Dear Matthew, Cory, et al., (01)
I'm sorry for not responding sooner, but I have
been tied up with some pressing deadlines for
the past week or so. (02)
I'll start with Matthew's note: (03)
MW> If I've got you right, I should look at the UF,
> and be happy as long as it makes sense with a 4D
> interpretation, whilst others should be able to
> look at it with a 3D interpretation.
>
> And actually me looking at it from that perspective
> would be useful in making sure that the UF did not
> have an implicit interpretation. (04)
Yes. The basic point of the Unified Framework is to
focus on the low-level and mid-level concept types
and to avoid any commitment to any upper level. (05)
For detailed reasoning, the upper level is extremely
important, but in reasoning about different kinds of
problems from different perspectives for different
purposes, you need very different assumptions about
physics, ontology, and all the *big* questions of
business, engineering, and life. (06)
The purpose of the UF is to concentrate on the middle
levels and to leave the upper levels to various upper
ontologies -- of which there is no shortage whatever.
Upper ontologies are so great that we have an abundance
of them, and anybody who has one has no intention of
abandoning it in favor of anybody else's. (07)
The purpose of the UF is to throw out *all* upper levels
and make do with just the middle and lower levels and
with a bare *minimum* of axioms. If you throw out the
upper levels and most of the axioms, you minimize the
risk of contradictions. But then you can't do much
reasoning with just the UF alone. To do any reasoning
or any computation of any kind, you import the UF into
your pet system with your choice of detailed axioms
and ontological commitments. (08)
In order to talk about *which* upper level to use and how
to relate it to various vocabularies in the UF, you need to
do some metalevel reasoning, which leads to Cory's note: (09)
CC> While the full extent of context may be difficult, it
> is my belief that that being able to assign multiple dimensions
> of context and select the appropriate statements for that
> context is tractable since it is reasonably easy to see how
> a program or set of rules could be written to do so. The
> behavior of these rules that I have in mind follows closely
> to the meta-levels approach in the paper. (010)
To a very large extent, I agree. In his note, Barry made
a point about the complexity and confusion about various notions
of context. I also agree with Barry that the literature is
filled with various definitions of "context". For that reason,
I suggest that we use the phrase "metalevel approach". (011)
CC> Files, Global name spaces and concepts not separated from
> terms would not seem to scale well for the purposes of this
> group as I understand it. Perhaps context is a better
> organizational principle than files or web URLS for sets
> of ontological statements? (012)
In my paper "Laws, Facts, and Contexts", which you are discussing
in your note, I defined the word "context" in a very narrow sense
as a collection of statements in some version of logic and with
a particular method for relating such collections to one another.
To avoid conflicts with other uses of the word, I suggest that
we call such a collection of statements a *module*: (013)
A _module_ is a collection of statements in some version of
logic, which is used to define or axiomatize some collection
of concept and relation types (or in terms of predicate
calculus, some collection of predicates). (014)
This definition does not restrict the size of a module. A single
module could be as large as Cyc, but I assume that the typical
size would be closer to what Cyc calls a microtheory. I would
also assume that the upper levels of any ontology should be
organized in a hierarchy consisting of multiple smaller modules. (015)
In Cyc terms, that would imply replacing the entire upper level
with a single type called "Thing". All of Cyc (or any other
major ontology) would be repackaged in modules (or microtheories)
from top to bottom. The method of organizing the ontology gets
into the notion of a lattice of theories, which I've discussed
before and which I'll comment on later. (016)
CC> The same set of problems we have run into with modeling in
> the large seem to apply to Ontologies in the large. If we were
> successful in applying context we would not have to impoverish
> COSMO due to conflicting domains but would separate these concepts
> into the appropriate context. In addition we would have a better
> way to handle the multiple terms assigned to concepts and reduce
> the number of statements that would need be applied to any one
> computation. Does this make sense? (017)
Yes, provided that we replace the word "context" with "module". (018)
CC> I suspect much of this is worked out in CL, is that a
> candidate language? (019)
Actually, none of these issues are addressed by Common Logic directly,
although many of the people who have worked on CL have thought a
great deal about them. Pat Hayes, for example, worked with the W3C
in order to ensure that the LBase semantics for RDF and OWL can be
supported by CL and that the CL naming scheme can accommodate the
URIs used for the WWW. But CL is neutral on all of these issues. (020)
In other words, CL can accommodate any of these solutions, but it
is designed to avoid any ontological commitment. That's why I believe
it's a good candidate for a base-level logic. To support modal logic
on top of CL, I would suggest an approach based on Dunn's semantics,
as I discussed in the laws.htm paper. (021)
CC> Another interesting source that I mentioned before, but as we
> explore this I am thinking may be very relevant; "Semantics of
> business vocabulary and business rules"
> http://www.omg.org/docs/bei/05-08-01.pdf). In particular the
> vocabulary part introduces a modal and non-monotonic formalism
> based on but extending FOL, specifically designed to capture
> shared vocabularies. (022)
It's relevant, but my major concern about SBVR is that it goes
in the opposite direction. Instead of emphasizing modularity,
it bundles up the logic, the ontology, and the surface-level
notation in one monolithic lump. As presented in that document,
SBVR is inconsistent with *every* upper-level ontology we have
been considering in this WG. I've expressed that concern in
another forum, and I hope that they repackage SBVR in a more
modular fashion. (023)
John (024)
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