Re: SUO: Re: Charter vs. Consensus
John, Eric and others,
I am probably preaching to the choir again, but I think this needs some
comment in order for people to understand my current thinking of how the IFF
applies to modularity and centralization.
The description below is precisely the rationale and motivation for
representing the library of modules in the IFF as a diagram of theories, or
even as multiple diagrams of theories. Each theory can be left in place
undisturbed. Various operations such as subsetting, summing and quotienting
can be applied to these theories to generate new theories. If it is desired
to compose a "great big hierarchy with modules copied in, frozen into place,
and relabeled to avoid inconsistencies", this is accomplished in a
straightforward manner:
1. Informally identify the theories that will be used in the
composition.
2. Formally create a (transient, since it will be used only for this
computation) diagram of theories T = {T_n} that indicates this
selection.
3. Form the colimit T* = col(T) of this diagram of theories, with the
following sub-steps.
3.i. Compute the underlying base diagram of languages L = base(T)
= {L_n}= {base(T_n)}.
3.ii. Form the colimit L* = col(L) of this diagram of languages with
associated colimit injection language morphisms
{l_n : L_n --> L*}.
3.iii. Move the individual theories in T = {T_n} along the language
colimit injection morphisms to the lattice of theories LOT(L*),
getting the homogeneous diagram of theories flow(T) =
{flow(T)_n}, where each theory flow(T)_n = dir(expr(l_n))(T_n)
has the same underlying base language L* (the meaning of
homogeneous in this instance).
3.iv. Compute the meet (union) of the diagram flow(T) within the
lattice LOT(L*) getting the colimit theory
T* = col(T) = meet(flow(T)).
The colimit T* is the desired "great big [centralized] hierarchy". In the
larger picture, it is just another theory. The original theories have been
left in place undisturbed.
Robert E. Kent
rekent@ontologos.org
----- Original Message -----
From: "John F. Sowa" <sowa@bestweb.net>
To: "Eric Peterson" <epeterson@CCAAVA.com>
Cc: <jim.s3@juno.com>; <standard-upper-ontology@ieee.org>
Sent: Friday, June 27, 2003 3:21 AM
Subject: Re: SUO: Re: Charter vs. Consensus
[snip]
> That is just a repackaging of exactly the same mathematics, but
> to avoid inconsistencies, it uses relabeling instead of modules.
> However, I have not given up on modules. They are an essential
> step toward the development of the single hierarchy, and they are
> much more flexible for the development of special purpose ontologies.
>
> We could have both. If you want to regard the single hierarchy
> with lots of relabeled subtypes as "The Standard", be my guest --
> just as long as each of the subtypes is cross indexed to some module
> or modules in the registry from which the axioms were derived.
>
> Nevertheless, the modular approach gives you vastly more flexibility
> and potential for reuse. It allows you to reuse the same modules
> in different ways in different places. When you import a module into
> the big hierarchy and relabel the names to accommodate the particular
> position into which you inserted it, it is very hard to extract it
> again and reuse it somewhere else.
>
> And by the way, I never used the word "competing" for the modules,
> and the single hierarchy just moves any "competition" between modules
> into competition between disjoint subtypes. I would prefer to say
> that the modules are complementary, since many of the more general
> ones can be reused in multiple ways in many different places in
> the big hierarchy.
>
> Summary: I regard the lattice of modules to be the most important
> ontological resource we could develop. But I have no objections
> to having a great big hierarchy with modules copied in, frozen into
> place, and relabeled to avoid inconsistencies.