ONT Re: Inquiry Driven Systems
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| Document History
|
| Subject: Inquiry Driven Systems: An Inquiry Into Inquiry
| Contact: Jon Awbrey <jawbrey@oakland.edu>
| Version: Draft 8.70
| Created: 23 Jun 1996
| Revised: 06 Jan 2002
| Advisor: M.A. Zohdy
| Setting: Oakland University, Rochester, Michigan, USA
| Excerpt: Section 1.3.4 (Discussion of Formalization: Concrete Examples)
| Excerpt: Subsection 1.3.4.16 (Integration of Frameworks)
|
| http://members.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm
1.3.4.16 Integration of Frameworks
A large number of the problems arising in this work have to do with the
integration of different interpretive frameworks over a common objective
basis, or the prospective bases that may be provided by shared objectives.
The main concern of this project continues to be the integration of dynamic
and symbolic frameworks for understanding intelligent systems, concentrating
on the kinds of interpretive agents that are capable of involvement in inquiry.
Integrating divergent IF's and reconciling their objectifications is,
generally speaking, a very difficult maneuver to carry out successfully.
Two factors that contribute to the near intractability of this task can be
described and addressed as follows:
1. The trouble is partly due to the obligatory tactics and
the ossified taxonomies and that arise through time and
training to inhabit the conceptual landscapes of agents,
especially if they have spent the majority of their time
operating according to a single IF. The IF informs their
activities in ways they no longer have to think about, and
thus rarely find a reason to modify. But it also inhibits
their interpretive and practical conduct to the customary
ways of seeing and doing things that are granted by that
framework, and it binds them to the "forms of intuition"
that are suggested and sanctioned by the operative IF.
Without critical reflection, or mechanisms to make
amendments to its own constitution, an IF tends to
operate behind the scenes of observation in such a
way as to obliterate any inkling of flexibility in
practice or thinking and to obstruct every hint or
threat (often so perceived) of conceptual revision.
2. Apparently it is so much easier to devise techniques for
taking things apart than it is to find ways of putting them
back together again that there seem to be but a few heuristic
strategies of general application that are available to guide
the work of integration. A few of the tools and the materials
that are needed for these constructions have been illustrated
in concrete form throughout the presentation of examples in
this Section. An overall survey of their principles can
be summed up as follows:
a. One integration heuristic is the "lattice" metaphor, frequently
called the "partial order" or the "common denominator" paradigm.
When IF's can be objectified as OF's that are organized according
to the principles of suitably ordered sets, then it may be possible
to "lift" or extend their order properties to the space of frameworks
themselves, and thereby to enable construction of the desired kinds of
integrative frameworks as upper and lower bounds in the higher ordering.
b. Another heuristic of integration is the "mosaic" metaphor, also
known as the "stereoscopic" or the "inverse projection" paradigm.
This technique is illustrated especially well by the methods used
throughout this Section to analyze the three-dimensional structures
of sign relations. In fact, the picture of any sign relation offers
a paradigm in microcosm for the macroscopic enterprise of integration,
showing how reductive aspects of structure are often projected from a
shared but irreducible reality. The extent to which the "full-bodied"
structure of a 3-adic sign relation can be reconstructed from the data
of its 2-adic projections, although it is a limited extent in general,
presents a near perfect epitome of the larger task in this situation,
namely, to find an integrated framework that embodies the diverse
facets of reality severally observed from inside the individual
frameworks. Acting as gnomonic recipes for the higher order
processes they limn and delimit, sign relations keep before
the mind the ways in which a higher dimensional structure
determines its fragmentary aspects but is not in general
determined by them.
To express the nature of this integration task in logical terms, it combines
aspects of both proof theory and model theory, interweaving these two themes:
1. A phase that develops theories about the symbolic competence
or "knowledge" of intelligent agents, using abstract formal
systems to represent the theories and using phenomenological
data to constrain them.
2. A phase that seeks concrete and dynamic models of these theories,
looking to the varieties of mathematical structure that have
dynamic or system-theoretic interpretations, and compiling
the constraints that a recursive conceptual analysis
imposes on the ultimate elements of construction.
The set of sign relations {L(A), L(B)} affords an example of an extremely
simple formal system, encapsulating aspects of the symbolic competence and
the pragmatic performance that might be exhibited by potentially intelligent
interpretive agents, however abstractly and partially given at this stage of
description. The symbols of a formal system like {L(A), L(B)} can be held
subject to abstract constraints, having their meanings in relation to each
other determined by definitions and axioms, for example, the laws defining
an equivalence relation, making it possible to manipulate the resulting
information by means of the inference rules in a logical proof system.
This illustrates the "proof-theoretic" aspect of a symbol system.
Suppose that a formal system like {L(A), L(B)} is initially approached from
a theoretical direction, in other words, by listing the abstract properties
that one thinks it ought to have. Then the existence of an extensional model
that satisfies these constraints, as exhibited by way of sign relation tables,
demonstrates that one's theoretical description is logically consistent, even
if the models that first come to mind are still a bit too abstractly symbolic
and lack all of the dynamic concreteness that is demanded of system-theoretic
interpretations. This account is tantamount to the other side of the ledger,
the "model-theoretic" aspect of a symbol system, at least in so far as the
present discussion has dealt with it.
More is required of the modeler, however, in order to find the desired
kinds of system-theoretic models, for example, state transition systems,
and this brings the search for realizations of formal systems down to the
tougher part of the exercise. Some of the problems that emerge have already
been highlighted in the story of A and B. Although it is ordinarily possible
to construct state transition systems in which the states of the interpreters
correspond relatively directly to the acceptance of the primitive signs given,
the conflict of interpretations that develops between different interpreters
from these prima facie implementations is a sign that there is something
superficial about this approach.
The integration of model-theoretic and proof-theoretic aspects
of "physical symbol systems", besides being closely analogous
to the integration of denotative and connotative aspects of
sign relations, is also relevant to the job of integrating
dynamic and symbolic frameworks for intelligent systems.
This is so because the search for dynamic realizations
of symbol systems is only a more pointed exercise in
model theory, where the mathematical materials made
available for modeling are further constrained by
system-theoretic principles, like being able to
say what the states are and how the transitions
happen to be determined, to the extent they are.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤