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INTRO. Note 1

The following essay is intended to provide NKS readers
with background information on the pragmatic theory of
inquiry and its relationship to the pragmatic theory of
signs, at least, insofar as I currently understand them.

Jon Awbrey

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INTRO. Note 2

Introduction to Inquiry Driven Systems

1. Aspects of Inquiry

"Inquiry" is a word in common use for a process that resolves doubt
and creates knowledge. Computers are involved in inquiry today, and
are likely to become more so as time goes on. The aim of my research
is to improve the service that computers bring to inquiry. I plan to
approach this task by analyzing the nature of inquiry processes, with
an eye to those elements that can be given a computational basis.

I am interested in the kinds of inquiries which human beings
carry on in all the varieties of learning and reasoning from
everyday life to scientific practice. I would like to design
software that people could use to carry their inquiries further,
higher, faster. Needless to say, this could be an important
component of all intelligent software systems in the future.
In any application where a knowledge base is maintained,
it will become more and more important to examine the
processes that deliver the putative knowledge.

Jon Awbrey

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INTRO. Note 3

1.1. Preliminary Questions

Three questions immediately arise in the connection
between inquiry and computation. As they reflect on
the very idea of inquiry, they have to do with its
integrity, its effectiveness, and its complexity.
These questions ask in their turn whether all such
processes that are dubbed "inquiry" have anything
essential in common, whether any useful parts of
these processes can be automated in practice, and
just how deep is the takedown needed to reach the
level of routine steps. The issues of effectiveness
and complexity will be discussed throughout the rest
of this work, but the problem of integrity must be
dealt with immediately, since doubts about it may
interfere with my ability to exercise this title
to "inquiry".

Thus, we must examine the integrity, or well-definedness,
of the very idea of inquiry, that is, "inquiry" as a general
concept rather than a catch-all word. Is the faculty of inquiry
a principled capacity, leading to a disciplined form of conduct,
or is it only a disjointed collection of unrelated skills? As it
is currently being carried out on computers today, inquiry includes
everything from database searches, through dynamic simulation and
statistical reasoning, to mathematical theorem proving. Insofar
as these tasks constitute specialized efforts, each of them demands
software that is tailored to its individual purpose. Insofar as
these different modes of investigation contribute to larger
inquiries, our present methods for coordinating their separate
findings are mostly ad hoc and still a matter of human skill.
Thus, we might question whether the very name "inquiry" succeeds
in referring to a coherent and independent process.

Do all the varieties of inquiry have something in common, a structure
or a function that defines the essence of inquiry itself? I will say
"yes". One advantage of this answer is that it brings the topic of
inquiry within human scope, and also within my capacity to research.
Without this, the field of inquiry would be impossible for any one
human being to survey, because a person would have to cover the
union of all the areas that employ inquiry. By grasping what is
shared by all inquiries, I can focus on the intersection of their
generating principles. Another benefit of opting for this answer
is that it promises a common medium for inquiry, one in which the
many disparate pieces of our puzzling nature may be bound together
in a unified whole.

When I look at other examples of instruments that people have
used to extend their capacities, I see that two questions must
be faced. First, what are the principles that enable human
performance? Second, what are the principles that can be
augmented by available technology? I will refer to these
two issues as the question of original principles and the
question of technical extensions, respectively. Following
this model leads me to examine the human capacity for inquiry,
asking which of its principles can be reflected in the
computational medium, and which of its faculties can be
sharpened in the process. It is not likely that everybody
with the same interests and applications would answer these
questions the same way, but I will describe how I approach
them, what has resulted so far, and what directions I plan
to explore next.

Jon Awbrey

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INTRO. Note 4

1.2. Initial Approach

The focus of this work will narrow in three steps:

1. First, I intend to concentrate on the design of
   intelligent software systems that support inquiry.
   
   
2. Next, I will select mathematical systems theory as an
   indispensable tool, both for the analysis of inquiry
   itself and for the design of programs to support it.
   
   
3. Finally, I plan to develop a theory of qualitative
   differential equations, implement methods for their
   computation and their solution, and then apply the
   resulting body of techniques to two kinds of
   recalcitrant problems:
   

1. Situations where an inquiry must begin
   with too little information to justify
   quantitative methods.
   
   
2. Situations where a complete logical analysis
   is necessary to identify critical assumptions.
   

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INTRO. Note 5

1.2. Initial Approach (concl.)

There are several implications of my approach that I need
to emphasize. Many distractions can be avoided if we guide
our approach by the two questions that were raised above, of
principles and extensions, and if we guard against confounding
what they ask with what they do not ask. The issues that surround
these points, concerning the actual nature and the possible nurture
of the capacity for inquiry, will be taken up shortly. But first
I need to deal with a preliminary source of confusion. This arises
from the two vocabularies, the language of the application domain,
which talks about higher order functions and intentions of software
users, and the language of the resource domain, which describes the
primitive computational elements to which software designers must
try to reduce the problem. We are forced to use, or at least to
mention, both of these terminologies in our effort to bridge the
gap between them, but each of these languages plays a different
role in the work.

In studies of formal specifications the designations "reduced language"
and "reducing language" are often used to discuss the two roles that
are encountered here, that of the "application", "practice", or
"target" domain, on the one hand, and that of the "base", "method",
or "(re)source" domain, on the other. I will be using all of
these terms, with the following two qualifications.

First, I must note a trivial caution. Our sense of "source" and
"target" will often get switched depending on our direction of work.
Furthermore, these words are reserved in category theory to refer to
the domain and the codomain of an "arrow", that is, a function,
a mapping, a morphism, or a transformation. This will limit
their use in the above sense to the more informal contexts.

Now, I must deal with a more substantive issue. In attempting
to automate a fraction of such grand capacities as intelligence
and inquiry, it is seldom that we totally succeed in reducing
one domain to the other. The reduction attempt will usually
result in our saying something like this: that we have reduced
the capacity A in the application domain to the sum of the
capacity B in our base domain plus some residue C of unanalyzed
abilities that must be called in from outside the basic set.
The residual abilities will then be assigned to the human side
of the interface, that is, attributed to the conscious observation,
common sense, or creative ingenuity of users and programmers.
In the theory of recursive functions, we would say that A is
"relatively computable", given an "oracle" for C. For this
reason, I will often speak of "relating" a task to a method,
rather than fully "reducing" it. A measure of initial success
is often achieved when we can relate or connect an application
task to a basic method, long before we can completely reduce
one set of them to the other. The catch will always be whether
the basic set of resources has already been implemented, or is
just being promised, and whether the residual ability has a
lower complexity than the original task, or is actually more
difficult in practice.

Jon Awbrey

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INTRO. Note 6

1.3. Model of Inquiry

I can now return to the task of analyzing and extending the
capacity for inquiry. Any effort to enhance a human capacity
must lead off with a beginning comprehension of its nature and
must develop concurrently with an evolving understanding of the
underlying process that supports this capacity.

To extend a human capacity we need to know the critical functions
that support that ability, and this involves us in a theory of the
practice domain. This means that most of the language describing
the target functions will come from sources outside the areas of
systems theory and software engineering. The first thoughts that
we take for our specifications will come from the common parlance
that everybody uses to talk about learning and reasoning, and the
rest will come from the special fields that study these abilities,
from psychology, education, logic, and the philosophy of science.
This particular hybrid of work easily fits under the broad banner
of artificial intelligence, yet I need to repeat that my principal
aim is not to build any kind of autonomous intelligence, but simply
to amplify our own capacity for inquiry.

Jon Awbrey

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INTRO. Note 7

1.3. Model of Inquiry (concl.)

There are many well-reasoned and well-respected paradigms
for the study of learning and reasoning, any one of which
I might have chosen as a blueprint for the architecture of
inquiry. The model of inquiry that works best for me is one
with a solid standing in the philosophy of science and whose
origins are entwined with the very beginnings of symbolic logic.
Its practical applications to education and social issues have
been studied in depth, and aspects of it have received attention
in the AI literature (Refs. 1-8). This is the pragmatic model of
inquiry, formulated by C.S. Peirce from his lifelong investigations
of classical logic and experimental reasoning. For my purposes, all
this certification means is that the model has survived many years of
hard-knocks testing, and is therefore a good candidate for further trial.
Since we are still near the beginning of efforts to computerize inquiry,
it is not necessary to prove that this is the best of all possible models.
At this early stage, any good ideas would help.

My purpose in looking to the practical arena of inquiry and to its
associated literature is to extract a body of tasks in real demand
and to start with a stock of plausible suggestions for ways to meet
these requirements. Some of what we find depicted in contemporary
pictures of learning and reasoning may turn out to be inconsistent
postulations or unrealizable projections, beyond the scope of our
present or any possible technology. But this is the very sort of
thing that we should be interested in finding out! It is one of
the benefits of submitting theories to trial by computer that we
obtain just this brand of knowledge. Of course, the fact that
no one can presently find a way to make a concept effectively
computable does not in itself prove that it is unworkable,
but it does place the idea in a different class.

This should be enough to say about why we sometimes need to cite
the terms and critically reflect on the concepts of other fields
in the process of doing work within the disciplines of systems
theory and software engineering. To sum it up, it is not a
question of entering another field or absorbing its materials,
but of finding a good standpoint on our own grounds from which
to tackle the problems that the outside world presents.

Sorting out which procedures are effective in inquiry and finding out
which functions are feasible to implement is a job that we can do
better in the hard light demanded by fully formalized programs.
But there is nothing wrong in principle with a top-down approach,
so long as we do come down to familiar ground. I will follow
the analogy of a recursive program that progresses down steps
to its base, stepwise refining the details of higher-level
specifications. One of the best reinforcements for such
a program is to maintain a parallel effort that builds up
competencies from fundamental rudiments.

Jon Awbrey

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INTRO. Note 8

1.4. System-Theoretic Method

Once I have addressed the question as to "what" are
the principles that enable human inquiry it brings me
to the question as to "how" I would set out to improve
the human capacity for inquiry by computational means.

Within the field of AI there are many ways of simulating
and supporting learning and reasoning that would not of
necessity involve us in systems theory proper, that is,
in reflecting on mathematically defined systems or in
considering the dynamical trajectories that automata
trace out through abstract state spaces. However,
I have chosen to take the system-theoretic route
for several reasons, which I will now discuss.

First, if we succeed in understanding intelligent inquiry in
terms of system-theoretic properties and processes, it equips
this knowledge with the greatest degree of transferability
between comparable systems. In short, it makes our knowledge
robust, and keeps it from becoming too narrowly limited to
a particular instantiation of the target capacity.

Second, if we organize our thinking in terms of a coherent
system or an integral agent that carries out inquiries,
it helps to manage the complexity of the design problem
by splitting it into discrete stages. This strategy is
especially useful in dealing with the recursive or the
reflexive quality that bedevils all such inquiries into
inquiry itself. This aspect of self-application to the
problem is probably unavoidable, due to the following facts.
Human beings are extremely complex agents, and any system
that is likely to support significant human inquiry is
bound to surpass the complexity of most systems that we
are currently able to analyze in full. Research into
complex systems is one of the jobs that will depend on
intelligent software tools to advance in the future.
For this we need programs that can follow the drift of
inquiry and perhaps even help us to scout out fruitful
directions of exploration. Programs to do this will
need to acquire a heuristic model of the inquiry process
that they are being designed to assist. And so it goes.
Programs for inquiry will be required to pull themselves up
by their own bootstraps.

Jon Awbrey

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INTRO. Note 9

1.5. Inquiry Driven Systems

Taking as given the system-theoretic approach from now on,
I can focus and rephrase my question about the technical
enhancement of inquiry:

How can we put computational foundations
under the theoretical models of inquiry,
at least, the ones that we discover to
be accessible?

To ask the same question in greater detail:
What is the depth and the content of the
task analysis that is needed to relate
the higher order functions of inquiry
with the primitive elements that are
given in systems theory and software
engineering?

Connecting the requirements of a formal theory of inquiry
with the resources of mathematical systems theory has led
me to the concept of an "inquiry driven system" (IDS).

Jon Awbrey

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INTRO. Note 10

1.5. Inquiry Driven Systems (cont.)

The concept of an inquiry driven system is intended to capture
the essential properties of a broad class of intelligent systems,
and to highlight the crucial processes which support learning and
reasoning in natural and cultural systems. The defining properties
of inquiry driven systems are discussed in the next few paragraphs.
I then consider what is needed to supply these abstractions with
operational definitions, concentrating on the terms of mathematical
systems theory as a suitable foundation. After this, I discuss my
plans to implement a software system that is designed to help analyze
the qualitative behavior of complex systems, inquiry driven systems
in particular.

An inquiry driven system has components of state, accessible to
the system itself, which characterize the norms of its experience.
The idea of a norm has two meanings, both of which are useful here.

In one sense of the word "norm", we have the descriptive
regularities that are observed in summaries of past experience.
These norms govern the expectable sequences of future states,
as determined by natural laws.

In another sense of the word "norm", we have the prescriptive
policies that are selected with an eye to future experience.
These norms govern the intendable goals of processes,
as controlled by deliberate choices.

Collectively, these two orders of norms go to make up
the "knowledge base", or the "intellectual component",
of the intelligent agent or the inquiry driven system.

Jon Awbrey

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INTRO. Note 11

1.5. Inquiry Driven Systems (concl.)

An inquiry driven system, in the simplest cases worth talking about,
requires at least three different modalities of knowledge component,
referred to as "expectations", "intentions", and "observations" of
the system. Each of these components has the status of a theory,
that is, a propositional code that the agent of the system carries
along and maintains with itself through all of its changes of state,
possibly updating it as the need arises in experience. However, all
of these theories have reference to a common world, and they indicate
under their varying lights more or less overlapping regions in the
state space of the system, or in some derivative or extension of
the basic state space.

The inquiry process is driven by the nature, the degree,
and the extent of the differences that exist at any time
among its operative theories, for example, the differences
among the expectations, the intentions, and the observations
of the inquiry agent or the relevant community of inquiry.
These discrepancies are evidenced by differences in the
assemblies of models, empirical or theoretical, that
are held to satisfy the respective theories.

Normally, human beings experience a high level of disparity
among these theories as a dissatisfying situation, a condition
of cognitive discord. For people, the incongruity of cognitive
elements is accompanied by an unsettled affective state, in Peirce's
phrase, the "irritation of doubt". A person in this situation is
usually motivated to reduce the annoying disturbance by some action,
all of which activities we may classify under the heading of inquiry
processes.

Without insisting on strict determinism, we may say that the inquiry
process is lawful if there is any kind of informative relationship
connecting the state of cognitive discord at each time with the
ensuing state transitions of the system.

Expressed in human terms, a difference between expectations
and observations is experienced as a surprise to be explained,
a difference between intentions and observations is experienced
as a problem to be solved. We begin to understand a particular
example of inquiry when we can describe the relation between the
momentary intellectual state of its agent and the subsequent
action that the agent undertakes.

These simple facts, the features of inquiry outlined above,
already raise a number of issues, some of which are open
problems that my research will have to address. Given
the goal of constructing supports for inquiry on the
grounds of systems theory, each of these difficulties
is an obstacle to progress in the chosen direction,
to understanding the capacity for inquiry as
a systems property.

Jon Awbrey

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INTRO. Note 12

1.6. The Irritation of Doubt

In the next few paragraphs I discuss a critical problem
to be solved in this approach, indicating its character
to the extent I can succeed at present, and I suggest a
reasonable way of proceeding.

In human inquiry there is always a relation between affective
and cognitive features of experience. We have a sense of how
much discord or harmony is present in a situation, and we rely
on the intensity of this sensation as one measure of how to
proceed with inquiry. This works so automatically that we
have trouble distinguishing the affective and cognitive
aspects of the irritating doubt that drives the process.

In the artificial systems we build to support inquiry,
what measures can we take to supply this sense or arrange
a substitute for it? If the proper measure of doubt cannot
be formalized, then all responsibility for judging it will
have to be assigned to the human side of the interface.
This would greatly reduce the usefulness of the
projected software.

The unsettled state that instigates inquiry is characterized
by a high level of uncertainty. The settled state of knowledge
at the end of inquiry is achieved by reducing this uncertainty to
a minimum, at least to the point where action is not misguided.

Within the framework of information theory we already have a
concept of uncertainty, the entropy of a probability distribution,
as being something that we can measure. Certainly, how we feel
about entropy does not enter the equation. Can we form a connection
between the kind of doubt that drives human inquiry and the kind of
uncertainty that is measured on scales of information content? If so,
this would allow salient dynamic properties of inquiry driven systems
to be studied in abstraction from the affective qualities of the
anomalies, the disagreeabilities, and the incongruities that now drive
them in the spheres of human experience. With respect to measurable
qualities of uncertainty, inquiry driven systems could be taken as
special types of control systems, where the variable to be controlled
is the total amount of discrepancy, disparity, or dispersion in the
knowledge base of the system.

The assumption of modularity, that the affective and the intellectual
aspects of inquiry can be disentangled into separate components of
the system, is a natural one to make. Whenever it holds, even
approximately, it simplifies the task of understanding and permits
the analyst or designer to assign responsibility for these factors
to independent modules of the simulation or the implementation.

However, the assumption of modularity appears to be false in general,
or true and useful only in approaching certain properties of inquiry.
Many other features of inquiry are not completely understandable on
this basis. To tackle these more refractory properties, I will be
forced to examine the concept of a measure that separates the
affective and intellectual impacts of disorder. To the extent
that this issue can be resolved by analysis, I believe that it
hinges on the characters that make a measure "objective", in effect,
invariant over many perspectives and interpretations, as opposed to
being merely the measure of a subjective moment, an impression that
is limited to a special interpretation or a transient perspective.

Jon Awbrey

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INTRO. Note 13

1.7. The Orbit of Inquiry

The preceding discussion has indicated a few of the properties
that are attributed to inquiry and its agents, and has initiated
an analysis of their underlying principles. Now we engage the task
of giving these processes operational definitions within the framework
of mathematical systems theory.

Let us consider an inquiry driven system
as described by a set of variables:

x_1, ..., x_k, a_1, ..., a_m.

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INTRO. Note 14

2. Approaches to Inquiry

In this Chapter I lay out the "pragmatic theory of inquiry" that
I will use in my study of inquiry driven systems. I begin with
the basic features of one standard model of inquiry processes.
Then I outline two different approaches to the functional
structure of inquiry. Finally, I discuss a collection
of computational routines that I have implemented to
study various aspects of this model of inquiry.

Jon Awbrey

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INTRO. Note 15

2.1. The Pragmatic Approach to Inquiry

This Division sketches the main features
of a canonical model of inquiry that will be
employed throughout the rest of this project.

The pragmatic model or theory of inquiry was extracted
by Charles Sanders Peirce from its raw materials in
classical logic and refined in parallel with the
early development of symbolic logic to address
problems about the nature of scientific reasoning.
Borrowing a brace of concepts from Aristotle, Peirce
examined three fundamental modes of reasoning that play
a role in inquiry, commonly known as abductive, deductive,
and inductive inference.

In rough terms, "abduction" is what we use to generate
a likely hypothesis or an initial diagnosis in response
to a phenomenon of interest or a problem of concern, while
"deduction" is used to clarify, to derive, and to explicate
the relevant consequences of the selected hypothesis, and
"induction" is used to test the sum of the predictions
against the sum of the data.

These three processes typically operate in a cyclic fashion,
systematically operating to reduce the uncertainties and the
difficulties that initiated the inquiry in question, and in
this way, to the extent that inquiry is successful, leading
to an increase in knowledge or in skills.

In the pragmatic way of thinking everything has a purpose,
and the purpose of each thing is the first thing we should try
to note about it. The purpose of inquiry is to reduce doubt and
lead to a state of belief, which a person in that state will usually
call "knowledge" or "certainty". As they contribute to the end of
inquiry, we should appreciate that the three kinds of inference
describe a cycle that can be understood only as a whole, and
none of the three makes complete sense in isolation from the
others. For instance, the purpose of abduction is to generate
guesses of a kind that deduction can explicate and that induction
can evaluate. This places a mild but meaningful constraint on the
production of hypotheses, since it is not just any wild guess at
explanation that submits itself to reason and bows out when
defeated in a match with reality. In a similar fashion,
each of the other types of inference realizes its purpose
only in accord with its proper role in the whole cycle of
inquiry. No matter how much it may be necessary to study
these processes in abstraction from each other, the
integrity of inquiry places strong limitations on the
effective modularity of its principal components.

Jon Awbrey

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