Re: SUO: Question
John,
In your proposal of an (infinite) lattice of all possible theories, do modules
that are ill formed also fit into this lattice (e.g. do not have any stated
or consistent methodology, are defective or inappropriate in some other way)?
I assume so since it is "all possible theories" even poorly formed or simply
false theories ( I am using what I believe is a widely accepted definition
of a theory - something that can be assigned a truth value). If one can
have both p and ~p in the lattice how will one decide which to use?
How will one know that both p and ~p are present (or not present)
in the module of theories one selects to use? It seems to me that one must
have some test of compatibility if one is asked to select some theories from
a much larger (infinite?) number to use.
I believe a FCA type analysis can be useful but what level of assertion would
be used in the analysis - axiom, theory, module (of supposedly consistent
theories?) or something else? I view lattices as very promising but I have
difficulty understanding your proposal. If both SUMO and OpenCyc were in
the lattice would they be considered as a single module or broken down into
component modules? Would the component modules be considered a single theory
or would they be evaluated on the basis of the individual theories that compose
the component modules? Could the individual theories be recombined to form
new modules? Assuming one has an method of evaluation, how does one chose
among a number of acceptable modules? A standard should be appropriate and
used for most purposes (85 - 90%).
A tutorial would be very welcome.
Bob
John F. Sowa wrote:
3CB257E1.6050604@bestweb.net">
Bill, Adam, Pierluigi, et al.,
Several things have happened recently, of which the biggest was
the very large gift of OpenCyc, which has been dropped into the mix.
This raises the very serious question of what to do with or about it,
and how it relates to the other work that has been going on for the
past two years.
I have been talking about the lattice of all possible theories, and
some people, especially the IFF developers, have said that their
system will support it. However, the IFF documentation still remains
rather impenetrable to most ordinary citizens, and the question of
how IFF would relate to SUMO, OpenCyc, and all the other available
ontological resources has never been spelled out in detail (other
than, of course, the very detailed mathematical details of IFF).
Suggestion: I propose that we start a new project that will take
a good hard look at the available resources and determine how they
relate to one another. I have made a long-standing claim that they
could be analyzed into neat little modules that could be fit into
a lattice of theories. But that claim requires quite a bit of work
to substantiate in detail:
1. A specification of the lattice operators that would relate the
modules to one another. That would also require some tutorial
documentation about what a lattice is and why it is an appropriate
mathematical structure for relating theories.
2. A comparison of selected modules from SUMO, OpenCyc, and other
resources with an analysis of the similarities and differences
in their axiomatizations of the same or similar topics. If all
the axioms are identical (which is highly unlikely), then there
would be nothing further to do in order to relate SUMO to OpenCyc.
But if they are different, then there are many questions that
would have to be answered about why, how, and whether they are
actually different in their implications or merely in the choice
of which propositions to take as axioms and which are to be proved
as theorems.
3. For modules that differ in SUMO and OpenCyc, it would be useful
to show how they could be related by means of the lattice. For
example, what is their common generalization (supremum)? What
is their common specialization (infimum)? Is the infimum consistent
or does it degenerate to the absurd (i.e., contradictory) theory
at the bottom of the lattice.
4. When SUMO and OpenCyc are broken down into modules, it then becomes
possible to evaluate them individually for consistency and other
properties. Ian, for example, said that much of SUMO was developed
by putting together modules taken from other resources. What are
those other resources? How well were they tested, documented, or
maintained? Can we begin to specify what kind of metalelvel
information should be kept with each module, such as author(s),
revision history, cerification, validation, etc.?
5. Many people on this list have worked with Cyc, and some, such as
Bill Andersen, have participated in a major effort in analyzing
the structure of the Cyc hierarchy and writing programs that can
automatically extract axioms from it. Perhaps Bill and his
colleagues could help us with some of the analysis of both OpenCyc
and SUMO or at least give us some pointers on how to do it, what
were some of the problems and issues, and what should we consider
as criteria for success.
There is a lot more that would have to be done in order to develop what
I would consider an adequate basis for an ontology standard. Since I
have been doing the most talking about lattices, I am willing to begin
by putting together some documentation as a contribution to point #1
above. I already have a lot of that material in various places on my
web site, and I could assemble it into an HTML document that could serve
as a tutorial and reference for the work on organizing modules.
Points #2, #3, and #4 could best be done by people who have already
done quite a bit of work with and on the SUMO and CYC systems. Other
people, such as the IFF developers and I, could help them by analyzing
the material they select and answering questions about how it could
fit into a lattice.
This proposal will take quite a bit of work, but it has many different
subparts, which could be done by people with different expertise.
John Sowa