just by way of a midstream memo on the point of this thread,
it began with RK's note copied below, and continued with my
question about the meaning of the term "base language fiber"
as used in the sentence: "The lattice of theories is the
base language fiber in the category of theories, whereas
the truth concept lattice is the base language fiber in
the category of closed theories."
The relevance of this question to IFF as an architecture for SUO and
to working out the details of the various "lattice of theories" and
"libraries of modules" ideas, that John Sowa has steadfastly been
keeping in the air all about us, ought to be clear.
Pursuant to the task of supporting IFF with a negotiable infrastructure,
I have in the meantime, in the medium of my dialogues with Robert Kent,
been seeking to connect the more abstract ideas of IFF to a number of
decidedly more concrete, exoteric, simple, and standard concepts
from applied math and computer science. An oppportune way of
doing this has been to develop a concrete and simple example
that I borrowed from John Sowa's "Top Level Categories",
which has incidentally been assimilated -- somehow the
phrase "resistance is futile" comes to mind -- into
the SUMO contributary to the prospective SUO.
That should indicate where some of the stakes are staked out
on grounds of pressing import for multiple goals of our work.
Okay, back to the grinstone ...
Jon Awbrey
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Robert E. Kent wrote:
>
> All,
>
> I have posted the PDF document "The IFF Glossary for the Lattice of
> Theories" at the address http://suo.ieee.org/IFF/LOT-glossary.pdf.
>
> This graphically illustrates and briefly discusses the core functionality
> for both the truth concept lattice and the lattice of theories, two notions
> that are equivalent from the order-theoretic viewpoint. The lattice of theories
> is the base language fiber in the category of theories, whereas the truth concept
> lattice is the base language fiber in the category of closed theories.
>
> Please regard this as a mid-range report -- I am developing a new
> version of the theory namespace axiomatization that contains all
> of this. This will offer a baseline axiomatization in the IFF for
> the notions of a "lattice of theories" and a "library of modules".
>
> As always, all constructive comments are welcomed.
>
> Robert E. Kent
> rekent@ontologos.org
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