Tom, (01)
Those are several very important questions, which I'll
address separately. (02)
TB> Perhaps you might help me understand how logic (or most
> other upper ontologies for that matter) can describe and
> reason about inexact "real-world" concept/attribute values
> while retaining its mathematical correctness. (03)
First of all, attribute/value pairs are an extremely simple
version of logic. The most widely used version of logic is
the WHERE clause of SQL, which has the expressive power of
first-order logic. That version of logic is used to support
the world economy, and it's fast enough to support databases
with terabytes of data. (04)
However, the problems of expressing real-world knowledge
precisely in logic have been recognized since the time
of Plato, Aristotle, Leibniz, and Kant up to more recent
logicians, such as Peirce, Wittgenstein, and Whitehead.
I have summarized those and many more recent remarks in
my paper on knowledge soup: (05)
http://www.jfsowa.com/pubs/challenge.pdf
The Challenge of Knowledge Soup (06)
On the other hand, we know quite well that the mathematical
techniques of science and engineering are good enough to design
bridges that don't fall down (most of the time) and airplanes
that stay up well enough that most of us are willing to bet our
lives on the accuracy of the computations. (And I include math
as just one important special case of logic.) (07)
So we can characterize many things well enough for many purposes,
but there is always a left-over margin of error. In short,
there's a lot that can be done with logic, but there's even
more that is very hard to express precisely in any language,
natural or artificial. (08)
> For many domains and problems, it would seem that similarity/
> case-based reasoning is a better representational choice. (09)
I certainly agree. And I make the point that both formal logic
and case-based reasoning are special cases of analogy. Logic is
good for areas in which well developed theories exist, and CBR
is better suited for subjects like medicine and law for which
reliable theories are harder to find. Following are two papers
that address that issue: (010)
http://www.jfsowa.com/pubs/analog.htm
Analogical Reasoning (011)
> I am also puzzled by absence of mechanisms in all of these
> upper ontology systems to describe the importance of an attribute
> and to measure the certainty of a value. It would seem to me
> that any robust reasoning system would require representation
> of these features to have realistically high performance. (012)
There are important, but orthogonal problems: (013)
1. How to represent the subject matter. That's the object level
for which the theories are represented in some version of
logic -- such as a relational database, attribute/value pairs,
or many kinds of mathematics. (014)
2. How to talk about the representation. That is the same kind
of documentation that is needed for any kind of software,
such as programs, databases, etc. (015)
3. How to deal with the inevitable experimental errors and
approximations. Every branch of science and engineering has
to deal with that, and the metalevel information about an
ontology should accommodate that. (016)
Partly for these and other reasons, I do not believe that there
is any such thing as a one-size-fits-all ontology that can be
used for every purpose -- not even for all subproblems in a single
domain, such as bridge design, automobile engineering, or medicine. (017)
John Sowa (018)
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