Dear Matthew, (01)
The lattice of theories accommodates "all possible theories" that
can be stated with a given logic. It explicitly shows how they are
related: generalization, specialization, consistent, inconsistent. (02)
All the ontologies we are starting with are inconsistent with each
other in one way or another. But they contain many subtheories
that would be consistent with subtheories of the others if they
were modularized. The purpose of the lattice is to enable the
big theories to be broken up into modules that show all the
interrelationships. (03)
It's not required to break them up, however. As I said, you can build
a one-level hierarchy immediately: At the top, you have the universal
theory that contains nothing but tautologies like (p -> p). Just below
the top, you have all the starting theories hanging down: OpenCyc,
SUMO, DOLCE, BFO, etc. (04)
You can build that one-level hierarchy instantly. But it won't show
how the subparts can be extracted and recombined. If you ever want
to share data between a system that uses SUMO and a system that uses
OpenCyc, you need to do that. Of course, you don't have to do that.
You can just send the data and hope that it works -- that's what
people have been doing for the past half century. It sometimes works.
There's a technical term for that approach: crapshoot. (05)
MW> Unfortunately, most lower level ontologies have an implicit upper
> ontology - usually 3D. That automatically makes them inconsistent
> with the alternative upper ontololgy. (06)
The fact that a given lower-level module happened to be written
for given upper-level means that it is consistent with its original
upper level. Whether or not it happens to be consistent with a
different upper level must be verified. That can be done by the
methodology I described in my previous note. (07)
MW> As I said elsewhere, there is hope to do that, but I believe it will
> take careful crafting to remove the implicit upper ontologies first. (08)
Yes. The lattice shows exactly what kind of crafting must be done,
exactly where the inconsistencies lie, and what kinds of methodologies
can be used to show which modules are consistent or inconsistent with
other modules. Without such a procedure, sharing data is a crapshoot. (09)
John (010)
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