SUO: Re: General Design
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> Stephen M. Richard wrote:
>
> Jon -- can you indicate what sort of tool or process one
> might use to actually implement a knowledge representation
> using the 'indirect approach' you make reference to?
This was (a slightly tenuous) reference
to some earlier remarks on the SUO List:
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Subj: Direct and Indirect Use of Axiom Systems
Date: Sat, 05 Jul 2003 10:06:36 -0400
From: Jon Awbrey <jawbrey@att.net>
To: SUO <standard-upper-ontology@ieee.org>
At: http://suo.ieee.org/email/msg10352.html
General Idea. Distinction betweeen Direct and Indirect Use of Axiom Systems
There are two different ways of using axiom systems to describe an object system,
like common sense, domain knowledge, intelligent conduct, linguistic competence,
linguistic performance, and so on. It has taken three years for this recognition
to precipitate out of a suspension of nagging senses that we are talking in ways
that are radically skew to one another, but I think that I can safely describe it
now as a difference between the "direct" and the "indirect" use of axiom systems.
Example. Sensus Communis
For example, consider the case of common sense belief systems
and the performance systems that depend on them for guidance.
1. Common sense belief and behavior might be represented directly
as an axiom-based inference system, where the axioms give us
the starting points of belief and behavior and the inference
rules and proof chains provide us with literal simulations
of the processes that apply this knowledge in practice,
whether proceeding "in the head" or in external action.
2. Common sense belief and behavior might be regarded as arising
from the states and transformations of an object system, and
this object system might be described by an axiomatic theory,
and yet the relationship of theory to model is more indirect,
in that the axioms and inferences occurring in the theory are
not the axioms and inferences occurring in the object system.
Elaboration and Revision.
As a matter of fact, the indirect approach allows us to deal with
a much wider range of object systems than just those that conduct
themselves like literal deductive systems. For instance, we might
be dealing with systems of belief and behavior that are configured
at several different levels and that are composed of many diverse
components, not all of which are consistent with each other, and
that interact in non-deterministic ways. Indeed, many of these
components may not even have all the structure of axiom systems
but may operate more like automatic associative complexes or
even like very primitive reactive processes.
For instance, systems of heuristics often have this structure, with
one sage maxim contradicting the next deep truth, it all depending
on practical judgment, what the Greeks called "phronesis", I think,
to decide which rule of thumb applies in which immediate instance.
In light of these possibilities, it might be better
to revise my description of the indirect approach
in something like the following way:
2. Common sense belief and behavior might be regarded as arising
from the states and transformations of an object system, and
this object system might be described by an axiomatic theory,
and yet the relationship of theory to model is more indirect,
in that the axioms and inferences occurring in the theory are
not literal representations of the initial conditions and the
transitional processes that take place in the object system.
I think that it would help to clarify many of our discussions
if we able to reflect on which implicit model we were using
in each case, and to make a point of making that explicit.
Of course, it is also perfectly conceivable that we will be
using a mixture of both direct and indirect modalities in
our models and theories.
Continuation.
Taking the indirect approach allows us to loosen up our thinking about
the object system in a couple of different directions. First, it is
more tolerant of the ambiguities and inconsistencies that may occur
in the object system, especially if we should attempt to cast it
as a strict deductive system. Second, even though we're hoping
to find an axiomatic theory that describes the object system,
in all its "do I contradict myself?" glory, we can proceed
in a prospective and provisional way, in the usual style
of hypothetico-deducto-probationary scientific method.
In effect, we are always saying, "I have faith that
this system is lawful and law abiding, it's just
that I do not of necessity know all the laws
that it follows yet". Thus relaxing the
brittleness and rigidity that axiom
systems otherwise tend to have
adds agility and robustness
to our methodology.
And, of course, I am hardly the first person
to have said these general sorts of things.
Nor do I hope that I will be the last.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Steve,
I seem to be caught in some sort of cross-posting draft
beteeen the Ontology, Protege, and SUO lists, and only
ran across your reply by accident, so I will register
with Protege's Cerberus, and Charon Char alike.
Just by way of briefest possible biographical background,
I started work trying to write my own theorem-prover in
1980, on account of some problems in graph theory and
group theory that I really needed help with, worked in
Lisp initially, exploting some of Peirce's ideas about
logical graphs, forced by the times to translate it all
into Pascal (!), studied general resolution methods at
UIUC, by 1986 became convinced that there just had to be
a better way to integrate "empirical" and "rational" or
model-theoretic and proof-theoretic methods, and so left
the mainstream about that time to work on the conceptual
and fundamental issues. The very primitive prototype
implementations that I developed for my Master's work
all focused on the problems of integrating data-driven
empirical systems with concept-driven logical systems.
Currently working on a "capstone" type dissertation in
systems engineering that tries to integrate symbolic
and dynamic approaches to intelligent systems engin.
So you see the theme, the impossible dream, it's
always been about the unification of opposites.
> I'm involved with ontology development for geoscience knowledge interchange/reuse,
> driven by the government geological survey information serving requirements. Because
> of the 'knowledge soup' that geologists typically swim in, the terminology and maps that
> are the 'sign system' used to convey knowledge are quite subjective.
This is precisely the same problem that physics faced in the 1800's, where each
observer's frame of reference generated a different map of the physical system
in question, say, planetary dynamics or thermodynamics, as two of the biggies.
The mathematics that more or less made progress possible was worked out by
Riemann in the 1850's, with his "theory of manifolds". Today one speaks
quite literally of "atlases" of "charts" that are pasted together to
describe the underlying "manifold". This is the context in which
one currently does mathematical systems theory and applies it
to the analysis and the engineering of real systems.
One of the main foci of my work over the last decade has been
developing the logical, qualitative, or symbolic analogues
of the decidely quantitative methods from manifold theory.
Here is one possible insertion site:
DARM. Differential And Riemannian Manifolds -- Commentary Notes
01. http://suo.ieee.org/ontology/msg04782.html
Will have to break here and get to the rest later ...
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
> I'm thinking that integrating ontologies from different sources might in
> the end require some sort of similarity measure -- building on the kind of
> similarity measures used in Case-based reasoning systems to locate related
> cases. Such a measure might be constructed analytically in part (e.g. based
> on separation from a most specific subsuming term in a taxonomy...), but in
> the end might work best based on empirical/subjective data (how many instances
> of X in A's ontology are the same as Y in B's ontology, based on assessment by
> subjects A, B, C....), or even purely subjective (some 'power users'/experts look
> at the scope of terms in the two ontologies and guesses a similarity measure (0..1?)).
> Queries against a merged ontology would return results with a 'similarity index' --
> basically a fuzzy logic sort of system?? Has anybody (besides Clinton Smyth) tried
> to implement this kind of knowledge representation?
>
> steve
>
>
> Jon Awbrey wrote:
> >
> > the only still "logical" alternative seems to be something like the indirect approach,
> > via the explicit recignition that our models are abductively approximate analogues of
> > the real thing that is ever out there, beyond us, and thus that we have no choice but
> > to begin in more amorphous, proto-formal settings like sign relations, taking serious
> > Peirce's notion of "logic as (a specialized form of) semiotics".
> >
> > John F. Sowa wrote:
> > > ... no ontology or
> > > knowledge base can ever be adequate unless it comes
> > > to grips with what I have called the "knowledge soup"
> > > -- the loosely organized, semi-structured mix of
> > > whatever people have in their heads. It certainly
> > > does not look anything like a rigid ontology.
> > > WordNet is probably a lot closer -- but still not
> > > close enough. There is a lot more to say on this
> > > topic, but I'll leave it for later.
>
> --
> Stephen M. Richard
> Arizona Geological Survey
> 416 W. Congress St., #100
> Tucson, Arizona, 85701
> USA
> phone: (520) 770-3500. FAX: (520) 770-3505
> email: srichard<at>iname.com
> or: steve.richard<at>azgs.az.gov
>
> -----------------------------------------------------------
> To un/subscribe go to http://protege.stanford.edu/lists.html
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o